Nonmetric, multidimensional scaling NMDS

In this chapter, we would like to demonstrate that one of the very old MVA tools, nonmetric multidimensional scaling (nMDS) [3], can work well as an unsupervised truly data-driven method for data reduction. We first explain an efficient maximally nonmetric algorithm [4] and then demonstrate its superiority to linear MVA methods. We also demonstrate that the subsequent application of linear MVA after data reduction by nMDS can often be a powerful data mining technique. 

There have been attempts to deal with the issue of nonlinearity in data sets. Detrended principal components (DPC) use a polynomial expression to remove the nonlinear relationships from the PCA axes. DPC are useful for data sets of moderate nonlinearity. Detrended correspondence analysis uses a more complex algorithm to eliminate the nonlinearity but requires a more complex computation. Nonmetric multidimensional scaling (NMDS) is a robust method that deals with nonlinearities by using ranks. 

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