Feature selection - Knowledge

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with a series of much smaller problems, each of which only involves two variables, it thus uses pairwise joint probabilities which are more robust. In certain situations the algorithm may underestimate the usefulness of features as it has no way to measure interactions between features which can increase relevancy. This can lead to poor performance when the features are individually useless, but are useful when combined (a pathological case is found when the class is a

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error rate. This is an exhaustive search of the space, and is computationally intractable for all but the smallest of feature sets. The choice of evaluation metric heavily influences the algorithm, and it is these evaluation metrics which distinguish between the three main categories of feature selection algorithms: wrappers, filters and embedded methods.

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giving lower prediction performance than a wrapper. However the feature set doesn't contain the assumptions of a prediction model, and so is more useful for exposing the relationships between the features. Many filters provide a feature ranking rather than an explicit best feature subset, and the cut off point in the ranking is chosen via

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Filter type methods select variables regardless of the model. They are based only on general features like the correlation with the variable to predict. Filter methods suppress the least interesting variables. The other variables will be part of a classification or a regression model used to classify

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Local learning based feature selection. Compared with traditional methods, it does not involve any heuristic search, can easily handle multi-class problems, and works for both linear and nonlinear problems. It is also supported by a strong theoretical foundation. Numeric experiments showed that the

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The mRMR algorithm is an approximation of the theoretically optimal maximum-dependency feature selection algorithm that maximizes the mutual information between the joint distribution of the selected features and the classification variable. As mRMR approximates the combinatorial estimation problem

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method for constructing a linear model, which penalizes the regression coefficients with an L1 penalty, shrinking many of them to zero. Any features which have non-zero regression coefficients are 'selected' by the LASSO algorithm. Improvements to the LASSO include Bolasso which bootstraps samples;

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for each class/feature combinations. Filters are usually less computationally intensive than wrappers, but they produce a feature set which is not tuned to a specific type of predictive model. This lack of tuning means a feature set from a filter is more general than the set from a wrapper, usually

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Wrapper methods use a predictive model to score feature subsets. Each new subset is used to train a model, which is tested on a hold-out set. Counting the number of mistakes made on that hold-out set (the error rate of the model) gives the score for that subset. As wrapper methods train a new model

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are shown to be redundant. A recent method called regularized tree can be used for feature subset selection. Regularized trees penalize using a variable similar to the variables selected at previous tree nodes for splitting the current node. Regularized trees only need build one tree model (or one

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A feature selection algorithm can be seen as the combination of a search technique for proposing new feature subsets, along with an evaluation measure which scores the different feature subsets. The simplest algorithm is to test each possible subset of features finding the one which minimizes the

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to search through the space of possible features and evaluate each subset by running a model on the subset. Wrappers can be computationally expensive and have a risk of over fitting to the model. Filters are similar to wrappers in the search approach, but instead of evaluating against a model, a

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that grades a subset of features. Exhaustive search is generally impractical, so at some implementor (or operator) defined stopping point, the subset of features with the highest score discovered up to that point is selected as the satisfactory feature subset. The stopping criterion varies by

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The correlation feature selection (CFS) measure evaluates subsets of features on the basis of the following hypothesis: "Good feature subsets contain features highly correlated with the classification, yet uncorrelated to each other". The following equation gives the merit of a feature subset

1522:. Feature selection finds the relevant feature set for a specific target variable whereas structure learning finds the relationships between all the variables, usually by expressing these relationships as a graph. The most common structure learning algorithms assume the data is generated by a 1282:

and thus do not compute any actual 'distance' – they should rather be regarded as 'scores'. These scores are computed between a candidate feature (or set of features) and the desired output category. There are, however, true metrics that are a simple function of the mutual information; see

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Filter methods tend to select redundant variables when they do not consider the relationships between variables. However, more elaborate features try to minimize this problem by removing variables highly correlated to each other, such as the Fast Correlation Based Filter (FCBF) algorithm.

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proposed a feature selection method that can use either mutual information, correlation, or distance/similarity scores to select features. The aim is to penalise a feature's relevancy by its redundancy in the presence of the other selected features. The relevance of a feature set

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mRMR is a typical example of an incremental greedy strategy for feature selection: once a feature has been selected, it cannot be deselected at a later stage. While mRMR could be optimized using floating search to reduce some features, it might also be reformulated as a global

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Embedded methods have been recently proposed that try to combine the advantages of both previous methods. A learning algorithm takes advantage of its own variable selection process and performs feature selection and classification simultaneously, such as the FRMT algorithm.

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Nguyen X. Vinh, Jeffrey Chan, Simone Romano and James Bailey, "Effective Global Approaches for Mutual Information based Feature Selection". Proceedings of the 20th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD'14), August 24–27, New York City, 2014.

1154:; and FeaLect which scores all the features based on combinatorial analysis of regression coefficients. AEFS further extends LASSO to nonlinear scenario with autoencoders. These approaches tend to be between filters and wrappers in terms of computational complexity. 6374:

problem) optimization problems for which there is no classical solving methods. Generally, a metaheuristic is a stochastic algorithm tending to reach a global optimum. There are many metaheuristics, from a simple local search to a complex global search algorithm.

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creates new features from functions of the original features, whereas feature selection returns a subset of the features. Feature selection techniques are often used in domains where there are many features and comparatively few samples (or data points).

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Broadhurst, D.; Goodacre, R.; Jones, A.; Rowland, J. J.; Kell, D. B. (1997). "Genetic algorithms as a method for variable selection in multiple linear regression and partial least squares regression, with applications to pyrolysis mass spectrometry".

4426:{\displaystyle \mathrm {HSIC_{Lasso}} :\min _{\mathbf {x} }{\frac {1}{2}}\sum _{k,l=1}^{n}x_{k}x_{l}{\mbox{HSIC}}(f_{k},f_{l})-\sum _{k=1}^{n}x_{k}{\mbox{HSIC}}(f_{k},c)+\lambda \|\mathbf {x} \|_{1},\quad {\mbox{s.t.}}\ x_{1},\ldots ,x_{n}\geq 0,} 2856: 5040: 5423:{\displaystyle \mathrm {HSIC_{Lasso}} :\min _{\mathbf {x} }{\frac {1}{2}}\left\|{\bar {\mathbf {L} }}-\sum _{k=1}^{n}x_{k}{\bar {\mathbf {K} }}^{(k)}\right\|_{F}^{2}+\lambda \|\mathbf {x} \|_{1},\quad {\mbox{s.t.}}\ x_{1},\ldots ,x_{n}\geq 0,} 4537: 4669: 1779: 4718: 1325:

The choice of optimality criteria is difficult as there are multiple objectives in a feature selection task. Many common criteria incorporate a measure of accuracy, penalised by the number of features selected. Examples include

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For high-dimensional and small sample data (e.g., dimensionality > 10 and the number of samples < 10), the Hilbert-Schmidt Independence Criterion Lasso (HSIC Lasso) is useful. HSIC Lasso optimization problem is given as

1134:. Filter methods have also been used as a preprocessing step for wrapper methods, allowing a wrapper to be used on larger problems. One other popular approach is the Recursive Feature Elimination algorithm, commonly used with 3334: 2132: 1668: 1108:

Filter methods use a proxy measure instead of the error rate to score a feature subset. This measure is chosen to be fast to compute, while still capturing the usefulness of the feature set. Common measures include the

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of the features). Overall the algorithm is more efficient (in terms of the amount of data required) than the theoretically optimal max-dependency selection, yet produces a feature set with little pairwise redundancy.

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represents relative feature weights. QPFS is solved via quadratic programming. It is recently shown that QFPS is biased towards features with smaller entropy, due to its placement of the feature self redundancy term

3710: 9009:Üstünkar, Gürkan; Özöğür-Akyüz, Süreyya; Weber, Gerhard W.; Friedrich, Christoph M.; Aydın Son, Yeşim (2012). "Selection of representative SNP sets for genome-wide association studies: A metaheuristic approach". 3703:

as a good score for feature selection. The score tries to find the feature, that adds the most new information to the already selected features, in order to avoid redundancy. The score is formulated as follows:

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Nguyen, H., Franke, K., Petrovic, S. (2010). "Towards a Generic Feature-Selection Measure for Intrusion Detection", In Proc. International Conference on Pattern Recognition (ICPR), Istanbul, Turkey.

5176:-norm. HSIC always takes a non-negative value, and is zero if and only if two random variables are statistically independent when a universal reproducing kernel such as the Gaussian kernel is used. 8259: 1201:, which iteratively evaluates a candidate subset of features, then modifies the subset and evaluates if the new subset is an improvement over the old. Evaluation of the subsets requires a scoring 3715: 5960: 6420:

Wrapper methods evaluate subsets of variables which allows, unlike filter approaches, to detect the possible interactions amongst variables. The two main disadvantages of these methods are:

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that adds the best feature (or deletes the worst feature) at each round. The main control issue is deciding when to stop the algorithm. In machine learning, this is typically done by

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Subset selection evaluates a subset of features as a group for suitability. Subset selection algorithms can be broken up into wrappers, filters, and embedded methods. Wrappers use a

5497: 4881: 2543: 5698: 5661: 4570: 1460: 3126: 1421: 1385: 3526: 3010:{\displaystyle \mathrm {QPFS} :\min _{\mathbf {x} }\left\{\alpha \mathbf {x} ^{T}H\mathbf {x} -\mathbf {x} ^{T}F\right\}\quad {\mbox{s.t.}}\ \sum _{i=1}^{n}x_{i}=1,x_{i}\geq 0} 9727: 9260: 8497: 6358:. Regularized random forest (RRF) is one type of regularized trees. The guided RRF is an enhanced RRF which is guided by the importance scores from an ordinary random forest. 5110: 5069: 2478: 6044: 5464: 5147: 3314: 4966: 4961: 4921: 6346:

Regularized trees naturally handle numerical and categorical features, interactions and nonlinearities. They are invariant to attribute scales (units) and insensitive to

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which finds low-dimensional projections of the data that score highly: the features that have the largest projections in the lower-dimensional space are then selected.

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Embedded methods are a catch-all group of techniques which perform feature selection as part of the model construction process. The exemplar of this approach is the

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Long, N.; Gianola, D.; Weigel, K. A (2011). "Dimension reduction and variable selection for genomic selection: application to predicting milk yield in Holsteins".

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for each subset, they are very computationally intensive, but usually provide the best performing feature set for that particular type of model or typical problem.

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This is a survey of the application of feature selection metaheuristics lately used in the literature. This survey was realized by J. Hammon in her 2013 thesis.

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Brank, Janez; Mladenić, Dunja; Grobelnik, Marko; Liu, Huan; Mladenić, Dunja; Flach, Peter A.; Garriga, Gemma C.; Toivonen, Hannu; Toivonen, Hannu (2011),

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Das, Abhimanyu; Kempe, David (2011). "Submodular meets Spectral: Greedy Algorithms for Subset Selection, Sparse Approximation and Dictionary Selection".

3460:{\displaystyle \mathrm {SPEC_{CMI}} :\max _{\mathbf {x} }\left\{\mathbf {x} ^{T}Q\mathbf {x} \right\}\quad {\mbox{s.t.}}\ \|\mathbf {x} \|=1,x_{i}\geq 0} 913: 8495:

Peng, H. C.; Long, F.; Ding, C. (2005). "Feature selection based on mutual information: criteria of max-dependency, max-relevance, and min-redundancy".

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are two distinct notions, since one relevant feature may be redundant in the presence of another relevant feature with which it is strongly correlated.

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Proceedings / IEEE Computational Systems Bioinformatics Conference, CSB. IEEE Computational Systems Bioinformatics Conference, pages 301-309, 2005.

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Zhang, Y.; Wang, S.; Phillips, P. (2014). "Binary PSO with Mutation Operator for Feature Selection using Decision Tree applied to Spam Detection".

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The feature selection methods are typically presented in three classes based on how they combine the selection algorithm and the model building.

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Yamada, M.; Jitkrittum, W.; Sigal, L.; Xing, E. P.; Sugiyama, M. (2014). "High-Dimensional Feature Selection by Feature-Wise Non-Linear Lasso".

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García-Torres, Miguel; Gómez-Vela, Francisco; Divina, Federico; Pinto-Roa, Diego P.; Noguera, José Luis Vázquez; Román, Julio C. Mello (2021).

6047: 4046:{\displaystyle {\begin{aligned}JMI(f_{i})&=\sum _{f_{j}\in S}(I(f_{i};c)+I(f_{i};c|f_{j}))\\&=\sum _{f_{j}\in S}{\bigl }\end{aligned}}} 1174:. In statistics, some criteria are optimized. This leads to the inherent problem of nesting. More robust methods have been explored, such as 1118: 961: 7226:

Sarangi, Susanta; Sahidullah, Md; Saha, Goutam (September 2020). "Optimization of data-driven filterbank for automatic speaker verification".

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In Proceedings of the 11th Annual conference on Genetic and evolutionary computation, GECCO '09, pages 201-208, New York, NY, USA, 2009. ACM.

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Kraskov, Alexander; Stögbauer, Harald; Andrzejak, Ralph G; Grassberger, Peter (2003). "Hierarchical Clustering Based on Mutual Information".

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Hernandez, J. C. H.; Duval, B.; Hao, J.-K. (2007). "A Genetic Embedded Approach for Gene Selection and Classification of Microarray Data".

5470:. The optimization problem is a Lasso problem, and thus it can be efficiently solved with a state-of-the-art Lasso solver such as the dual 918: 769: 3531: 1871: 500: 9164: 7973:

Hazimeh, Hussein; Mazumder, Rahul; Saab, Ali (2020). "Sparse Regression at Scale: Branch-and-Bound rooted in First-Order Optimization".

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algorithm; possible criteria include: a subset score exceeds a threshold, a program's maximum allowed run time has been surpassed, etc.

9348:"Molecular classification of cancer types from microarray data using the combination of genetic algorithms and support vector machines" 8811: 8392:

Einicke, G. A. (2018). "Maximum-Entropy Rate Selection of Features for Classifying Changes in Knee and Ankle Dynamics During Running".

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Chuang, L.-Y.; Yang, C.-H. (2009). "Tabu search and binary particle swarm optimization for feature selection using microarray data".

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Proceedings of the NIPS 2009 Workshop on Discrete Optimization in Machine Learning: Submodularity, Sparsity & Polyhedra (DISCML)

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Huerta, E. B.; Duval, B.; Hao, J.-K. (2006). "A Hybrid GA/SVM Approach for Gene Selection and Classification of Microarray Data".

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Meiri, R.; Zahavi, J. (2006). "Using simulated annealing to optimize the feature selection problem in marketing applications".

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Recommender system based on feature selection. The feature selection methods are introduced into recommender system research.

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Optimisation combinatoire pour la sélection de variables en régression en grande dimension: Application en génétique animale

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mRMR is an instance of a large class of filter methods which trade off between relevancy and redundancy in different ways.

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Muni, D. P.; Pal, N. R.; Das, J. (2006). "Genetic programming for simultaneous feature selection and classifier design".

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Kapetanios, G. (2007). "Variable Selection in Regression Models using Nonstandard Optimisation of Information Criteria".

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The central premise when using a feature selection technique is that the data contains some features that are either

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Yishi Zhang; Shujuan Li; Teng Wang; Zigang Zhang (2013). "Divergence-based feature selection for separate classes".

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Liu, Huan; Yu, Lei (2005). "Toward Integrating Feature Selection Algorithms for Classification and Clustering".

7909:"Scoring relevancy of features based on combinatorial analysis of Lasso with application to lymphoma diagnosis" 6632: 6481: 5616:{\displaystyle \mathrm {Merit} _{S_{k}}={\frac {k{\overline {r_{cf}}}}{\sqrt {k+k(k-1){\overline {r_{ff}}}}}}.} 4057: 1352: 1126: 994: 890: 654: 475: 8834:

ICML'03: Proceedings of the Twentieth International Conference on International Conference on Machine Learning

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Senliol, Baris; et al. (2008). "Fast Correlation Based Filter (FCBF) with a different search strategy".

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is a kernel-based independence measure called the (empirical) Hilbert-Schmidt independence criterion (HSIC),

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Jourdan, L.; Dhaenens, C.; Talbi, E.-G. (2005). "Linkage disequilibrium study with a parallel adaptive GA".

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or to predict data. These methods are particularly effective in computation time and robust to overfitting.

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Some learning algorithms perform feature selection as part of their overall operation. These include:

5086: 5045: 5035:{\displaystyle \mathbf {\Gamma } =\mathbf {I} _{m}-{\frac {1}{m}}\mathbf {1} _{m}\mathbf {1} _{m}^{T}} 2428: 7405: 6582: 1345: 987: 593: 361: 231: 9618: 9274: 8312: 7454:. In Fitzgibbon, Andrew; Lazebnik, Svetlana; Perona, Pietro; Sato, Yoichi; Schmid, Cordelia (eds.). 6005: 5436: 5119: 4532:{\displaystyle {\mbox{HSIC}}(f_{k},c)={\mbox{tr}}({\bar {\mathbf {K} }}^{(k)}{\bar {\mathbf {L} }})} 3270: 9935: 8785: 8596: 8511: 7187: 7145: 5700:

is the average value of all feature-feature correlations. The CFS criterion is defined as follows:

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method can achieve a close-to-optimal solution even when data contains >1M irrelevant features.

4664:{\displaystyle {\bar {\mathbf {K} }}^{(k)}=\mathbf {\Gamma } \mathbf {K} ^{(k)}\mathbf {\Gamma } } 9777: 7721:

Urbanowicz, Ryan J.; Meeker, Melissa; LaCava, William; Olson, Randal S.; Moore, Jason H. (2018).

7157: 1135: 1049: 562: 411: 311: 138: 8769:", Proceedings of the 2012 International Joint Conference on Neural Networks (IJCNN), IEEE, 2012 8260:

High-dimensional feature selection via feature grouping: A Variable Neighborhood Search approach

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is defined by the average value of all mutual information values between the individual feature

1560: 9391:. Lecture Notes in Computer Science. Vol. 4447. Berlin: Springer Verlag. pp. 90–101. 9269: 8506: 7135: 6962: 6711: 6657: 6537: 6513: 6054:. Hall's dissertation uses neither of these, but uses three different measures of relatedness, 5152: 4573: 1537:

of the target node, and in a Bayesian Network, there is a unique Markov Blanket for each node.

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Shah, S. C.; Kusiak, A. (2004). "Data mining and genetic algorithm based gene/SNP selection".

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However, there are different approaches, that try to reduce the redundancy between features.

1519: 1424: 696: 518: 470: 326: 241: 113: 9181: 8484: 8111:"Category-specific models for ranking effective paraphrases in community Question Answering" 7402:"Relevant and invariant feature selection of hyperspectral images for domain generalization" 1462:, maximum dependency feature selection, and a variety of new criteria that are motivated by 1191:

simpler filter is evaluated. Embedded techniques are embedded in, and specific to, a model.

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The mRMR criterion is a combination of two measures given above and is defined as follows:

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Soufan, Othman; Kleftogiannis, Dimitrios; Kalnis, Panos; Bajic, Vladimir B. (2015-02-26).

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Evolutionary Computation, Machine Learning and Data Mining in Bioinformatics. EvoBIO 2007

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Select the feature with the largest score and add it to the set of select features (e.g.

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Another score derived for the mutual information is based on the conditional relevancy:

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analysis are two cases where feature selection is used. It should be distinguished from

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Learning to Rank Effective Paraphrases from Query Logs for Community Question Answering

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F.C. Garcia-Lopez, M. Garcia-Torres, B. Melian, J.A. Moreno-Perez, J.M. Moreno-Vega.

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F.C. Garcia-Lopez, M. Garcia-Torres, B. Melian, J.A. Moreno-Perez, J.M. Moreno-Vega.

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Model Selection and Multimodel Inference: A practical information-theoretic approach

7962:. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). 7674: 7548: 6436: 9872: 9860: 9744: 9736: 9603: 9581: 9548: 9538: 9507: 9482: 9462: 9425: 9392: 9359: 9318: 9279: 9230: 9220: 9162:

Gene Selection in Cancer Classification using PSO-SVM and GA-SVM Hybrid Algorithms.

9135: 9108: 9080: 9053: 9030: 9018: 8983: 8948: 8911: 8901: 8730: 8708: 8669: 8649: 8516: 8401: 8330: 8206: 8162: 8130: 8122: 8074: 8033: 8015: 7930: 7920: 7871: 7846: 7815: 7782:"An extensive empirical study of feature selection metrics for text classification" 7752: 7744: 7640: 7632: 7595: 7575: 7528: 7491: 7469: 7436: 7414: 7343: 7297: 7245: 7177: 6412: 1523: 1238: 1195: 1187: 1175: 1167: 1151: 827: 580: 530: 440: 424: 394: 256: 251: 201: 191: 89: 9258:

Oh, I. S.; Moon, B. R. (2004). "Hybrid genetic algorithms for feature selection".

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Hinkle, Jacob; Muralidharan, Prasanna; Fletcher, P. Thomas; Joshi, Sarang (2012).

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A memetic algorithm for gene selection and molecular classification of an cancer.

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is a general description of an algorithm dedicated to solve difficult (typically

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Regularized trees, e.g. regularized random forest implemented in the RRF package

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The increasing overfitting risk when the number of observations is insufficient.

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Roffo, G.; Melzi, S.; Cristani, M. (2015-12-01). "Infinite Feature Selection".

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Proceedings of the 25th international conference on Machine learning - ICML '08

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simplification of models to make them easier to interpret by researchers/users,

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Filter feature selection is a specific case of a more general paradigm called

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or 'distance measures' in the mathematical sense, since they fail to obey the

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for scoring the different features. They usually use all the same algorithm:

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Proceedings of the Genetic and Evolutionary Computation Conference Companion

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criterion may also be used to select the most relevant subset of features.

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is the average value of all mutual information values between the feature

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IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics

8135: 7835:"Gene selection for cancer classification using support vector machines" 7562:

Hauberg, Søren; Lauze, François; Pedersen, Kim Steenstrup (2013-05-01).

3680:

is that it can be solved simply via finding the dominant eigenvector of

1540: 9684:

Submodular feature selection for high-dimensional acoustic score spaces

9429: 9171:

Congress on Evolutionary Computation, Singapore: Singapore (2007), 2007

7271:

Gareth James; Daniela Witten; Trevor Hastie; Robert Tibshirani (2013).

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The significant computation time when the number of variables is large.

1022: 749: 445: 371: 9919: 8705:

2008 23rd International Symposium on Computer and Information Sciences

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Repeat 3. and 4. until a certain number of features is selected (e.g.

1533:. The optimal solution to the filter feature selection problem is the 1076:, and can thus be removed without incurring much loss of information. 9915:

Minimum-redundancy-maximum-relevance (mRMR) feature selection program

9424:. Lecture Notes in Computer Science. Vol. 3907. pp. 34–44. 8181:

Solving feature subset selection problem by a Parallel Scatter Search

7832: 5663:

is the average value of all feature-classification correlations, and

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There are different Feature Selection mechanisms around that utilize

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to repeatedly construct a model and remove features with low weights.

908: 689: 9773:

A content-based recommender system for computer science publications

8563: 8275: 7059: 4128:

Hilbert-Schmidt Independence Criterion Lasso based feature selection

3663:{\displaystyle Q_{ij}=(I(f_{i};c|f_{j})+I(f_{j};c|f_{i}))/2,i\neq j} 1340:, which have a penalty of 2 for each added feature. AIC is based on 8884: 8564:

Rodriguez-Lujan, I.; Huerta, R.; Elkan, C.; Santa Cruz, C. (2010).

7979: 7739: 7523: 7240: 6046:

variables are referred to as correlations, but are not necessarily

1969:{\displaystyle D(S,c)={\frac {1}{|S|}}\sum _{f_{i}\in S}I(f_{i};c)} 9668: 9008: 8766: 8644: 8243:

Solving Feature Subset Selection Problem by a Hybrid Metaheuristic

7957: 7464: 7098:-regularization techniques, such as sparse regression, LASSO, and 6448: 4064:

to estimate the redundancy between the already selected features (

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Naive Bayes implementation with feature selection in Visual Basic

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Feature Selection Package, Arizona State University (Matlab Code)

8744:

Nguyen, Hai; Franke, Katrin; Petrovic, Slobodan (December 2009).

8468:

Brown, Gavin; Pocock, Adam; Zhao, Ming-Jie; Luján, Mikel (2012).

7225: 6391: 6347: 684: 1150:, which combines the L1 penalty of LASSO with the L2 penalty of 7704:

A comparative study on feature selection in text categorization

7507:"Universal Approximations of Invariant Maps by Neural Networks" 7449: 435: 9728:

IEEE Transactions on Pattern Analysis and Machine Intelligence

9703:

Submodular Attribute Selection for Action Recognition in Video

9261:

IEEE Transactions on Pattern Analysis and Machine Intelligence

9097: 8498:

IEEE Transactions on Pattern Analysis and Machine Intelligence

8258:

M. Garcia-Torres, F. Gomez-Vela, B. Melian, J.M. Moreno-Vega.

7993: 6087:; then the above can be rewritten as an optimization problem: 2818:{\displaystyle \mathrm {mRMR} =\max _{x\in \{0,1\}^{n}}\left.} 8845: 8843: 6808: 6343:

tree ensemble model) and thus are computationally efficient.

6308:{\displaystyle \mathrm {CFS} =\max _{x\in \{0,1\}^{n}}\left.} 3699:

In a study of different scores Brown et al. recommended the

1835:

Minimum-redundancy-maximum-relevance (mRMR) feature selection

679: 674: 401: 9578:

2015 IEEE International Conference on Computer Vision (ICCV)

9305:

Xuan, P.; Guo, M. Z.; Wang, J.; Liu, X. Y.; Liu, Y. (2011).

2545:. The above may then be written as an optimization problem: 7720: 1266:

Two popular filter metrics for classification problems are

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Feature selection techniques are used for several reasons:

9922:(Open source Feature Selection algorithms in C and MATLAB) 9771:

D.H. Wang, Y.C. Liang, D.Xu, X.Y. Feng, R.C. Guan(2018), "

8840: 8702: 7958:

Kai Han; Yunhe Wang; Chao Zhang; Chao Li; Chao Xu (2018).

2840: 9833:

Feature Selection for Knowledge Discovery and Data Mining

9422:

Applications of Evolutionary Computing. EvoWorkshops 2006

9174: 8629: 7723:"Relief-Based Feature Selection: Introduction and Review" 7287: 6318:

The combinatorial problems above are, in fact, mixed 0–1

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improve data's compatibility with a learning model class,

9499:

International Journal of Foundations of Computer Science

9197:. Journal of the American Statistical Association, 2007. 8686:

Correlation-based Feature Selection for Machine Learning

6915:

Classification accuracy (Leave-one-out cross-validation)

6875:

Classification accuracy (Leave-one-out cross-validation)

6833:

Classification accuracy (Leave-one-out cross-validation)

1021:(variables, predictors) for use in model construction. 967:

List of datasets in computer vision and image processing

8877: 8108: 8091: 8329:(1985), "Prediction and entropy", in Atkinson, A. C.; 5373: 4547: 4476: 4444: 4376: 4319: 4249: 3412: 3128:

is the vector of feature relevancy assuming there are

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First International Workshop on Hybrid Metaheuristics

7106: 7075: 6361: 6096: 6008: 5971: 5709: 5669: 5632: 5500: 5439: 5188: 5155: 5122: 5089: 5048: 4969: 4929: 4889: 4821: 4730: 4677: 4602: 4582: 4545: 4442: 4142: 4103: 4070: 3713: 3534: 3476: 3337: 3273: 3237: 3138: 3026: 2859: 2554: 2486: 2431: 2146: 2011: 1874: 1790: 1689: 1603: 1563: 1541:

Information Theory Based Feature Selection Mechanisms

1472: 1433: 1397: 1361: 9720: 9525:

Zhang, Y.; Dong, Z.; Phillips, P.; Wang, S. (2015).

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E. Alba, J. Garia-Nieto, L. Jourdan et E.-G. Talbi.

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Guyon I.; Weston J.; Barnhill S.; Vapnik V. (2002).

7564:"Unscented Kalman Filtering on Riemannian Manifolds" 7561: 1677:

Calculate the score which might be derived from the

9853:

IEEE Transactions on Knowledge and Data Engineering

9796:"An Introduction to Variable and Feature Selection" 7972: 7960:

Autoencoder inspired unsupervised feature selection

7675:"An Introduction to Variable and Feature Selection" 7609:Kratsios, Anastasis; Hyndman, Cody (June 8, 2021). 9575: 9195:Shotgun stochastic search for 'large p' regression 9180:B. Duval, J.-K. Hao et J. C. Hernandez Hernandez. 8746:"Optimizing a class of feature selection measures" 7400:Persello, Claudio; Bruzzone, Lorenzo (July 2014). 7119: 7088: 6307: 6038: 5994: 5955:{\displaystyle \mathrm {CFS} =\max _{S_{k}}\left.} 5954: 5692: 5655: 5615: 5458: 5422: 5168: 5141: 5104: 5063: 5034: 4955: 4915: 4875: 4807: 4712: 4663: 4588: 4564: 4531: 4425: 4116: 4089: 4045: 3662: 3520: 3459: 3308: 3258: 3231:is the matrix of feature pairwise redundancy, and 3223: 3120: 3009: 2817: 2537: 2472: 2359: 2126: 1968: 1812: 1773: 1662: 1582: 1498: 1454: 1415: 1379: 1125:, and inter/intra class distance or the scores of 9386: 8973: 8761: 8759: 8617:Advances in Neural Information Processing Systems 8394:IEEE Journal of Biomedical and Health Informatics 8152: 8143: 7602: 7407:2014 IEEE Geoscience and Remote Sensing Symposium 7060:Feature selection embedded in learning algorithms 3323: 1209:Alternative search-based techniques are based on 1017:is the process of selecting a subset of relevant 9927: 9617:Roffo, Giorgio; Melzi, Simone (September 2016). 8878:Saghapour, E.; Kermani, S.; Sehhati, M. (2017). 7399: 6112: 5725: 5477: 5226: 4808:{\displaystyle K_{i,j}^{(k)}=K(u_{k,i},u_{k,j})} 4180: 3369: 2878: 2573: 2165: 1597:Select the feature with the largest score (e.g. 1162:, the most popular form of feature selection is 9619:"Features Selection via Eigenvector Centrality" 8360: 7608: 7452:"Polynomial Regression on Riemannian Manifolds" 7368: 7292:, in Sammut, Claude; Webb, Geoffrey I. (eds.), 6449:Application of feature selection metaheuristics 3691:also handles second-order feature interaction. 2360:{\displaystyle \mathrm {mRMR} =\max _{S}\left.} 9793: 9419: 9304: 8756: 7672: 7668: 7666: 7664: 3224:{\displaystyle H_{n\times n}=_{i,j=1\ldots n}} 1670:) and add it to the set of selected features ( 1499:{\displaystyle {\sqrt {2\log {\frac {p}{q}}}}} 1119:Pearson product-moment correlation coefficient 962:List of datasets for machine-learning research 9721:Sun, Y.; Todorovic, S.; Goodison, S. (2010). 8799: 8797: 8109:Figueroa, Alejandro; Guenter Neumann (2014). 8092:Figueroa, Alejandro; Guenter Neumann (2013). 7296:, Boston, MA: Springer US, pp. 402–406, 4034: 4027: 3945: 3882: 995: 9073:Computational Statistics & Data Analysis 8494: 7700: 6135: 6122: 5447: 5440: 5359: 5350: 5130: 5123: 4362: 4353: 3429: 3421: 2596: 2583: 16:Procedure in machine learning and statistics 9043: 8546: 7661: 7369:Kratsios, Anastasis; Hyndman, Cody (2021). 3694: 9794:Guyon, Isabelle; Elisseeff, Andre (2003). 9616: 9452: 9125: 9070: 8938: 8812:Lille University of Science and Technology 8794: 7696: 7694: 7673:Guyon, Isabelle; Elisseeff, André (2003). 7568:Journal of Mathematical Imaging and Vision 6486:Feature Selection using Feature Similarity 1980:The redundancy of all features in the set 1002: 988: 9829: 9748: 9667: 9552: 9542: 9363: 9322: 9273: 9234: 9224: 8915: 8905: 8643: 8623: 8607: 8566:"Quadratic programming feature selection" 8510: 8281: 8134: 8037: 8019: 7978: 7934: 7924: 7850: 7756: 7738: 7644: 7522: 7463: 7239: 2425:in the globally optimal feature set. Let 1166:, which is a wrapper technique. It is a 69:Learn how and when to remove this message 9661: 9046:European Journal of Operational Research 8463: 8461: 8459: 8457: 8434: 8361:Burnham, K. P.; Anderson, D. R. (2002), 8185:European Journal of Operational Research 8060: 7504: 6435: 6411: 6390: 5116:-dimensional vector with all ones, and 3259:{\displaystyle \mathbf {x} _{n\times 1}} 1290:Other available filter metrics include: 32:This article includes a list of general 9810: 9531:Frontiers in Computational Neuroscience 8976:Journal of Animal Breeding and Genetics 8767:Feature Selection via Regularized Trees 8391: 7900: 7859: 7701:Yang, Yiming; Pedersen, Jan O. (1997). 7691: 7274:An Introduction to Statistical Learning 4097:) and the feature under investigation ( 2841:Quadratic programming feature selection 9928: 9257: 9206: 8851:Choosing SNPs using feature selection. 8849:T. M. Phuong, Z. Lin et R. B. Altman. 8777: 8775: 8608:Yang, Howard Hua; Moody, John (2000). 8590: 8588: 8325: 7779: 7329: 7047:Structural Associative Classification 6623:Simulated annealing, genetic algorithm 4876:{\displaystyle L_{i,j}=L(c_{i},c_{j})} 1320: 9911:(includes executable and source code) 9850: 9644:Wrappers for feature subset selection 8824: 8803: 8454: 8187:, vol. 169, no. 2, pp. 477–489, 2006. 7030:Average Precision, Accuracy, ROC AUC 6440:Embedded method for Feature selection 6322:problems that can be solved by using 2538:{\displaystyle a_{ij}=I(f_{i};f_{j})} 1513: 1344:, and is effectively derived via the 9800:Journal of Machine Learning Research 9345: 8692:(PhD thesis). University of Waikato. 8682: 8557: 8475:Journal of Machine Learning Research 8444:Journal of Machine Learning Research 8349:from the original on August 30, 2019 7906: 7865: 7789:Journal of Machine Learning Research 7616:Journal of Machine Learning Research 7375:Journal of Machine Learning Research 6416:Wrapper Method for Feature selection 6329: 5693:{\displaystyle {\overline {r_{ff}}}} 5656:{\displaystyle {\overline {r_{cf}}}} 1466:(FDR), which use something close to 18: 9830:Liu, Huan; Motoda, Hiroshi (1998). 8941:Artificial Intelligence in Medicine 8772: 8585: 7866:Bach, Francis R (2008). "Bolasso". 7264: 6395:Filter Method for feature selection 4565:{\displaystyle {\mbox{tr}}(\cdot )} 1557:as score for between all features ( 1455:{\displaystyle {\sqrt {2\log {p}}}} 1316:Correlation-based feature selection 1313:Consistency-based feature selection 1194:Many popular search approaches use 1181: 957:Glossary of artificial intelligence 13: 9787: 8825:Yu, Lei; Liu, Huan (August 2003). 6431: 6378: 6362:Overview on metaheuristics methods 6104: 6101: 6098: 5717: 5714: 5711: 5515: 5512: 5509: 5506: 5503: 5216: 5213: 5210: 5207: 5204: 5200: 5196: 5193: 5190: 4170: 4167: 4164: 4161: 4158: 4154: 4150: 4147: 4144: 3359: 3356: 3353: 3349: 3345: 3342: 3339: 3121:{\displaystyle F_{n\times 1}=^{T}} 2870: 2867: 2864: 2861: 2565: 2562: 2559: 2556: 2157: 2154: 2151: 2148: 1416:{\displaystyle {\sqrt {\log {n}}}} 1380:{\displaystyle {\sqrt {\log {n}}}} 38:it lacks sufficient corresponding 14: 9952: 9880: 7727:Journal of Biomedical Informatics 6978:Classification accuracy (10-fold) 6934:Classification accuracy (10-fold) 6895:Classification accuracy (10-fold) 6872:All paired Support Vector Machine 6765:Classification accuracy (10-fold) 6742:Classification accuracy (10-fold) 6542:Predicted residual sum of squares 6518:Classification accuracy (10-fold) 6407: 6048:Pearson's correlation coefficient 5179:The HSIC Lasso can be written as 4596:is the regularization parameter, 3521:{\displaystyle Q_{ii}=I(f_{i};c)} 2850:optimization problem as follows: 2416:indicates absence of the feature 9128:Journal of Computational Biology 8988:10.1111/j.1439-0388.2011.00917.x 8115:Expert Systems with Applications 7294:Encyclopedia of Machine Learning 7154:networks with a bottleneck-layer 6563:Classification accuracy (5-fold) 6386: 5354: 5306: 5257: 5231: 5105:{\displaystyle \mathbf {1} _{m}} 5092: 5064:{\displaystyle \mathbf {I} _{m}} 5051: 5017: 5005: 4980: 4971: 4706: 4701: 4696: 4682: 4657: 4640: 4634: 4608: 4516: 4490: 4357: 4185: 3425: 3401: 3387: 3374: 3240: 2922: 2913: 2899: 2883: 2473:{\displaystyle c_{i}=I(f_{i};c)} 1391:(MDL) which asymptotically uses 23: 9765: 9714: 9695: 9676: 9655: 9636: 9610: 9569: 9518: 9489: 9446: 9413: 9380: 9339: 9311:Genetics and Molecular Research 9298: 9251: 9200: 9187: 9154: 9119: 9091: 9064: 9037: 9002: 8967: 8932: 8871: 8818: 8737: 8696: 8676: 8601: 8488: 8428: 8385: 8354: 8319: 8269: 8252: 8235: 8190: 8173: 8102: 8085: 8054: 7987: 7966: 7951: 7826: 7799: 7773: 7714: 7505:Yarotsky, Dmitry (2021-04-30). 5371: 4374: 3410: 2940: 1824:The simplest approach uses the 1355:(BIC), which uses a penalty of 1094: 9813:Regression Modeling Strategies 9193:C. Hans, A. Dobra et M. West. 8804:Hamon, Julie (November 2013). 8782:RRF: Regularized Random Forest 8266:, vol. 326, pp. 102-118, 2016. 7555: 7498: 7443: 7393: 7362: 7323: 7281: 7219: 6809:Leave-one-out cross-validation 6198: 6153: 6039:{\displaystyle r_{f_{i}f_{j}}} 5939: 5831: 5584: 5572: 5459:{\displaystyle \|\cdot \|_{F}} 5329: 5323: 5317: 5310: 5261: 5249: 5142:{\displaystyle \|\cdot \|_{1}} 4950: 4933: 4910: 4893: 4870: 4844: 4802: 4764: 4753: 4747: 4720:are input and output centered 4686: 4651: 4645: 4625: 4619: 4612: 4559: 4553: 4526: 4520: 4507: 4501: 4494: 4482: 4469: 4450: 4344: 4325: 4281: 4255: 4058:conditional mutual information 4022: 4015: 3988: 3979: 3953: 3937: 3918: 3909: 3890: 3844: 3841: 3827: 3807: 3798: 3779: 3773: 3740: 3727: 3637: 3634: 3620: 3600: 3591: 3577: 3557: 3551: 3515: 3496: 3324:Conditional mutual information 3309:{\displaystyle I(f_{i};f_{i})} 3303: 3277: 3194: 3190: 3164: 3158: 3109: 3105: 3086: 3071: 3052: 3046: 2795: 2760: 2532: 2506: 2467: 2448: 2346: 2320: 2268: 2259: 2246: 2227: 2194: 2186: 2121: 2095: 2043: 2034: 2021: 2015: 1963: 1944: 1911: 1903: 1890: 1878: 1800: 1792: 1768: 1765: 1746: 1715: 1657: 1654: 1635: 1629: 1353:Bayesian information criterion 1178:and piecewise linear network. 377:Relevance vector machine (RVM) 1: 9365:10.1016/s0014-5793(03)01275-4 9113:10.1016/S0003-2670(97)00065-2 8435:Aliferis, Constantin (2010). 8079:10.1016/j.compind.2015.01.005 7302:10.1007/978-0-387-30164-8_306 7213: 7053:Shaharanee & Hadzic 2014 5478:Correlation feature selection 866:Computational learning theory 430:Expectation–maximization (EM) 8953:10.1016/j.artmed.2004.04.002 8907:10.1371/journal.pone.0184203 8167:10.1016/j.knosys.2014.03.015 8061:Figueroa, Alejandro (2015). 8021:10.1371/journal.pone.0117988 7820:10.1016/j.neucom.2012.06.036 7413:. IEEE. pp. 3562–3565. 6651:Multiple Linear Regression, 5685: 5648: 5602: 5556: 1526:, and so the structure is a 1328:Akaike information criterion 1274:, although neither are true 1261:Variable neighborhood search 1115:pointwise mutual information 823:Coefficient of determination 670:Convolutional neural network 382:Support vector machine (SVM) 7: 9397:10.1007/978-3-540-71783-6_9 8342:, Springer, pp. 1–24, 8336:A Celebration of Statistics 7926:10.1186/1471-2164-14-S1-S14 7474:10.1007/978-3-642-33712-3_1 7456:Computer Vision – ECCV 2012 7419:10.1109/igarss.2014.6947252 7198:Hyperparameter optimization 7171: 6854:Sensitivity and specificity 6350:, and thus, require little 6324:branch-and-bound algorithms 5472:augmented Lagrangian method 1253:Targeted projection pursuit 1248:Particle swarm optimization 1244:Greedy backward elimination 1216:Search approaches include: 1211:targeted projection pursuit 1062:present in the input space. 974:Outline of machine learning 871:Empirical risk minimization 10: 9957: 9085:10.1016/j.csda.2007.04.006 9058:10.1016/j.ejor.2004.09.010 8713:10.1109/ISCIS.2008.4717949 8127:10.1016/j.eswa.2014.02.004 7533:10.1007/s00365-021-09546-1 7511:Constructive Approximation 7208:Relief (feature selection) 6992:Infinite Feature Selection 6056:minimum description length 5995:{\displaystyle r_{cf_{i}}} 5083:: the number of samples), 4090:{\displaystyle f_{j}\in S} 1583:{\displaystyle f_{i}\in F} 1389:minimum description length 1148:Elastic net regularization 611:Feedforward neural network 362:Artificial neural networks 9512:10.1142/S0129054105002978 9467:10.1109/TSMCB.2005.854499 9023:10.1007/s11590-011-0419-7 8406:10.1109/JBHI.2017.2711487 7749:10.1016/j.jbi.2018.07.014 7580:10.1007/s10851-012-0372-9 7250:10.1016/j.dsp.2020.102795 7228:Digital Signal Processing 7020:Eigenvector Centrality FS 6807:Classification accuracy ( 6583:Artificial Neural Network 5169:{\displaystyle \ell _{1}} 5042:is the centering matrix, 3684:, thus is very scalable. 1346:maximum entropy principle 594:Artificial neural network 9642:R. Kohavi and G. John, " 9544:10.3389/fncom.2015.00066 7330:Kramer, Mark A. (1991). 7277:. Springer. p. 204. 7188:Dimensionality reduction 7146:Random multinomial logit 6823:Hybrid genetic algorithm 4589:{\displaystyle \lambda } 3701:joint mutual information 3695:Joint mutual information 1828:as the "derived" score. 1590:) and the target class ( 1387:for each added feature, 903:Journals and conferences 850:Mathematical foundations 760:Temporal difference (TD) 616:Recurrent neural network 536:Conditional random field 459:Dimensionality reduction 207:Dimensionality reduction 169:Quantum machine learning 164:Neuromorphic engineering 124:Self-supervised learning 119:Semi-supervised learning 9778:Knowledge-Based Systems 9649:Artificial intelligence 9226:10.1186/1471-2105-6-148 8211:10.1145/3449726.3459481 8155:Knowledge-Based Systems 7876:10.1145/1390156.1390161 7852:10.1023/A:1012487302797 7780:Forman, George (2003). 7033:Roffo & Melzi 2016 6733:PSO + Genetic algorithm 6663:Broadhurst et al. 1997 6060:symmetrical uncertainty 4956:{\displaystyle L(c,c')} 4916:{\displaystyle K(u,u')} 2406:indicates presence and 2374:full-set features. Let 2370:Suppose that there are 1136:Support Vector Machines 1123:Relief-based algorithms 1050:curse of dimensionality 1045:shorter training times, 312:Apprenticeship learning 53:more precise citations. 9741:10.1109/tpami.2009.190 9652:97.1-2 (1997): 273-324 9580:. pp. 4202–4210. 9284:10.1109/tpami.2004.105 9101:Analytica Chimica Acta 8810:(Thesis) (in French). 8521:10.1109/TPAMI.2005.159 8307:Cite journal requires 7121: 7090: 6975:Support vector machine 6951:Support Vector Machine 6931:Support Vector Machine 6912:Support Vector Machine 6892:Support Vector Machine 6850:Support Vector Machine 6762:Support Vector Machine 6739:Support Vector Machine 6712:Support Vector Machine 6658:root-mean-square error 6441: 6417: 6396: 6309: 6229: 6176: 6076:be the set membership 6040: 5996: 5956: 5694: 5657: 5617: 5460: 5424: 5290: 5170: 5143: 5106: 5065: 5036: 4963:are kernel functions, 4957: 4917: 4877: 4809: 4714: 4665: 4590: 4566: 4533: 4427: 4307: 4227: 4118: 4091: 4047: 3664: 3522: 3461: 3310: 3260: 3225: 3122: 3011: 2971: 2819: 2783: 2724: 2678: 2635: 2539: 2474: 2383:be the set membership 2361: 2128: 1970: 1814: 1775: 1664: 1584: 1500: 1456: 1417: 1381: 1303:Probabilistic distance 861:Bias–variance tradeoff 743:Reinforcement learning 719:Spiking neural network 129:Reinforcement learning 9586:10.1109/ICCV.2015.478 9324:10.4238/vol10-2gmr969 9140:10.1089/cmb.2007.0211 8765:H. Deng, G. Runger, " 8067:Computers in Industry 7348:10.1002/aic.690370209 7122: 7120:{\displaystyle l_{1}} 7091: 7089:{\displaystyle l_{1}} 7041:Symmetrical Tau (ST) 6786:Posterior Probability 6776:Iterated local search 6755:Iterated Local Search 6653:Partial Least Squares 6439: 6415: 6394: 6310: 6209: 6156: 6041: 5997: 5957: 5695: 5658: 5618: 5461: 5425: 5270: 5171: 5144: 5107: 5066: 5037: 4958: 4918: 4878: 4810: 4715: 4666: 4591: 4567: 4534: 4428: 4287: 4201: 4119: 4117:{\displaystyle f_{i}} 4092: 4048: 3665: 3523: 3462: 3311: 3261: 3226: 3123: 3012: 2951: 2848:quadratic programming 2820: 2763: 2698: 2658: 2615: 2540: 2475: 2362: 2129: 1971: 1815: 1813:{\displaystyle |S|=l} 1776: 1665: 1585: 1501: 1457: 1418: 1382: 697:Neural radiance field 519:Structured prediction 242:Structured prediction 114:Unsupervised learning 9865:10.1109/TKDE.2005.66 9811:Harrell, F. (2001). 9011:Optimization Letters 8752:. Vancouver, Canada. 8654:10.1162/NECO_a_00537 8264:Information Sciences 8205:. pp. 149–150. 7907:Zare, Habil (2013). 7104: 7073: 6814:Jirapech-Umpai 2005 6753:Genetic algorithm + 6334:The features from a 6094: 6006: 5969: 5707: 5667: 5630: 5498: 5437: 5186: 5153: 5120: 5087: 5046: 4967: 4927: 4887: 4819: 4728: 4675: 4600: 4580: 4543: 4440: 4140: 4101: 4068: 3711: 3532: 3474: 3335: 3271: 3235: 3136: 3024: 2857: 2552: 2484: 2429: 2144: 2009: 1872: 1788: 1687: 1601: 1561: 1470: 1464:false discovery rate 1431: 1395: 1359: 1300:Inter-class distance 886:Statistical learning 784:Learning with humans 576:Local outlier factor 9941:Dimension reduction 9892:NIPS challenge 2003 9207:Aitken, S. (2005). 8898:2017PLoSO..1284203S 8292:2003q.bio....11039K 8012:2015PLoSO..1017988S 7629:2015NatSR...510312B 7290:"Feature Selection" 7050:Accuracy, Coverage 6963:Alzheimer's disease 6830:K Nearest Neighbors 6804:K Nearest Neighbors 6716:K Nearest Neighbors 6600:Simulated annealing 6554:Simulated annealing 6472:Evaluation Function 5343: 5031: 4883:are Gram matrices, 4757: 4056:The score uses the 3316:on the diagonal of 3132:features in total, 1351:Other criteria are 1321:Optimality criteria 1294:Class separability 1280:triangle inequality 1229:Simulated annealing 1164:stepwise regression 1160:regression analysis 729:Electrochemical RAM 636:reservoir computing 367:Logistic regression 286:Supervised learning 272:Multimodal learning 247:Feature engineering 192:Generative modeling 154:Rule-based learning 149:Curriculum learning 109:Supervised learning 84:Part of a series on 9907:2009-02-14 at the 9708:2015-11-18 at the 9689:2015-10-17 at the 9430:10.1007/11732242_4 9213:BMC Bioinformatics 9167:2016-08-18 at the 8856:2016-09-13 at the 8632:Neural Computation 8249:, pp. 59–68, 2004. 7870:. pp. 33–40. 7193:Feature extraction 7117: 7086: 6721:Euclidean Distance 6442: 6418: 6397: 6352:data preprocessing 6320:linear programming 6305: 6258: 6145: 6078:indicator function 6036: 5992: 5952: 5740: 5690: 5653: 5613: 5456: 5420: 5377: 5247: 5236: 5166: 5139: 5102: 5061: 5032: 5015: 4953: 4913: 4873: 4805: 4731: 4710: 4661: 4586: 4562: 4551: 4529: 4480: 4448: 4423: 4380: 4323: 4253: 4190: 4114: 4087: 4062:mutual information 4043: 4041: 3879: 3772: 3660: 3518: 3457: 3416: 3379: 3306: 3256: 3221: 3118: 3007: 2946: 2888: 2815: 2606: 2535: 2470: 2385:indicator function 2357: 2316: 2223: 2173: 2124: 2091: 1966: 1940: 1826:mutual information 1810: 1771: 1713: 1679:mutual information 1660: 1627: 1580: 1555:mutual information 1547:mutual information 1520:structure learning 1514:Structure learning 1496: 1452: 1413: 1377: 1342:information theory 1272:mutual information 1127:significance tests 1111:mutual information 1088:Feature extraction 1031:feature extraction 297: • 212:Density estimation 9595:978-1-4673-8391-2 9439:978-3-540-33237-4 9406:978-3-540-71782-9 9346:Peng, S. (2003). 9268:(11): 1424–1437. 9134:(12): 1689–1703. 8722:978-1-4244-2880-9 8683:Hall, M. (1999). 8121:(10): 4730–4742. 7637:10.1038/srep10312 7483:978-3-642-33712-3 7428:978-1-4799-5775-0 7311:978-0-387-30768-8 7160:feature selection 7141:Memetic algorithm 7057: 7056: 7003:Average Precision 6945:Genetic algorithm 6926:Genetic algorithm 6906:Genetic algorithm 6886:Genetic algorithm 6866:Genetic algorithm 6844:Genetic algorithm 6798:Genetic algorithm 6645:Genetic algorithm 6506:Genetic algorithm 6330:Regularized trees 6296: 6243: 6111: 5943: 5942: 5724: 5688: 5651: 5608: 5607: 5605: 5559: 5381: 5376: 5313: 5264: 5245: 5225: 5001: 4689: 4615: 4550: 4523: 4497: 4479: 4447: 4384: 4379: 4322: 4252: 4199: 4179: 3857: 3750: 3420: 3415: 3368: 2950: 2945: 2877: 2805: 2690: 2572: 2281: 2279: 2201: 2199: 2164: 2056: 2054: 1918: 1916: 1691: 1605: 1494: 1492: 1450: 1411: 1375: 1297:Error probability 1241:forward selection 1234:Genetic algorithm 1015:Feature selection 1012: 1011: 817:Model diagnostics 800:Human-in-the-loop 643:Boltzmann machine 556:Anomaly detection 352:Linear regression 267:Ontology learning 262:Grammar induction 237:Semantic analysis 232:Association rules 217:Anomaly detection 159:Neuro-symbolic AI 79: 78: 71: 9948: 9876: 9847: 9826: 9807: 9782: 9769: 9763: 9762: 9752: 9735:(9): 1610–1626. 9718: 9712: 9699: 9693: 9680: 9674: 9673: 9671: 9659: 9653: 9640: 9634: 9633: 9631: 9629: 9623: 9614: 9608: 9607: 9573: 9567: 9566: 9556: 9546: 9522: 9516: 9515: 9493: 9487: 9486: 9450: 9444: 9443: 9417: 9411: 9410: 9384: 9378: 9377: 9367: 9343: 9337: 9336: 9326: 9302: 9296: 9295: 9277: 9255: 9249: 9248: 9238: 9228: 9204: 9198: 9191: 9185: 9178: 9172: 9158: 9152: 9151: 9123: 9117: 9116: 9095: 9089: 9088: 9068: 9062: 9061: 9041: 9035: 9034: 9017:(6): 1207–1218. 9006: 9000: 8999: 8971: 8965: 8964: 8936: 8930: 8929: 8919: 8909: 8875: 8869: 8847: 8838: 8837: 8831: 8822: 8816: 8815: 8801: 8792: 8779: 8770: 8763: 8754: 8753: 8741: 8735: 8734: 8707:. pp. 1–4. 8700: 8694: 8693: 8691: 8680: 8674: 8673: 8647: 8627: 8621: 8620: 8614: 8605: 8599: 8592: 8583: 8582: 8570: 8561: 8555: 8550: 8544: 8540: 8514: 8505:(8): 1226–1238. 8492: 8486: 8483: 8465: 8452: 8451: 8441: 8432: 8426: 8425: 8400:(4): 1097–1103. 8389: 8383: 8381: 8367:(2nd ed.), 8358: 8352: 8350: 8348: 8341: 8323: 8317: 8316: 8310: 8305: 8303: 8295: 8285: 8273: 8267: 8256: 8250: 8239: 8233: 8232: 8194: 8188: 8177: 8171: 8170: 8150: 8141: 8140: 8138: 8106: 8100: 8099: 8089: 8083: 8082: 8058: 8052: 8051: 8041: 8023: 7991: 7985: 7984: 7982: 7970: 7964: 7963: 7955: 7949: 7948: 7938: 7928: 7919:(Suppl 1): S14. 7904: 7898: 7897: 7863: 7857: 7856: 7854: 7845:(1–3): 389–422. 7839:Machine Learning 7830: 7824: 7823: 7803: 7797: 7796: 7786: 7777: 7771: 7770: 7760: 7742: 7718: 7712: 7711: 7709: 7698: 7689: 7688: 7670: 7659: 7658: 7648: 7606: 7600: 7599: 7559: 7553: 7552: 7526: 7502: 7496: 7495: 7467: 7447: 7441: 7440: 7412: 7397: 7391: 7390: 7366: 7360: 7359: 7327: 7321: 7320: 7319: 7318: 7285: 7279: 7278: 7268: 7262: 7261: 7243: 7223: 7178:Cluster analysis 7128: 7126: 7124: 7123: 7118: 7116: 7115: 7097: 7095: 7093: 7092: 7087: 7085: 7084: 6637:Kapetanios 2007 6534:Filter + Wrapper 6456: 6455: 6314: 6312: 6311: 6306: 6301: 6297: 6295: 6294: 6293: 6284: 6283: 6274: 6273: 6257: 6239: 6238: 6228: 6223: 6207: 6206: 6205: 6196: 6195: 6186: 6185: 6175: 6170: 6151: 6144: 6143: 6142: 6107: 6045: 6043: 6042: 6037: 6035: 6034: 6033: 6032: 6023: 6022: 6001: 5999: 5998: 5993: 5991: 5990: 5989: 5988: 5961: 5959: 5958: 5953: 5948: 5944: 5938: 5937: 5936: 5935: 5920: 5919: 5896: 5895: 5894: 5893: 5884: 5883: 5860: 5859: 5858: 5857: 5848: 5847: 5821: 5820: 5819: 5818: 5817: 5816: 5790: 5789: 5788: 5787: 5767: 5766: 5765: 5764: 5746: 5739: 5738: 5737: 5720: 5699: 5697: 5696: 5691: 5689: 5684: 5683: 5671: 5662: 5660: 5659: 5654: 5652: 5647: 5646: 5634: 5622: 5620: 5619: 5614: 5609: 5606: 5601: 5600: 5588: 5562: 5561: 5560: 5555: 5554: 5542: 5536: 5531: 5530: 5529: 5528: 5518: 5465: 5463: 5462: 5457: 5455: 5454: 5429: 5427: 5426: 5421: 5410: 5409: 5391: 5390: 5379: 5378: 5374: 5367: 5366: 5357: 5342: 5337: 5332: 5328: 5327: 5326: 5315: 5314: 5309: 5304: 5300: 5299: 5289: 5284: 5266: 5265: 5260: 5255: 5246: 5238: 5235: 5234: 5221: 5220: 5219: 5175: 5173: 5172: 5167: 5165: 5164: 5148: 5146: 5145: 5140: 5138: 5137: 5115: 5111: 5109: 5108: 5103: 5101: 5100: 5095: 5082: 5074: 5070: 5068: 5067: 5062: 5060: 5059: 5054: 5041: 5039: 5038: 5033: 5030: 5025: 5020: 5014: 5013: 5008: 5002: 4994: 4989: 4988: 4983: 4974: 4962: 4960: 4959: 4954: 4949: 4922: 4920: 4919: 4914: 4909: 4882: 4880: 4879: 4874: 4869: 4868: 4856: 4855: 4837: 4836: 4814: 4812: 4811: 4806: 4801: 4800: 4782: 4781: 4756: 4745: 4719: 4717: 4716: 4711: 4709: 4704: 4699: 4691: 4690: 4685: 4680: 4670: 4668: 4667: 4662: 4660: 4655: 4654: 4643: 4637: 4629: 4628: 4617: 4616: 4611: 4606: 4595: 4593: 4592: 4587: 4571: 4569: 4568: 4563: 4552: 4548: 4538: 4536: 4535: 4530: 4525: 4524: 4519: 4514: 4511: 4510: 4499: 4498: 4493: 4488: 4481: 4477: 4462: 4461: 4449: 4445: 4432: 4430: 4429: 4424: 4413: 4412: 4394: 4393: 4382: 4381: 4377: 4370: 4369: 4360: 4337: 4336: 4324: 4320: 4317: 4316: 4306: 4301: 4280: 4279: 4267: 4266: 4254: 4250: 4247: 4246: 4237: 4236: 4226: 4221: 4200: 4192: 4189: 4188: 4175: 4174: 4173: 4123: 4121: 4120: 4115: 4113: 4112: 4096: 4094: 4093: 4088: 4080: 4079: 4052: 4050: 4049: 4044: 4042: 4038: 4037: 4031: 4030: 4018: 4013: 4012: 4000: 3999: 3978: 3977: 3965: 3964: 3949: 3948: 3930: 3929: 3902: 3901: 3886: 3885: 3878: 3871: 3870: 3850: 3840: 3839: 3830: 3819: 3818: 3791: 3790: 3771: 3764: 3763: 3739: 3738: 3690: 3683: 3679: 3673:An advantage of 3669: 3667: 3666: 3661: 3644: 3633: 3632: 3623: 3612: 3611: 3590: 3589: 3580: 3569: 3568: 3547: 3546: 3527: 3525: 3524: 3519: 3508: 3507: 3489: 3488: 3466: 3464: 3463: 3458: 3450: 3449: 3428: 3418: 3417: 3413: 3409: 3405: 3404: 3396: 3395: 3390: 3378: 3377: 3364: 3363: 3362: 3319: 3315: 3313: 3312: 3307: 3302: 3301: 3289: 3288: 3265: 3263: 3262: 3257: 3255: 3254: 3243: 3230: 3228: 3227: 3222: 3220: 3219: 3189: 3188: 3176: 3175: 3154: 3153: 3131: 3127: 3125: 3124: 3119: 3117: 3116: 3098: 3097: 3064: 3063: 3042: 3041: 3016: 3014: 3013: 3008: 3000: 2999: 2981: 2980: 2970: 2965: 2948: 2947: 2943: 2939: 2935: 2931: 2930: 2925: 2916: 2908: 2907: 2902: 2887: 2886: 2873: 2824: 2822: 2821: 2816: 2811: 2807: 2806: 2804: 2803: 2802: 2793: 2792: 2782: 2777: 2758: 2757: 2756: 2747: 2746: 2737: 2736: 2723: 2718: 2696: 2691: 2689: 2688: 2687: 2677: 2672: 2656: 2655: 2654: 2645: 2644: 2634: 2629: 2613: 2605: 2604: 2603: 2568: 2544: 2542: 2541: 2536: 2531: 2530: 2518: 2517: 2499: 2498: 2479: 2477: 2476: 2471: 2460: 2459: 2441: 2440: 2424: 2415: 2405: 2395: 2382: 2373: 2366: 2364: 2363: 2358: 2353: 2349: 2345: 2344: 2332: 2331: 2315: 2308: 2307: 2295: 2294: 2280: 2278: 2277: 2276: 2271: 2262: 2253: 2239: 2238: 2222: 2215: 2214: 2200: 2198: 2197: 2189: 2180: 2172: 2160: 2133: 2131: 2130: 2125: 2120: 2119: 2107: 2106: 2090: 2083: 2082: 2070: 2069: 2055: 2053: 2052: 2051: 2046: 2037: 2028: 2001: 1993:and the feature 1992: 1983: 1975: 1973: 1972: 1967: 1956: 1955: 1939: 1932: 1931: 1917: 1915: 1914: 1906: 1897: 1864: 1860: 1851: 1847: 1819: 1817: 1816: 1811: 1803: 1795: 1780: 1778: 1777: 1772: 1758: 1757: 1745: 1744: 1714: 1712: 1705: 1704: 1673: 1669: 1667: 1666: 1661: 1647: 1646: 1628: 1626: 1619: 1618: 1593: 1589: 1587: 1586: 1581: 1573: 1572: 1524:Bayesian Network 1505: 1503: 1502: 1497: 1495: 1493: 1485: 1474: 1461: 1459: 1458: 1453: 1451: 1449: 1435: 1427:/ RIC which use 1422: 1420: 1419: 1414: 1412: 1410: 1399: 1386: 1384: 1383: 1378: 1376: 1374: 1363: 1188:search algorithm 1182:Subset selection 1176:branch and bound 1172:cross-validation 1168:greedy algorithm 1152:ridge regression 1132:cross-validation 1058:encode inherent 1004: 997: 990: 951:Related articles 828:Confusion matrix 581:Isolation forest 526:Graphical models 305: 304: 257:Learning to rank 252:Feature learning 90:Machine learning 81: 80: 74: 67: 63: 60: 54: 49:this article by 40:inline citations 27: 26: 19: 9956: 9955: 9951: 9950: 9949: 9947: 9946: 9945: 9936:Model selection 9926: 9925: 9909:Wayback Machine 9883: 9844: 9823: 9790: 9788:Further reading 9785: 9770: 9766: 9719: 9715: 9710:Wayback Machine 9700: 9696: 9691:Wayback Machine 9681: 9677: 9660: 9656: 9641: 9637: 9627: 9625: 9621: 9615: 9611: 9596: 9574: 9570: 9523: 9519: 9494: 9490: 9451: 9447: 9440: 9418: 9414: 9407: 9385: 9381: 9344: 9340: 9303: 9299: 9275:10.1.1.467.4179 9256: 9252: 9205: 9201: 9192: 9188: 9179: 9175: 9169:Wayback Machine 9159: 9155: 9124: 9120: 9096: 9092: 9069: 9065: 9042: 9038: 9007: 9003: 8972: 8968: 8937: 8933: 8892:(9): e0184203. 8876: 8872: 8858:Wayback Machine 8848: 8841: 8829: 8823: 8819: 8802: 8795: 8780: 8773: 8764: 8757: 8742: 8738: 8723: 8701: 8697: 8689: 8681: 8677: 8628: 8624: 8612: 8606: 8602: 8593: 8586: 8568: 8562: 8558: 8551: 8547: 8493: 8489: 8466: 8455: 8439: 8433: 8429: 8390: 8386: 8379: 8369:Springer-Verlag 8359: 8355: 8346: 8339: 8331:Fienberg, S. E. 8324: 8320: 8308: 8306: 8297: 8296: 8274: 8270: 8257: 8253: 8240: 8236: 8221: 8195: 8191: 8178: 8174: 8151: 8144: 8107: 8103: 8090: 8086: 8059: 8055: 8006:(2): e0117988. 7992: 7988: 7971: 7967: 7956: 7952: 7905: 7901: 7886: 7864: 7860: 7831: 7827: 7804: 7800: 7784: 7778: 7774: 7719: 7715: 7707: 7699: 7692: 7671: 7662: 7607: 7603: 7560: 7556: 7503: 7499: 7484: 7448: 7444: 7429: 7410: 7398: 7394: 7367: 7363: 7328: 7324: 7316: 7314: 7312: 7286: 7282: 7269: 7265: 7224: 7220: 7216: 7203:Model selection 7174: 7111: 7107: 7105: 7102: 7101: 7099: 7080: 7076: 7074: 7071: 7070: 7068: 7062: 6987:Computer vision 6954:EH-DIALL, CLUMP 6898:Hernandez 2007 6571:Segments parole 6451: 6434: 6432:Embedded method 6410: 6389: 6381: 6379:Main principles 6364: 6332: 6289: 6285: 6279: 6275: 6266: 6262: 6247: 6234: 6230: 6224: 6213: 6208: 6201: 6197: 6191: 6187: 6181: 6177: 6171: 6160: 6152: 6150: 6146: 6138: 6134: 6115: 6097: 6095: 6092: 6091: 6085: 6074: 6028: 6024: 6018: 6014: 6013: 6009: 6007: 6004: 6003: 5984: 5980: 5976: 5972: 5970: 5967: 5966: 5925: 5921: 5915: 5911: 5910: 5906: 5889: 5885: 5879: 5875: 5874: 5870: 5853: 5849: 5843: 5839: 5838: 5834: 5812: 5808: 5804: 5800: 5783: 5779: 5775: 5771: 5760: 5756: 5752: 5748: 5747: 5745: 5741: 5733: 5729: 5728: 5710: 5708: 5705: 5704: 5676: 5672: 5670: 5668: 5665: 5664: 5639: 5635: 5633: 5631: 5628: 5627: 5593: 5589: 5587: 5547: 5543: 5541: 5537: 5535: 5524: 5520: 5519: 5502: 5501: 5499: 5496: 5495: 5480: 5450: 5446: 5438: 5435: 5434: 5405: 5401: 5386: 5382: 5372: 5362: 5358: 5353: 5338: 5333: 5316: 5305: 5303: 5302: 5301: 5295: 5291: 5285: 5274: 5256: 5254: 5253: 5252: 5248: 5237: 5230: 5229: 5203: 5199: 5189: 5187: 5184: 5183: 5160: 5156: 5154: 5151: 5150: 5133: 5129: 5121: 5118: 5117: 5113: 5096: 5091: 5090: 5088: 5085: 5084: 5080: 5077:identity matrix 5072: 5055: 5050: 5049: 5047: 5044: 5043: 5026: 5021: 5016: 5009: 5004: 5003: 4993: 4984: 4979: 4978: 4970: 4968: 4965: 4964: 4942: 4928: 4925: 4924: 4902: 4888: 4885: 4884: 4864: 4860: 4851: 4847: 4826: 4822: 4820: 4817: 4816: 4790: 4786: 4771: 4767: 4746: 4735: 4729: 4726: 4725: 4705: 4700: 4695: 4681: 4679: 4678: 4676: 4673: 4672: 4656: 4644: 4639: 4638: 4633: 4618: 4607: 4605: 4604: 4603: 4601: 4598: 4597: 4581: 4578: 4577: 4546: 4544: 4541: 4540: 4515: 4513: 4512: 4500: 4489: 4487: 4486: 4485: 4475: 4457: 4453: 4443: 4441: 4438: 4437: 4408: 4404: 4389: 4385: 4375: 4365: 4361: 4356: 4332: 4328: 4318: 4312: 4308: 4302: 4291: 4275: 4271: 4262: 4258: 4248: 4242: 4238: 4232: 4228: 4222: 4205: 4191: 4184: 4183: 4157: 4153: 4143: 4141: 4138: 4137: 4130: 4108: 4104: 4102: 4099: 4098: 4075: 4071: 4069: 4066: 4065: 4040: 4039: 4033: 4032: 4026: 4025: 4014: 4008: 4004: 3995: 3991: 3973: 3969: 3960: 3956: 3944: 3943: 3925: 3921: 3897: 3893: 3881: 3880: 3866: 3862: 3861: 3848: 3847: 3835: 3831: 3826: 3814: 3810: 3786: 3782: 3759: 3755: 3754: 3743: 3734: 3730: 3714: 3712: 3709: 3708: 3697: 3689: 3685: 3681: 3678: 3674: 3640: 3628: 3624: 3619: 3607: 3603: 3585: 3581: 3576: 3564: 3560: 3539: 3535: 3533: 3530: 3529: 3503: 3499: 3481: 3477: 3475: 3472: 3471: 3445: 3441: 3424: 3411: 3400: 3391: 3386: 3385: 3384: 3380: 3373: 3372: 3352: 3348: 3338: 3336: 3333: 3332: 3326: 3317: 3297: 3293: 3284: 3280: 3272: 3269: 3268: 3244: 3239: 3238: 3236: 3233: 3232: 3197: 3193: 3184: 3180: 3171: 3167: 3143: 3139: 3137: 3134: 3133: 3129: 3112: 3108: 3093: 3089: 3059: 3055: 3031: 3027: 3025: 3022: 3021: 2995: 2991: 2976: 2972: 2966: 2955: 2941: 2926: 2921: 2920: 2912: 2903: 2898: 2897: 2893: 2889: 2882: 2881: 2860: 2858: 2855: 2854: 2843: 2831:parity function 2798: 2794: 2788: 2784: 2778: 2767: 2759: 2752: 2748: 2742: 2738: 2729: 2725: 2719: 2702: 2697: 2695: 2683: 2679: 2673: 2662: 2657: 2650: 2646: 2640: 2636: 2630: 2619: 2614: 2612: 2611: 2607: 2599: 2595: 2576: 2555: 2553: 2550: 2549: 2526: 2522: 2513: 2509: 2491: 2487: 2485: 2482: 2481: 2455: 2451: 2436: 2432: 2430: 2427: 2426: 2422: 2417: 2412: 2407: 2402: 2397: 2393: 2388: 2380: 2375: 2371: 2340: 2336: 2327: 2323: 2303: 2299: 2290: 2286: 2285: 2272: 2267: 2266: 2258: 2257: 2252: 2234: 2230: 2210: 2206: 2205: 2193: 2185: 2184: 2179: 2178: 2174: 2168: 2147: 2145: 2142: 2141: 2115: 2111: 2102: 2098: 2078: 2074: 2065: 2061: 2060: 2047: 2042: 2041: 2033: 2032: 2027: 2010: 2007: 2006: 1999: 1994: 1990: 1985: 1981: 1951: 1947: 1927: 1923: 1922: 1910: 1902: 1901: 1896: 1873: 1870: 1869: 1862: 1858: 1853: 1849: 1845: 1837: 1799: 1791: 1789: 1786: 1785: 1753: 1749: 1722: 1718: 1700: 1696: 1695: 1690: 1688: 1685: 1684: 1671: 1642: 1638: 1614: 1610: 1609: 1604: 1602: 1599: 1598: 1591: 1568: 1564: 1562: 1559: 1558: 1543: 1531:graphical model 1516: 1484: 1473: 1471: 1468: 1467: 1445: 1434: 1432: 1429: 1428: 1406: 1398: 1396: 1393: 1392: 1370: 1362: 1360: 1357: 1356: 1337: 1323: 1184: 1158:In traditional 1097: 1008: 979: 978: 952: 944: 943: 904: 896: 895: 856:Kernel machines 851: 843: 842: 818: 810: 809: 790:Active learning 785: 777: 776: 745: 735: 734: 660:Diffusion model 596: 586: 585: 558: 548: 547: 521: 511: 510: 466:Factor analysis 461: 451: 450: 434: 397: 387: 386: 307: 306: 290: 289: 288: 277: 276: 182: 174: 173: 139:Online learning 104: 92: 75: 64: 58: 55: 45:Please help to 44: 28: 24: 17: 12: 11: 5: 9954: 9944: 9943: 9938: 9924: 9923: 9917: 9912: 9899: 9889: 9882: 9881:External links 9879: 9878: 9877: 9859:(4): 491–502. 9848: 9842: 9827: 9821: 9808: 9789: 9786: 9784: 9783: 9764: 9713: 9701:Zheng et al., 9694: 9675: 9654: 9635: 9609: 9594: 9568: 9517: 9506:(2): 241–260. 9488: 9461:(1): 106–117. 9445: 9438: 9412: 9405: 9379: 9358:(2): 358–362. 9338: 9317:(2): 588–603. 9297: 9250: 9199: 9186: 9173: 9153: 9118: 9107:(1–3): 71–86. 9090: 9063: 9052:(3): 842–858. 9036: 9001: 8982:(4): 247–257. 8966: 8947:(3): 183–196. 8931: 8870: 8839: 8817: 8793: 8771: 8755: 8736: 8721: 8695: 8675: 8638:(1): 185–207. 8622: 8600: 8584: 8556: 8545: 8512:10.1.1.63.5765 8487: 8453: 8427: 8384: 8377: 8353: 8318: 8309:|journal= 8268: 8251: 8234: 8219: 8189: 8172: 8142: 8101: 8084: 8053: 7986: 7965: 7950: 7899: 7884: 7858: 7825: 7808:Neurocomputing 7798: 7772: 7713: 7690: 7660: 7601: 7574:(1): 103–120. 7554: 7497: 7482: 7442: 7427: 7392: 7361: 7342:(2): 233–243. 7322: 7310: 7280: 7263: 7217: 7215: 7212: 7211: 7210: 7205: 7200: 7195: 7190: 7185: 7180: 7173: 7170: 7169: 7168: 7165: 7161: 7155: 7149: 7143: 7138: 7133: 7130: 7114: 7110: 7083: 7079: 7061: 7058: 7055: 7054: 7051: 7048: 7045: 7042: 7039: 7035: 7034: 7031: 7028: 7025: 7022: 7017: 7013: 7012: 7009: 7000: 6997: 6994: 6989: 6983: 6982: 6979: 6976: 6973: 6970: 6968:Welch's t-test 6965: 6959: 6958: 6955: 6952: 6949: 6946: 6943: 6939: 6938: 6935: 6932: 6929: 6927: 6924: 6920: 6919: 6916: 6913: 6910: 6907: 6904: 6900: 6899: 6896: 6893: 6890: 6887: 6884: 6880: 6879: 6876: 6873: 6870: 6867: 6864: 6860: 6859: 6856: 6851: 6848: 6845: 6842: 6838: 6837: 6834: 6831: 6828: 6825: 6820: 6816: 6815: 6812: 6805: 6802: 6799: 6796: 6792: 6791: 6788: 6783: 6780: 6777: 6774: 6770: 6769: 6766: 6763: 6760: 6757: 6751: 6747: 6746: 6743: 6740: 6737: 6734: 6731: 6727: 6726: 6723: 6718: 6709: 6706: 6697: 6693: 6692: 6689: 6686: 6681: 6678: 6669: 6665: 6664: 6661: 6655: 6649: 6646: 6643: 6639: 6638: 6635: 6630: 6627: 6624: 6621: 6617: 6616: 6613: 6607: 6604: 6601: 6598: 6594: 6593: 6590: 6585: 6580: 6577: 6572: 6568: 6567: 6566:Ustunkar 2011 6564: 6561: 6560:Naive bayesian 6558: 6556: 6551: 6547: 6546: 6543: 6540: 6538:Naive Bayesian 6535: 6532: 6527: 6523: 6522: 6519: 6516: 6511: 6508: 6503: 6499: 6498: 6495: 6492: 6490: 6487: 6484: 6478: 6477: 6474: 6469: 6466: 6463: 6460: 6450: 6447: 6433: 6430: 6429: 6428: 6425: 6409: 6408:Wrapper method 6406: 6388: 6385: 6380: 6377: 6363: 6360: 6331: 6328: 6316: 6315: 6304: 6300: 6292: 6288: 6282: 6278: 6272: 6269: 6265: 6261: 6256: 6253: 6250: 6246: 6242: 6237: 6233: 6227: 6222: 6219: 6216: 6212: 6204: 6200: 6194: 6190: 6184: 6180: 6174: 6169: 6166: 6163: 6159: 6155: 6149: 6141: 6137: 6133: 6130: 6127: 6124: 6121: 6118: 6114: 6110: 6106: 6103: 6100: 6083: 6072: 6031: 6027: 6021: 6017: 6012: 5987: 5983: 5979: 5975: 5963: 5962: 5951: 5947: 5941: 5934: 5931: 5928: 5924: 5918: 5914: 5909: 5905: 5902: 5899: 5892: 5888: 5882: 5878: 5873: 5869: 5866: 5863: 5856: 5852: 5846: 5842: 5837: 5833: 5830: 5827: 5824: 5815: 5811: 5807: 5803: 5799: 5796: 5793: 5786: 5782: 5778: 5774: 5770: 5763: 5759: 5755: 5751: 5744: 5736: 5732: 5727: 5723: 5719: 5716: 5713: 5687: 5682: 5679: 5675: 5650: 5645: 5642: 5638: 5624: 5623: 5612: 5604: 5599: 5596: 5592: 5586: 5583: 5580: 5577: 5574: 5571: 5568: 5565: 5558: 5553: 5550: 5546: 5540: 5534: 5527: 5523: 5517: 5514: 5511: 5508: 5505: 5487:consisting of 5479: 5476: 5468:Frobenius norm 5453: 5449: 5445: 5442: 5431: 5430: 5419: 5416: 5413: 5408: 5404: 5400: 5397: 5394: 5389: 5385: 5370: 5365: 5361: 5356: 5352: 5349: 5346: 5341: 5336: 5331: 5325: 5322: 5319: 5312: 5308: 5298: 5294: 5288: 5283: 5280: 5277: 5273: 5269: 5263: 5259: 5251: 5244: 5241: 5233: 5228: 5224: 5218: 5215: 5212: 5209: 5206: 5202: 5198: 5195: 5192: 5163: 5159: 5136: 5132: 5128: 5125: 5099: 5094: 5058: 5053: 5029: 5024: 5019: 5012: 5007: 5000: 4997: 4992: 4987: 4982: 4977: 4973: 4952: 4948: 4945: 4941: 4938: 4935: 4932: 4912: 4908: 4905: 4901: 4898: 4895: 4892: 4872: 4867: 4863: 4859: 4854: 4850: 4846: 4843: 4840: 4835: 4832: 4829: 4825: 4804: 4799: 4796: 4793: 4789: 4785: 4780: 4777: 4774: 4770: 4766: 4763: 4760: 4755: 4752: 4749: 4744: 4741: 4738: 4734: 4708: 4703: 4698: 4694: 4688: 4684: 4659: 4653: 4650: 4647: 4642: 4636: 4632: 4627: 4624: 4621: 4614: 4610: 4585: 4561: 4558: 4555: 4528: 4522: 4518: 4509: 4506: 4503: 4496: 4492: 4484: 4474: 4471: 4468: 4465: 4460: 4456: 4452: 4434: 4433: 4422: 4419: 4416: 4411: 4407: 4403: 4400: 4397: 4392: 4388: 4373: 4368: 4364: 4359: 4355: 4352: 4349: 4346: 4343: 4340: 4335: 4331: 4327: 4315: 4311: 4305: 4300: 4297: 4294: 4290: 4286: 4283: 4278: 4274: 4270: 4265: 4261: 4257: 4245: 4241: 4235: 4231: 4225: 4220: 4217: 4214: 4211: 4208: 4204: 4198: 4195: 4187: 4182: 4178: 4172: 4169: 4166: 4163: 4160: 4156: 4152: 4149: 4146: 4129: 4126: 4111: 4107: 4086: 4083: 4078: 4074: 4054: 4053: 4036: 4029: 4024: 4021: 4017: 4011: 4007: 4003: 3998: 3994: 3990: 3987: 3984: 3981: 3976: 3972: 3968: 3963: 3959: 3955: 3952: 3947: 3942: 3939: 3936: 3933: 3928: 3924: 3920: 3917: 3914: 3911: 3908: 3905: 3900: 3896: 3892: 3889: 3884: 3877: 3874: 3869: 3865: 3860: 3856: 3853: 3851: 3849: 3846: 3843: 3838: 3834: 3829: 3825: 3822: 3817: 3813: 3809: 3806: 3803: 3800: 3797: 3794: 3789: 3785: 3781: 3778: 3775: 3770: 3767: 3762: 3758: 3753: 3749: 3746: 3744: 3742: 3737: 3733: 3729: 3726: 3723: 3720: 3717: 3716: 3696: 3693: 3687: 3676: 3659: 3656: 3653: 3650: 3647: 3643: 3639: 3636: 3631: 3627: 3622: 3618: 3615: 3610: 3606: 3602: 3599: 3596: 3593: 3588: 3584: 3579: 3575: 3572: 3567: 3563: 3559: 3556: 3553: 3550: 3545: 3542: 3538: 3517: 3514: 3511: 3506: 3502: 3498: 3495: 3492: 3487: 3484: 3480: 3468: 3467: 3456: 3453: 3448: 3444: 3440: 3437: 3434: 3431: 3427: 3423: 3408: 3403: 3399: 3394: 3389: 3383: 3376: 3371: 3367: 3361: 3358: 3355: 3351: 3347: 3344: 3341: 3325: 3322: 3305: 3300: 3296: 3292: 3287: 3283: 3279: 3276: 3253: 3250: 3247: 3242: 3218: 3215: 3212: 3209: 3206: 3203: 3200: 3196: 3192: 3187: 3183: 3179: 3174: 3170: 3166: 3163: 3160: 3157: 3152: 3149: 3146: 3142: 3115: 3111: 3107: 3104: 3101: 3096: 3092: 3088: 3085: 3082: 3079: 3076: 3073: 3070: 3067: 3062: 3058: 3054: 3051: 3048: 3045: 3040: 3037: 3034: 3030: 3018: 3017: 3006: 3003: 2998: 2994: 2990: 2987: 2984: 2979: 2975: 2969: 2964: 2961: 2958: 2954: 2938: 2934: 2929: 2924: 2919: 2915: 2911: 2906: 2901: 2896: 2892: 2885: 2880: 2876: 2872: 2869: 2866: 2863: 2842: 2839: 2826: 2825: 2814: 2810: 2801: 2797: 2791: 2787: 2781: 2776: 2773: 2770: 2766: 2762: 2755: 2751: 2745: 2741: 2735: 2732: 2728: 2722: 2717: 2714: 2711: 2708: 2705: 2701: 2694: 2686: 2682: 2676: 2671: 2668: 2665: 2661: 2653: 2649: 2643: 2639: 2633: 2628: 2625: 2622: 2618: 2610: 2602: 2598: 2594: 2591: 2588: 2585: 2582: 2579: 2575: 2571: 2567: 2564: 2561: 2558: 2534: 2529: 2525: 2521: 2516: 2512: 2508: 2505: 2502: 2497: 2494: 2490: 2469: 2466: 2463: 2458: 2454: 2450: 2447: 2444: 2439: 2435: 2420: 2410: 2400: 2391: 2378: 2368: 2367: 2356: 2352: 2348: 2343: 2339: 2335: 2330: 2326: 2322: 2319: 2314: 2311: 2306: 2302: 2298: 2293: 2289: 2284: 2275: 2270: 2265: 2261: 2256: 2251: 2248: 2245: 2242: 2237: 2233: 2229: 2226: 2221: 2218: 2213: 2209: 2204: 2196: 2192: 2188: 2183: 2177: 2171: 2167: 2163: 2159: 2156: 2153: 2150: 2135: 2134: 2123: 2118: 2114: 2110: 2105: 2101: 2097: 2094: 2089: 2086: 2081: 2077: 2073: 2068: 2064: 2059: 2050: 2045: 2040: 2036: 2031: 2026: 2023: 2020: 2017: 2014: 1997: 1988: 1978: 1977: 1965: 1962: 1959: 1954: 1950: 1946: 1943: 1938: 1935: 1930: 1926: 1921: 1913: 1909: 1905: 1900: 1895: 1892: 1889: 1886: 1883: 1880: 1877: 1861:and the class 1856: 1848:for the class 1836: 1833: 1822: 1821: 1809: 1806: 1802: 1798: 1794: 1782: 1770: 1767: 1764: 1761: 1756: 1752: 1748: 1743: 1740: 1737: 1734: 1731: 1728: 1725: 1721: 1717: 1711: 1708: 1703: 1699: 1694: 1681: 1675: 1659: 1656: 1653: 1650: 1645: 1641: 1637: 1634: 1631: 1625: 1622: 1617: 1613: 1608: 1595: 1579: 1576: 1571: 1567: 1553:Calculate the 1542: 1539: 1535:Markov blanket 1515: 1512: 1491: 1488: 1483: 1480: 1477: 1448: 1444: 1441: 1438: 1409: 1405: 1402: 1373: 1369: 1366: 1335: 1322: 1319: 1318: 1317: 1314: 1311: 1310: 1309: 1304: 1301: 1298: 1264: 1263: 1258: 1257:Scatter search 1255: 1250: 1245: 1242: 1236: 1231: 1226: 1221: 1183: 1180: 1156: 1155: 1139: 1106: 1096: 1093: 1066: 1065: 1064: 1063: 1056: 1053: 1046: 1043: 1027:DNA microarray 1010: 1009: 1007: 1006: 999: 992: 984: 981: 980: 977: 976: 971: 970: 969: 959: 953: 950: 949: 946: 945: 942: 941: 936: 931: 926: 921: 916: 911: 905: 902: 901: 898: 897: 894: 893: 888: 883: 878: 876:Occam learning 873: 868: 863: 858: 852: 849: 848: 845: 844: 841: 840: 835: 833:Learning curve 830: 825: 819: 816: 815: 812: 811: 808: 807: 802: 797: 792: 786: 783: 782: 779: 778: 775: 774: 773: 772: 762: 757: 752: 746: 741: 740: 737: 736: 733: 732: 726: 721: 716: 711: 710: 709: 699: 694: 693: 692: 687: 682: 677: 667: 662: 657: 652: 651: 650: 640: 639: 638: 633: 628: 623: 613: 608: 603: 597: 592: 591: 588: 587: 584: 583: 578: 573: 565: 559: 554: 553: 550: 549: 546: 545: 544: 543: 538: 533: 522: 517: 516: 513: 512: 509: 508: 503: 498: 493: 488: 483: 478: 473: 468: 462: 457: 456: 453: 452: 449: 448: 443: 438: 432: 427: 422: 414: 409: 404: 398: 393: 392: 389: 388: 385: 384: 379: 374: 369: 364: 359: 354: 349: 341: 340: 339: 334: 329: 319: 317:Decision trees 314: 308: 294:classification 284: 283: 282: 279: 278: 275: 274: 269: 264: 259: 254: 249: 244: 239: 234: 229: 224: 219: 214: 209: 204: 199: 194: 189: 187:Classification 183: 180: 179: 176: 175: 172: 171: 166: 161: 156: 151: 146: 144:Batch learning 141: 136: 131: 126: 121: 116: 111: 105: 102: 101: 98: 97: 86: 85: 77: 76: 31: 29: 22: 15: 9: 6: 4: 3: 2: 9953: 9942: 9939: 9937: 9934: 9933: 9931: 9921: 9918: 9916: 9913: 9910: 9906: 9903: 9900: 9897: 9893: 9890: 9888: 9885: 9884: 9874: 9870: 9866: 9862: 9858: 9854: 9849: 9845: 9843:0-7923-8198-X 9839: 9835: 9834: 9828: 9824: 9822:0-387-95232-2 9818: 9814: 9809: 9805: 9801: 9797: 9792: 9791: 9780: 9779: 9774: 9768: 9760: 9756: 9751: 9746: 9742: 9738: 9734: 9730: 9729: 9724: 9717: 9711: 9707: 9704: 9698: 9692: 9688: 9685: 9679: 9670: 9665: 9658: 9651: 9650: 9645: 9639: 9620: 9613: 9605: 9601: 9597: 9591: 9587: 9583: 9579: 9572: 9564: 9560: 9555: 9550: 9545: 9540: 9536: 9532: 9528: 9521: 9513: 9509: 9505: 9501: 9500: 9492: 9484: 9480: 9476: 9472: 9468: 9464: 9460: 9456: 9449: 9441: 9435: 9431: 9427: 9423: 9416: 9408: 9402: 9398: 9394: 9390: 9383: 9375: 9371: 9366: 9361: 9357: 9353: 9349: 9342: 9334: 9330: 9325: 9320: 9316: 9312: 9308: 9301: 9293: 9289: 9285: 9281: 9276: 9271: 9267: 9263: 9262: 9254: 9246: 9242: 9237: 9232: 9227: 9222: 9218: 9214: 9210: 9203: 9196: 9190: 9183: 9177: 9170: 9166: 9163: 9157: 9149: 9145: 9141: 9137: 9133: 9129: 9122: 9114: 9110: 9106: 9102: 9094: 9086: 9082: 9078: 9074: 9067: 9059: 9055: 9051: 9047: 9040: 9032: 9028: 9024: 9020: 9016: 9012: 9005: 8997: 8993: 8989: 8985: 8981: 8977: 8970: 8962: 8958: 8954: 8950: 8946: 8942: 8935: 8927: 8923: 8918: 8913: 8908: 8903: 8899: 8895: 8891: 8887: 8886: 8881: 8874: 8867: 8863: 8859: 8855: 8852: 8846: 8844: 8835: 8828: 8821: 8813: 8809: 8808: 8800: 8798: 8791: 8787: 8783: 8778: 8776: 8768: 8762: 8760: 8751: 8747: 8740: 8732: 8728: 8724: 8718: 8714: 8710: 8706: 8699: 8688: 8687: 8679: 8671: 8667: 8663: 8659: 8655: 8651: 8646: 8641: 8637: 8633: 8626: 8618: 8611: 8604: 8597: 8591: 8589: 8580: 8576: 8575: 8567: 8560: 8554: 8549: 8543: 8538: 8534: 8530: 8526: 8522: 8518: 8513: 8508: 8504: 8500: 8499: 8491: 8485: 8481: 8477: 8476: 8471: 8464: 8462: 8460: 8458: 8449: 8445: 8438: 8431: 8423: 8419: 8415: 8411: 8407: 8403: 8399: 8395: 8388: 8380: 8378:9780387953649 8374: 8370: 8366: 8365: 8357: 8345: 8338: 8337: 8332: 8328: 8322: 8314: 8301: 8293: 8289: 8284: 8283:q-bio/0311039 8279: 8272: 8265: 8261: 8255: 8248: 8244: 8238: 8230: 8226: 8222: 8220:9781450383516 8216: 8212: 8208: 8204: 8200: 8193: 8186: 8182: 8176: 8168: 8164: 8160: 8156: 8149: 8147: 8137: 8132: 8128: 8124: 8120: 8116: 8112: 8105: 8097: 8096: 8088: 8080: 8076: 8072: 8068: 8064: 8057: 8049: 8045: 8040: 8035: 8031: 8027: 8022: 8017: 8013: 8009: 8005: 8001: 7997: 7990: 7981: 7976: 7969: 7961: 7954: 7946: 7942: 7937: 7932: 7927: 7922: 7918: 7914: 7910: 7903: 7895: 7891: 7887: 7885:9781605582054 7881: 7877: 7873: 7869: 7862: 7853: 7848: 7844: 7840: 7836: 7829: 7821: 7817: 7813: 7809: 7802: 7794: 7790: 7783: 7776: 7768: 7764: 7759: 7754: 7750: 7746: 7741: 7736: 7732: 7728: 7724: 7717: 7706: 7705: 7697: 7695: 7686: 7682: 7681: 7676: 7669: 7667: 7665: 7656: 7652: 7647: 7642: 7638: 7634: 7630: 7626: 7622: 7618: 7617: 7612: 7605: 7597: 7593: 7589: 7585: 7581: 7577: 7573: 7569: 7565: 7558: 7550: 7546: 7542: 7538: 7534: 7530: 7525: 7520: 7516: 7512: 7508: 7501: 7493: 7489: 7485: 7479: 7475: 7471: 7466: 7461: 7457: 7453: 7446: 7438: 7434: 7430: 7424: 7420: 7416: 7409: 7408: 7403: 7396: 7388: 7384: 7380: 7376: 7372: 7365: 7357: 7353: 7349: 7345: 7341: 7337: 7336:AIChE Journal 7333: 7326: 7313: 7307: 7303: 7299: 7295: 7291: 7284: 7276: 7275: 7267: 7259: 7255: 7251: 7247: 7242: 7237: 7233: 7229: 7222: 7218: 7209: 7206: 7204: 7201: 7199: 7196: 7194: 7191: 7189: 7186: 7184: 7181: 7179: 7176: 7175: 7166: 7162: 7159: 7156: 7153: 7152:Auto-encoding 7150: 7147: 7144: 7142: 7139: 7137: 7136:Decision tree 7134: 7131: 7112: 7108: 7081: 7077: 7067: 7066: 7065: 7052: 7049: 7046: 7043: 7040: 7037: 7036: 7032: 7029: 7026: 7023: 7021: 7018: 7015: 7014: 7010: 7008: 7004: 7001: 6998: 6995: 6993: 6990: 6988: 6985: 6984: 6980: 6977: 6974: 6971: 6969: 6966: 6964: 6961: 6960: 6957:Jourdan 2005 6956: 6953: 6950: 6947: 6944: 6941: 6940: 6936: 6933: 6930: 6928: 6925: 6922: 6921: 6917: 6914: 6911: 6908: 6905: 6902: 6901: 6897: 6894: 6891: 6888: 6885: 6882: 6881: 6877: 6874: 6871: 6868: 6865: 6862: 6861: 6857: 6855: 6852: 6849: 6846: 6843: 6840: 6839: 6835: 6832: 6829: 6826: 6824: 6821: 6818: 6817: 6813: 6810: 6806: 6803: 6800: 6797: 6794: 6793: 6789: 6787: 6784: 6781: 6778: 6775: 6772: 6771: 6767: 6764: 6761: 6758: 6756: 6752: 6749: 6748: 6744: 6741: 6738: 6735: 6732: 6729: 6728: 6724: 6722: 6719: 6717: 6713: 6710: 6707: 6705: 6701: 6698: 6695: 6694: 6690: 6688:weighted cost 6687: 6685: 6684:Decision tree 6682: 6679: 6677: 6673: 6670: 6667: 6666: 6662: 6660:of prediction 6659: 6656: 6654: 6650: 6647: 6644: 6642:Spectral Mass 6641: 6640: 6636: 6634: 6631: 6628: 6625: 6622: 6619: 6618: 6614: 6611: 6608: 6605: 6602: 6599: 6596: 6595: 6592:Al-ani 2005 6591: 6589: 6586: 6584: 6581: 6578: 6576: 6573: 6570: 6569: 6565: 6562: 6559: 6557: 6555: 6552: 6549: 6548: 6544: 6541: 6539: 6536: 6533: 6531: 6530:Hill climbing 6528: 6525: 6524: 6520: 6517: 6515: 6514:Decision Tree 6512: 6509: 6507: 6504: 6501: 6500: 6496: 6493: 6491: 6488: 6485: 6483: 6480: 6479: 6475: 6473: 6470: 6467: 6464: 6461: 6458: 6457: 6454: 6446: 6438: 6426: 6423: 6422: 6421: 6414: 6405: 6401: 6393: 6387:Filter method 6384: 6376: 6373: 6369: 6368:metaheuristic 6359: 6357: 6356:normalization 6353: 6349: 6344: 6341: 6337: 6336:decision tree 6327: 6325: 6321: 6302: 6298: 6290: 6286: 6280: 6276: 6270: 6267: 6263: 6259: 6254: 6251: 6248: 6244: 6240: 6235: 6231: 6225: 6220: 6217: 6214: 6210: 6202: 6192: 6188: 6182: 6178: 6172: 6167: 6164: 6161: 6157: 6147: 6139: 6131: 6128: 6125: 6119: 6116: 6108: 6090: 6089: 6088: 6086: 6079: 6075: 6067: 6065: 6061: 6057: 6053: 6049: 6029: 6025: 6019: 6015: 6010: 5985: 5981: 5977: 5973: 5949: 5945: 5932: 5929: 5926: 5922: 5916: 5912: 5907: 5903: 5900: 5897: 5890: 5886: 5880: 5876: 5871: 5867: 5864: 5861: 5854: 5850: 5844: 5840: 5835: 5828: 5825: 5822: 5813: 5809: 5805: 5801: 5797: 5794: 5791: 5784: 5780: 5776: 5772: 5768: 5761: 5757: 5753: 5749: 5742: 5734: 5730: 5721: 5703: 5702: 5701: 5680: 5677: 5673: 5643: 5640: 5636: 5610: 5597: 5594: 5590: 5581: 5578: 5575: 5569: 5566: 5563: 5551: 5548: 5544: 5538: 5532: 5525: 5521: 5494: 5493: 5492: 5490: 5486: 5475: 5473: 5469: 5451: 5443: 5417: 5414: 5411: 5406: 5402: 5398: 5395: 5392: 5387: 5383: 5368: 5363: 5347: 5344: 5339: 5334: 5320: 5296: 5292: 5286: 5281: 5278: 5275: 5271: 5267: 5242: 5239: 5222: 5182: 5181: 5180: 5177: 5161: 5157: 5134: 5126: 5097: 5078: 5075:-dimensional 5056: 5027: 5022: 5010: 4998: 4995: 4990: 4985: 4975: 4946: 4943: 4939: 4936: 4930: 4906: 4903: 4899: 4896: 4890: 4865: 4861: 4857: 4852: 4848: 4841: 4838: 4833: 4830: 4827: 4823: 4797: 4794: 4791: 4787: 4783: 4778: 4775: 4772: 4768: 4761: 4758: 4750: 4742: 4739: 4736: 4732: 4723: 4722:Gram matrices 4692: 4648: 4630: 4622: 4583: 4575: 4556: 4504: 4472: 4466: 4463: 4458: 4454: 4420: 4417: 4414: 4409: 4405: 4401: 4398: 4395: 4390: 4386: 4371: 4366: 4350: 4347: 4341: 4338: 4333: 4329: 4313: 4309: 4303: 4298: 4295: 4292: 4288: 4284: 4276: 4272: 4268: 4263: 4259: 4243: 4239: 4233: 4229: 4223: 4218: 4215: 4212: 4209: 4206: 4202: 4196: 4193: 4176: 4136: 4135: 4134: 4125: 4109: 4105: 4084: 4081: 4076: 4072: 4063: 4059: 4019: 4009: 4005: 4001: 3996: 3992: 3985: 3982: 3974: 3970: 3966: 3961: 3957: 3950: 3940: 3934: 3931: 3926: 3922: 3915: 3912: 3906: 3903: 3898: 3894: 3887: 3875: 3872: 3867: 3863: 3858: 3854: 3852: 3836: 3832: 3823: 3820: 3815: 3811: 3804: 3801: 3795: 3792: 3787: 3783: 3776: 3768: 3765: 3760: 3756: 3751: 3747: 3745: 3735: 3731: 3724: 3721: 3718: 3707: 3706: 3705: 3702: 3692: 3671: 3657: 3654: 3651: 3648: 3645: 3641: 3629: 3625: 3616: 3613: 3608: 3604: 3597: 3594: 3586: 3582: 3573: 3570: 3565: 3561: 3554: 3548: 3543: 3540: 3536: 3512: 3509: 3504: 3500: 3493: 3490: 3485: 3482: 3478: 3454: 3451: 3446: 3442: 3438: 3435: 3432: 3406: 3397: 3392: 3381: 3365: 3331: 3330: 3329: 3321: 3298: 3294: 3290: 3285: 3281: 3274: 3251: 3248: 3245: 3216: 3213: 3210: 3207: 3204: 3201: 3198: 3185: 3181: 3177: 3172: 3168: 3161: 3155: 3150: 3147: 3144: 3140: 3113: 3102: 3099: 3094: 3090: 3083: 3080: 3077: 3074: 3068: 3065: 3060: 3056: 3049: 3043: 3038: 3035: 3032: 3028: 3004: 3001: 2996: 2992: 2988: 2985: 2982: 2977: 2973: 2967: 2962: 2959: 2956: 2952: 2936: 2932: 2927: 2917: 2909: 2904: 2894: 2890: 2874: 2853: 2852: 2851: 2849: 2838: 2835: 2832: 2812: 2808: 2799: 2789: 2785: 2779: 2774: 2771: 2768: 2764: 2753: 2749: 2743: 2739: 2733: 2730: 2726: 2720: 2715: 2712: 2709: 2706: 2703: 2699: 2692: 2684: 2680: 2674: 2669: 2666: 2663: 2659: 2651: 2647: 2641: 2637: 2631: 2626: 2623: 2620: 2616: 2608: 2600: 2592: 2589: 2586: 2580: 2577: 2569: 2548: 2547: 2546: 2527: 2523: 2519: 2514: 2510: 2503: 2500: 2495: 2492: 2488: 2464: 2461: 2456: 2452: 2445: 2442: 2437: 2433: 2423: 2413: 2403: 2394: 2386: 2381: 2354: 2350: 2341: 2337: 2333: 2328: 2324: 2317: 2312: 2309: 2304: 2300: 2296: 2291: 2287: 2282: 2273: 2263: 2254: 2249: 2243: 2240: 2235: 2231: 2224: 2219: 2216: 2211: 2207: 2202: 2190: 2181: 2175: 2169: 2161: 2140: 2139: 2138: 2116: 2112: 2108: 2103: 2099: 2092: 2087: 2084: 2079: 2075: 2071: 2066: 2062: 2057: 2048: 2038: 2029: 2024: 2018: 2012: 2005: 2004: 2003: 2000: 1991: 1960: 1957: 1952: 1948: 1941: 1936: 1933: 1928: 1924: 1919: 1907: 1898: 1893: 1887: 1884: 1881: 1875: 1868: 1867: 1866: 1859: 1842: 1832: 1829: 1827: 1807: 1804: 1796: 1783: 1762: 1759: 1754: 1750: 1741: 1738: 1735: 1732: 1729: 1726: 1723: 1719: 1709: 1706: 1701: 1697: 1692: 1682: 1680: 1676: 1651: 1648: 1643: 1639: 1632: 1623: 1620: 1615: 1611: 1606: 1596: 1577: 1574: 1569: 1565: 1556: 1552: 1551: 1550: 1548: 1538: 1536: 1532: 1529: 1525: 1521: 1511: 1509: 1489: 1486: 1481: 1478: 1475: 1465: 1446: 1442: 1439: 1436: 1426: 1407: 1403: 1400: 1390: 1371: 1367: 1364: 1354: 1349: 1347: 1343: 1339: 1338: 1329: 1315: 1312: 1308: 1305: 1302: 1299: 1296: 1295: 1293: 1292: 1291: 1288: 1286: 1281: 1277: 1273: 1269: 1262: 1259: 1256: 1254: 1251: 1249: 1246: 1243: 1240: 1237: 1235: 1232: 1230: 1227: 1225: 1222: 1219: 1218: 1217: 1214: 1212: 1207: 1204: 1200: 1199:hill climbing 1197: 1192: 1189: 1179: 1177: 1173: 1169: 1165: 1161: 1153: 1149: 1144: 1140: 1137: 1133: 1128: 1124: 1120: 1116: 1112: 1107: 1103: 1102: 1101: 1092: 1089: 1085: 1083: 1079: 1075: 1071: 1061: 1057: 1054: 1051: 1048:to avoid the 1047: 1044: 1041: 1040: 1039: 1038: 1037: 1034: 1032: 1028: 1024: 1020: 1016: 1005: 1000: 998: 993: 991: 986: 985: 983: 982: 975: 972: 968: 965: 964: 963: 960: 958: 955: 954: 948: 947: 940: 937: 935: 932: 930: 927: 925: 922: 920: 917: 915: 912: 910: 907: 906: 900: 899: 892: 889: 887: 884: 882: 879: 877: 874: 872: 869: 867: 864: 862: 859: 857: 854: 853: 847: 846: 839: 836: 834: 831: 829: 826: 824: 821: 820: 814: 813: 806: 803: 801: 798: 796: 795:Crowdsourcing 793: 791: 788: 787: 781: 780: 771: 768: 767: 766: 763: 761: 758: 756: 753: 751: 748: 747: 744: 739: 738: 730: 727: 725: 724:Memtransistor 722: 720: 717: 715: 712: 708: 705: 704: 703: 700: 698: 695: 691: 688: 686: 683: 681: 678: 676: 673: 672: 671: 668: 666: 663: 661: 658: 656: 653: 649: 646: 645: 644: 641: 637: 634: 632: 629: 627: 624: 622: 619: 618: 617: 614: 612: 609: 607: 606:Deep learning 604: 602: 599: 598: 595: 590: 589: 582: 579: 577: 574: 572: 570: 566: 564: 561: 560: 557: 552: 551: 542: 541:Hidden Markov 539: 537: 534: 532: 529: 528: 527: 524: 523: 520: 515: 514: 507: 504: 502: 499: 497: 494: 492: 489: 487: 484: 482: 479: 477: 474: 472: 469: 467: 464: 463: 460: 455: 454: 447: 444: 442: 439: 437: 433: 431: 428: 426: 423: 421: 419: 415: 413: 410: 408: 405: 403: 400: 399: 396: 391: 390: 383: 380: 378: 375: 373: 370: 368: 365: 363: 360: 358: 355: 353: 350: 348: 346: 342: 338: 337:Random forest 335: 333: 330: 328: 325: 324: 323: 320: 318: 315: 313: 310: 309: 302: 301: 296: 295: 287: 281: 280: 273: 270: 268: 265: 263: 260: 258: 255: 253: 250: 248: 245: 243: 240: 238: 235: 233: 230: 228: 225: 223: 222:Data cleaning 220: 218: 215: 213: 210: 208: 205: 203: 200: 198: 195: 193: 190: 188: 185: 184: 178: 177: 170: 167: 165: 162: 160: 157: 155: 152: 150: 147: 145: 142: 140: 137: 135: 134:Meta-learning 132: 130: 127: 125: 122: 120: 117: 115: 112: 110: 107: 106: 100: 99: 96: 91: 88: 87: 83: 82: 73: 70: 62: 52: 48: 42: 41: 35: 30: 21: 20: 9856: 9852: 9836:. Springer. 9832: 9815:. Springer. 9812: 9806:: 1157–1182. 9803: 9799: 9776: 9767: 9732: 9726: 9716: 9697: 9682:Liu et al., 9678: 9657: 9647: 9638: 9626:. Retrieved 9612: 9577: 9571: 9534: 9530: 9520: 9503: 9497: 9491: 9458: 9454: 9448: 9421: 9415: 9388: 9382: 9355: 9352:FEBS Letters 9351: 9341: 9314: 9310: 9300: 9265: 9259: 9253: 9216: 9212: 9202: 9189: 9176: 9156: 9131: 9127: 9121: 9104: 9100: 9093: 9076: 9072: 9066: 9049: 9045: 9039: 9014: 9010: 9004: 8979: 8975: 8969: 8944: 8940: 8934: 8889: 8883: 8873: 8833: 8820: 8806: 8749: 8739: 8704: 8698: 8685: 8678: 8635: 8631: 8625: 8616: 8603: 8581:: 1491–1516. 8578: 8572: 8559: 8548: 8502: 8496: 8490: 8479: 8473: 8447: 8443: 8430: 8397: 8393: 8387: 8363: 8356: 8335: 8321: 8300:cite journal 8271: 8263: 8254: 8246: 8237: 8202: 8192: 8184: 8175: 8158: 8154: 8136:10533/196878 8118: 8114: 8104: 8094: 8087: 8070: 8066: 8056: 8003: 7999: 7989: 7968: 7959: 7953: 7916: 7913:BMC Genomics 7912: 7902: 7867: 7861: 7842: 7838: 7828: 7814:(4): 32–42. 7811: 7807: 7801: 7795:: 1289–1305. 7792: 7788: 7775: 7730: 7726: 7716: 7703: 7684: 7678: 7620: 7614: 7604: 7571: 7567: 7557: 7514: 7510: 7500: 7455: 7445: 7406: 7395: 7381:(92): 1–51. 7378: 7374: 7364: 7339: 7335: 7325: 7315:, retrieved 7293: 7283: 7273: 7266: 7231: 7227: 7221: 7063: 7027:Independent 7016:Microarrays 6999:Independent 6918:Huerta 2006 6725:Chuang 2009 6497:Phuong 2005 6452: 6443: 6419: 6402: 6398: 6382: 6365: 6345: 6333: 6317: 6081: 6080:for feature 6070: 6068: 6052:Spearman's ρ 5964: 5625: 5488: 5484: 5481: 5432: 5178: 4572:denotes the 4435: 4131: 4055: 3698: 3672: 3469: 3327: 3019: 2844: 2836: 2827: 2418: 2408: 2398: 2389: 2387:for feature 2376: 2369: 2136: 1995: 1986: 1979: 1865:as follows: 1854: 1840: 1838: 1830: 1823: 1544: 1517: 1508:entropy rate 1506:. A maximum 1350: 1333: 1324: 1289: 1265: 1215: 1208: 1193: 1185: 1157: 1098: 1095:Introduction 1086: 1081: 1077: 1073: 1069: 1067: 1035: 1014: 1013: 881:PAC learning 568: 417: 412:Hierarchical 344: 298: 292: 65: 56: 37: 9628:12 November 9624:. NFmcp2016 9079:(1): 4–15. 8788:package on 8073:: 162–169. 7733:: 189–203. 7517:: 407–474. 7183:Data mining 7011:Roffo 2015 6981:Zhang 2015 6768:Duval 2009 6700:Tabu search 6691:Zhang 2014 6615:Meiri 2006 6459:Application 1268:correlation 765:Multi-agent 702:Transformer 601:Autoencoder 357:Naive Bayes 95:data mining 51:introducing 9930:Categories 9894:(see also 9781:, 157: 1-9 9219:(1): 148. 8836:: 856–863. 8619:: 687–693. 8450:: 171–234. 8327:Akaike, H. 7980:2004.06152 7740:1711.08421 7524:1804.10306 7317:2021-07-13 7241:2007.10729 7234:: 102795. 7214:References 7158:Submodular 6942:Microarray 6937:Muni 2006 6923:Microarray 6903:Microarray 6883:Microarray 6878:Peng 2003 6863:Microarray 6858:Xuan 2011 6841:Microarray 6819:Microarray 6795:Microarray 6790:Hans 2007 6782:Regression 6773:Microarray 6750:Microarray 6745:Alba 2007 6730:Microarray 6696:Microarray 6672:Binary PSO 6629:Regression 6606:Regression 6575:Ant colony 6545:Long 2007 6521:Shah 2004 6476:Reference 6468:Classifier 6338:or a tree 5491:features: 2396:, so that 1425:Bonferroni 1332:Mallows's 1330:(AIC) and 1224:Best first 1220:Exhaustive 1082:irrelevant 1074:irrelevant 1060:symmetries 1023:Stylometry 750:Q-learning 648:Restricted 446:Mean shift 395:Clustering 372:Perceptron 300:regression 202:Clustering 197:Regression 34:references 9669:1102.3975 9270:CiteSeerX 8645:1202.0515 8537:206764015 8507:CiteSeerX 8229:235770316 8161:: 22–31. 8030:1932-6203 7623:: 10312. 7588:1573-7683 7541:1432-0940 7465:1201.2395 7387:1533-7928 7356:1547-5905 7258:220665533 6620:Economics 6597:Marketing 6462:Algorithm 6252:≠ 6245:∑ 6211:∑ 6158:∑ 6120:∈ 5930:− 5901:⋯ 5865:⋯ 5795:⋯ 5686:¯ 5649:¯ 5603:¯ 5579:− 5557:¯ 5448:‖ 5444:⋅ 5441:‖ 5412:≥ 5396:… 5360:‖ 5351:‖ 5348:λ 5311:¯ 5272:∑ 5268:− 5262:¯ 5158:ℓ 5131:‖ 5127:⋅ 5124:‖ 4991:− 4972:Γ 4707:Γ 4697:Γ 4687:¯ 4658:Γ 4635:Γ 4613:¯ 4584:λ 4557:⋅ 4521:¯ 4495:¯ 4415:≥ 4399:… 4363:‖ 4354:‖ 4351:λ 4289:∑ 4285:− 4203:∑ 4082:∈ 3983:− 3941:− 3873:∈ 3859:∑ 3766:∈ 3752:∑ 3655:≠ 3452:≥ 3430:‖ 3422:‖ 3249:× 3214:… 3148:× 3078:… 3036:× 3002:≥ 2953:∑ 2918:− 2895:α 2765:∑ 2700:∑ 2693:− 2660:∑ 2617:∑ 2581:∈ 2310:∈ 2283:∑ 2250:− 2217:∈ 2203:∑ 2085:∈ 2058:∑ 1934:∈ 1920:∑ 1707:∈ 1621:∈ 1575:∈ 1482:⁡ 1443:⁡ 1404:⁡ 1368:⁡ 1078:Redundant 1070:redundant 909:ECML PKDD 891:VC theory 838:ROC curve 770:Self-play 690:DeepDream 531:Bayes net 322:Ensembles 103:Paradigms 59:July 2010 9905:Archived 9759:20634556 9706:Archived 9687:Archived 9563:26082713 9475:16468570 9374:14644442 9333:21491369 9292:15521491 9245:15958165 9165:Archived 9148:20047491 8996:21749471 8961:15302085 8926:28934234 8885:PLOS ONE 8866:16447987 8854:Archived 8662:24102126 8529:16119262 8482:: 27–66. 8422:49555941 8414:29969403 8344:archived 8333:(eds.), 8048:25719748 8000:PLOS ONE 7945:23369194 7767:30031057 7655:25988841 7549:13745401 7172:See also 6889:Embedded 6836:Oh 2004 6759:Embedded 6676:Mutation 6465:Approach 6354:such as 6348:outliers 6340:ensemble 5330:‖ 5250:‖ 4947:′ 4907:′ 4060:and the 1528:directed 1019:features 332:Boosting 181:Problems 9873:1607600 9750:3445441 9604:3223980 9554:4451357 9483:2073035 9236:1181625 9031:8075318 8917:5608217 8894:Bibcode 8731:8398495 8670:2742785 8542:Program 8288:Bibcode 8098:. AAAI. 8039:4342225 8008:Bibcode 7936:3549810 7758:6299836 7710:. ICML. 7646:4437376 7625:Bibcode 7596:8501814 7492:8849753 7437:8368258 7127:⁠ 7100:⁠ 7096:⁠ 7069:⁠ 7044:Filter 7024:Filter 7007:ROC AUC 6996:Filter 6948:Wrapper 6869:Wrapper 6847:Wrapper 6827:Wrapper 6801:Wrapper 6779:Wrapper 6736:Wrapper 6708:Wrapper 6680:Wrapper 6648:Wrapper 6626:Wrapper 6603:Wrapper 6579:Wrapper 6510:Wrapper 6372:NP-hard 6058:(MDL), 5466:is the 5149:is the 5112:is the 5071:is the 1307:Entropy 1276:metrics 914:NeurIPS 731:(ECRAM) 685:AlexNet 327:Bagging 47:improve 9871: 9840: 9819: 9757: 9747: 9602: 9592: 9561: 9551: 9537:: 66. 9481: 9473: 9436: 9403: 9372: 9331: 9290: 9272: 9243: 9233: 9146: 9029: 8994: 8959: 8924: 8914: 8864: 8729: 8719: 8668: 8660: 8535: 8527: 8509: 8420: 8412: 8375: 8227: 8217: 8046: 8036: 8028: 7943: 7933: 7894:609778 7892: 7882: 7765: 7755: 7653: 7643: 7594: 7586: 7547: 7539: 7490: 7480: 7435: 7425: 7385: 7354: 7308: 7256: 7148:(RMNL) 6972:Filter 6909:Hybrid 6489:Filter 6064:relief 6062:, and 5626:Here, 5433:where 5380: 4436:where 4383: 3470:where 3419: 3020:where 2949: 1841:et al. 1693:argmax 1607:argmax 1239:Greedy 1203:metric 1196:greedy 1113:, the 707:Vision 563:RANSAC 441:OPTICS 436:DBSCAN 420:-means 227:AutoML 36:, but 9920:FEAST 9869:S2CID 9664:arXiv 9622:(PDF) 9600:S2CID 9479:S2CID 9027:S2CID 8830:(PDF) 8727:S2CID 8690:(PDF) 8666:S2CID 8640:arXiv 8613:(PDF) 8569:(PDF) 8533:S2CID 8440:(PDF) 8418:S2CID 8347:(PDF) 8340:(PDF) 8278:arXiv 8245:. 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