Nonlinear Dimensionality Reduction and Data Visualization:A Review

Dimensionality reduction and data visualization are useful and important processes in pattern recognition.Many techniques have been developed in the recent years.The self-organizing map (SOM) can be an efficient method for this purpose.This paper reviews recent advances in this area and related approaches such as multidimensional scaling (MDS),nonlinear PCA,principal manifolds,as well as the connections of the SOM and its recent variant,the visualization induced SOM (ViSOM),with these approaches. The SOM is shown to produce a quantized,qualitative scaling and while the ViSOM a quantitative or metric scaling and approximates principal curve/surface.The SOM can also be regarded as a generalized MDS to relate two metric spaces by forming a topological mapping between them.The relationships among various recently proposed techniques such as ViSOM,Isomap,LLE,and eigenmap are discussed and compared.