A Distributed and Incremental SVD Algorithm for Agglomerative Data Analysis on Large Networks

TL;DR

This paper introduces a hierarchical, distributed, and incremental SVD algorithm designed for large network data, capable of efficiently recovering singular values and vectors with stability and bounded error, validated through experiments.

Contribution

The paper presents a novel hierarchical SVD algorithm that efficiently computes and recovers singular values and vectors for large matrices in a distributed setting.

Findings

Algorithm accurately recovers singular values and vectors.

Method is stable against roundoff errors and data corruption.

Numerical experiments confirm efficiency and parallel scalability.

Abstract

In this paper, we show that the SVD of a matrix can be constructed efficiently in a hierarchical approach. Our algorithm is proven to recover the singular values and left singular vectors if the rank of the input matrix $A$ is known. Further, the hierarchical algorithm can be used to recover the $d$ largest singular values and left singular vectors with bounded error. We also show that the proposed method is stable with respect to roundoff errors or corruption of the original matrix entries. Numerical experiments validate the proposed algorithms and parallel cost analysis.