Cartographie de Sammon

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Sammon mapping

Sammon mapping or Sammon projection is an algorithm that maps a high-dimensional space to a space of lower dimensionality (see multidimensional scaling) by trying to preserve the structure of inter-point distances in high-dimensional space in the lower-dimension projection. It is particularly suited for use in exploratory data analysis. The method was proposed by John W. Sammon in 1969.[1] 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 principal component analysis, which also makes it more difficult to use for classification applications.[2]

Denote the distance between ith and jth objects in the original space by {\displaystyle \scriptstyle d_{ij}^{*}}\scriptstyle d^{*}_{ij}, and the distance between their projections by {\displaystyle \scriptstyle d_{ij}^{}}\scriptstyle d^{}_{ij}. Sammon's mapping aims to minimize the following error function, which is often referred to as Sammon's stress or Sammon's error:

Source : Wikipedia Machine Learning