Modularity Component Analysis versus Principal Component Analysis

TL;DR

This paper establishes a precise linear relationship between modularity matrix eigenvectors and data matrix singular vectors, introducing modularity component analysis as a non-centered alternative to PCA for data clustering.

Contribution

It develops the exact relation between modularity matrix eigenvectors and data singular vectors, defining modularity components and demonstrating their use in clustering without data centering.

Findings

Modularity component analysis is analogous to PCA but does not require data centering.

The paper provides a mathematical foundation linking modularity matrices to data singular vectors.

Experimental results show effective clustering using modularity components.

Abstract

In this paper the exact linear relation between the leading eigenvectors of the modularity matrix and the singular vectors of an uncentered data matrix is developed. Based on this analysis the concept of a modularity component is defined, and its properties are developed. It is shown that modularity component analysis can be used to cluster data similar to how traditional principal component analysis is used except that modularity component analysis does not require data centering.