# Supporting Analysis of Dimensionality Reduction Results with Contrastive Learning

## TL;DR

This paper introduces ccPCA, a visual analytics method that enhances understanding of clusters in dimensionality reduction results by highlighting key features through contrastive analysis, aiding interpretation of high-dimensional data.

## Contribution

The paper presents ccPCA, a novel method that uses contrastive PCA to identify and visualize essential features characterizing specific clusters in DR results.

## Key findings

- ccPCA effectively highlights features distinguishing clusters.
- The interactive system aids in interpreting high-dimensional data.
- Case studies demonstrate the method's practical utility.

## Abstract

Dimensionality reduction (DR) is frequently used for analyzing and visualizing high-dimensional data as it provides a good first glance of the data. However, to interpret the DR result for gaining useful insights from the data, it would take additional analysis effort such as identifying clusters and understanding their characteristics. While there are many automatic methods (e.g., density-based clustering methods) to identify clusters, effective methods for understanding a cluster's characteristics are still lacking. A cluster can be mostly characterized by its distribution of feature values. Reviewing the original feature values is not a straightforward task when the number of features is large. To address this challenge, we present a visual analytics method that effectively highlights the essential features of a cluster in a DR result. To extract the essential features, we introduce an enhanced usage of contrastive principal component analysis (cPCA). Our method, called ccPCA (contrasting clusters in PCA), can calculate each feature's relative contribution to the contrast between one cluster and other clusters. With ccPCA, we have created an interactive system including a scalable visualization of clusters' feature contributions. We demonstrate the effectiveness of our method and system with case studies using several publicly available datasets.