Interpretable Discriminative Dimensionality Reduction and Feature Selection on the Manifold

TL;DR

This paper introduces I-KDR, an interpretable kernel dimensionality reduction method that enhances class separation and feature relevance, providing better interpretability and discriminative performance than existing algorithms.

Contribution

The paper presents a novel interpretable kernel DR algorithm that combines dimensionality reduction with feature selection, improving interpretability and discriminative ability.

Findings

I-KDR yields more interpretable embedding dimensions.

I-KDR achieves higher discriminative performance.

I-KDR effectively combines DR with feature selection.

Abstract

Dimensionality reduction (DR) on the manifold includes effective methods which project the data from an implicit relational space onto a vectorial space. Regardless of the achievements in this area, these algorithms suffer from the lack of interpretation of the projection dimensions. Therefore, it is often difficult to explain the physical meaning behind the embedding dimensions. In this research, we propose the interpretable kernel DR algorithm (I-KDR) as a new algorithm which maps the data from the feature space to a lower dimensional space where the classes are more condensed with less overlapping. Besides, the algorithm creates the dimensions upon local contributions of the data samples, which makes it easier to interpret them by class labels. Additionally, we efficiently fuse the DR with feature selection task to select the most relevant features of the original space to the discriminative objective. Based on the empirical evidence, I-KDR provides better interpretations for embedding dimensions as well as higher discriminative performance in the embedded space compared to the state-of-the-art and popular DR algorithms.