Visualization of High-dimensional Sensor Data and Analysis of their Class Structure Using Nonlinear Map

Abstract

An algorithm that constructs a nonlinear map from a high-dimensional feature space into a low-dimensional space was developed to enable analysis of the structure of data with high-dimensional characteristic features and their class information obtained using various sensors and analyzers. First, a nonlinear map is defined by summing nonlinear basis functions, and their optimal combination is derived using a genetic algorithm to avoid the “curse of dimensionality.” Next, the coefficients of the basis functions are derived using the Nelder-Mead method to flexibly cope with the various demands for the map that cannot always be expressed using statistics of the characteristic features. As a result, nine-dimensional sake data can be mapped into a two-dimensional space so as not only to discriminate the classes but also to preserve the order of distances between classes as much as possible.