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Multidimensional Scaling (MDS) is one of the first fundamental manifoldlearning methods. It can be categorized into several methods, i.e., classicalMDS, kernel classical MDS, metric MDS, and non-metric MDS. Sammon mapping andIsomap can be considered as special cases of metric MDS and kernel classicalMDS, respectively. In this tutorial and survey paper, we review the theory ofMDS, Sammon mapping, and Isomap in detail. We explain all the mentionedcategories of MDS. Then, Sammon mapping, Isomap, and kernel Isomap areexplained. Out-of-sample embedding for MDS and Isomap using eigenfunctions andkernel mapping are introduced. Then, Nystrom approximation and its use inlandmark MDS and landmark Isomap are introduced for big data embedding. We alsoprovide some simulations for illustrating the embedding by these methods.

Multidimensional Scaling, Sammon Mapping, and Isomap: Tutorial and Survey