Reliability of optimal linear projection of growing scale-free networks

TL;DR

This paper investigates the stability of truncated singular value decomposition (TSVD) projections when applied to evolving scale-free networks, assessing how well initial data projections remain reliable as networks grow.

Contribution

It provides an analysis of TSVD projection reliability specifically for growing scale-free networks, highlighting its stability at different scales over time.

Findings

TSVD projections remain stable at global scales during network growth

Local scale projections show more variability over time

The study offers insights into the applicability of TSVD for dynamic network analysis

Abstract

Singular Value Decomposition (SVD) is a technique based on linear projection theory, which has been frequently used for data analysis. It constitutes an optimal (in the sense of least squares) decomposition of a matrix in the most relevant directions of the data variance. Usually, this information is used to reduce the dimensionality of the data set in a few principal projection directions, this is called Truncated Singular Value Decomposition (TSVD). In situations where the data is continuously changing the projection might become obsolete. Since the change rate of data can be fast, it is an interesting question whether the TSVD projection of the initial data is reliable. In the case of complex networks, this scenario is particularly important when considering network growth. Here we study the reliability of the TSVD projection of growing scale free networks, monitoring its evolution at global and local scales.