Cluster Exploration using Informative Manifold Projections

TL;DR

This paper introduces a novel manifold optimization approach combining contrastive PCA and kurtosis projection pursuit to generate informative embeddings that reveal underlying data structures while accounting for prior knowledge.

Contribution

It presents a new method for dimensionality reduction that incorporates prior knowledge to improve visualization and cluster discovery in high-dimensional data.

Findings

Empirically validated across various datasets.

Effectively separates data structures considering prior knowledge.

Provides an automated framework for iterative visual exploration.

Abstract

Dimensionality reduction (DR) is one of the key tools for the visual exploration of high-dimensional data and uncovering its cluster structure in two- or three-dimensional spaces. The vast majority of DR methods in the literature do not take into account any prior knowledge a practitioner may have regarding the dataset under consideration. We propose a novel method to generate informative embeddings which not only factor out the structure associated with different kinds of prior knowledge but also aim to reveal any remaining underlying structure. To achieve this, we employ a linear combination of two objectives: firstly, contrastive PCA that discounts the structure associated with the prior information, and secondly, kurtosis projection pursuit which ensures meaningful data separation in the obtained embeddings. We formulate this task as a manifold optimization problem and validate it empirically across a variety of datasets considering three distinct types of prior knowledge. Lastly, we provide an automated framework to perform iterative visual exploration of high-dimensional data.