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The Sammon mapping has been one of the most successful nonlinear metric multidimensional scaling methods since its advent in 1969, but effort has been focused on algorithm improvement rather than on the form of the stress function.
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Lerner, B; Hugo
Guterman, Mayer Aladjem, Itshak Dinsteint, Yitzhak Romem (1998). "On pattern classification with Sammon's nonlinear mapping an experimental study".
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It is considered a non-linear approach as the mapping cannot be represented as a linear combination of the original variables as possible in techniques such as
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The number of iterations needs to be experimentally determined and convergent solutions are not always guaranteed.
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Lerner, B; H. Guterman, M. Aladjem and I. Dinstein (2000). "On the
Initialisation of Sammon's Nonlinear Mapping".
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J. Sun, M. Crowe, C. Fyfe (May 2011). "Extending metric multidimensional scaling with
Bregman divergences".
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The performance of the Sammon mapping has been improved by extending its stress function using left
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Many implementations prefer to use the first
Principal Components as a starting configuration.
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Sammon's mapping aims to minimize the following error function, which is often referred to as
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J. Sun, C. Fyfe, M. Crowe (2011). "Extending Sammon mapping with
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378:"Underrated But Fascinating ML Concepts #5 – CST, PBWM, SARSA, & Sammon Mapping"
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a high-dimensional space to a space of lower dimensionality (see
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