Nonlinear Dimension Reduction and Visualization of Labeled Data

Abstract

The amount of electronic information as well as the size and dimensionality of data sets have increased tremendously. Consequently, dimension reduction and visualization techniques have become increasingly popular in recent years. Dimension reduction is typically connected with loss of information. In supervised classification problems, class labels can be used to minimize the loss of information concerning the specific task. The aim is to preserve and potentially enhance the discrimination of classes in lower dimensions. Here we propose a prototype-based local relevance learning scheme, that results in an efficient nonlinear discriminative dimension reduction of labeled data sets. The method is introduced and discussed in terms of artificial and real world data sets.