Multigroup discrimination based on weighted local projections

TL;DR

This paper introduces a new supervised classification method for high-dimensional data using local projections based on class membership, combined with a visualization technique, implemented in the R package lop.

Contribution

It presents a novel local projection-based classification approach for high-dimensional data and a visualization method for group connectivity, with implementation in R.

Findings

Effective classification in high-dimensional settings

Improved visualization of group connectivity

Validated on three real-world datasets

Abstract

A novel approach for supervised classification analysis for high dimensional and flat data (more variables than observations) is proposed. We use the information of class-membership of observations to determine groups of observations locally describing the group structure. By projecting the data on the subspace spanned by those groups, local projections are defined based on the projection concepts from Ortner et al. (2017a) and Ortner et al. (2017b). For each local projection a local discriminant analysis (LDA) model is computed using the information within the projection space as well as the distance to the projection space. The models provide information about the quality of separation for each class combination. Based on this information, weights are defined for aggregating the LDA-based posterior probabilities of each subspace to a new overall probability. The same weights are used for classifying new observations. In addition to the provided methodology, implemented in the R-package lop, a method of visualizing the connectivity of groups in high-dimensional spaces is proposed on the basis of the posterior probabilities. A thorough evaluation is performed using three different real-world datasets, underlining the strengths of local projection based classification and the provided visualization methodology.