35:
or other multivariate statistical techniques. Data can be binary, ordinal, or continuous variables. It works by normalizing the differences between each pair of variables and then computing a weighted average of these differences. The distance was defined in 1971 by Gower and it takes values between
256:
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488:
580:
127:
397:
344:
291:
610:
515:
771:
751:
535:
364:
311:
122:
102:
82:
62:
622:
619:
and later Podani suggested extensions where the ordering of an ordinal feature is used. For example, Podani obtains relative rank differences as
615:
In its original exposition, the distance does not treat ordinal variables in a special manner. In the 1990s, first
Kaufman and
402:
932:
907:
957:
1014:
822:
786:
1019:
816:
540:
973:
Podani, János (May 1999). "Extending Gower's general coefficient of similarity to ordinal characters".
612:
between two objects is the weighted average of the similarities calculated for all their descriptors.
806:
782:
31:
that can handle different types of data within the same dataset and is particularly useful in
369:
316:
263:
585:
493:
8:
990:
874:
756:
736:
520:
349:
296:
251:{\displaystyle S_{ij}={\frac {\sum _{k=1}^{p}w_{ijk}s_{ijk}}{\sum _{k=1}^{p}w_{ijk}}},}
107:
87:
67:
47:
28:
953:
928:
903:
982:
866:
32:
616:
1008:
726:{\displaystyle s_{ijk}=1-{\frac {|r_{i}-r_{j}|}{\max {\{r\}}-\min {\{r\}}}}}
994:
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854:
20:
399:
are 0 or 1, with 1 denoting equality. If the variable is continuous,
986:
870:
832:
366:-th variable. If the variable is binary or ordinal, the values of
927:(Third English ed.). Amsterdam: Elsevier. pp. 278–280.
855:"A general coefficient of similarity and some of its properties"
753:
being the ranks corresponding to the ordered categories of the
781:
Many programming languages and statistical packages, such as
950:
Finding groups in data: an introduction to cluster analysis
346:
is the similarity between the two objects regarding their
36:
0 and 1 with smaller values indicating higher similarity.
900:
Modern multidimensional scaling: theory and applications
483:{\displaystyle s_{ijk}=1-{\frac {|x_{i}-x_{j}|}{R_{k}}}}
902:(2 ed.). New York : Springer. pp. 124–125.
789:, etc., include implementations of Gower's distance.
759:
739:
625:
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543:
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529:
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285:
250:
116:
96:
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1006:
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922:
706:
689:
948:Kaufman, Leonard; Rousseeuw, Peter J. (1990).
898:Borg, Ingwer; Groenen, Patrick J. F. (2005).
716:
710:
699:
693:
897:
776:
923:Legendre, Pierre; Legendre, Louis (2012).
293:are non-negative weights usually set to
1007:
972:
582:. As a result, the overall similarity
852:
27:between two mixed-type objects is a
952:. New York: Wiley. pp. 35–36.
575:{\displaystyle 0\leq s_{ijk}\leq 1}
13:
14:
1031:
537:-th variable and thus ensuring
966:
941:
916:
891:
846:
683:
655:
463:
435:
16:Distance measure in statistics
1:
839:
39:
104:descriptors, the similarity
7:
10:
1036:
812:StatMatch::gower.dist(X)
777:Software implementations
392:{\displaystyle s_{ijk}}
339:{\displaystyle s_{ijk}}
286:{\displaystyle w_{ijk}}
853:Gower, John C (1971).
767:
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727:
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605:{\displaystyle S_{ij}}
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484:
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360:
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828:gower.gower_matrix(X)
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510:{\displaystyle R_{k}}
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119:
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1015:Statistical distance
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1020:Similarity measures
517:being the range of
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29:similarity measure
934:978-0-444-53868-0
925:Numerical ecology
837:
836:
766:{\displaystyle k}
746:{\displaystyle r}
721:
530:{\displaystyle k}
478:
359:{\displaystyle k}
306:{\displaystyle 1}
243:
117:{\displaystyle S}
97:{\displaystyle p}
77:{\displaystyle j}
57:{\displaystyle i}
1027:
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1009:Categories
884:2024-06-03
859:Biometrics
840:References
260:where the
40:Definition
21:statistics
704:−
670:−
649:−
617:Rousseeuw
567:≤
548:≤
450:−
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207:∑
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879:2528823
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823:Python
787:Python
991:JSTOR
975:Taxon
875:JSTOR
801:Ref.
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490:with
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313:and
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