A random version of principal component analysis in data clustering

TL;DR

This paper introduces a modified PCA algorithm that effectively handles both well-dimensioned and degenerated high-dimensional datasets, overcoming traditional mathematical constraints.

Contribution

A novel variation of PCA that extends applicability to degenerated datasets, addressing limitations of standard PCA in high-dimensional data analysis.

Findings

Modified PCA works on degenerated datasets

Algorithm maintains performance with fewer samples

Enhances PCA applicability in high-dimensional analysis

Abstract

Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical constraints on the minimum number of different replicates or samples that must be included in the analysis. Here we show that a modified algorithm works not only on well dimensioned datasets, but also on degenerated ones.