Dimensionality Reduction Using pseudo-Boolean polynomials For Cluster Analysis

TL;DR

This paper presents a novel dimensionality reduction method using pseudo-Boolean polynomials for cluster analysis, effectively reducing high-dimensional data to lower dimensions while preserving cluster structure and interpretability.

Contribution

It introduces a penalty-based pseudo-Boolean polynomial approach for invariant dimensionality reduction in clustering, demonstrating its effectiveness on real datasets.

Findings

Reduced Iris dataset from 4D to 2D with preserved clusters

Reduced WDBC dataset from 30D to 3D maintaining accuracy

Achieved competitive clustering accuracy with clear interpretability

Abstract

We introduce usage of a reduction property of penalty-based formulation of pseudo-Boolean polynomials as a mechanism for invariant dimensionality reduction in cluster analysis processes. In our experiments, we show that multidimensional data, like 4-dimensional Iris Flower dataset can be reduced to 2-dimensional space while the 30-dimensional Wisconsin Diagnostic Breast Cancer (WDBC) dataset can be reduced to 3-dimensional space, and by searching lines or planes that lie between reduced samples we can extract clusters in a linear and unbiased manner with competitive accuracies, reproducibility and clear interpretation.