Analyzing Large and Sparse Tensor Data using Spectral Low-Rank Approximation

TL;DR

This paper introduces two spectral low-rank approximation methods for large, sparse 3-mode tensors, enabling efficient data clustering and expansion without dense computations, demonstrated on text, conference, and network data.

Contribution

It presents novel tensor approximation algorithms based on spectral methods that generalize graph partitioning and enable sparse tensor expansion.

Findings

Effective clustering of large sparse tensors.

Efficient low-rank approximation avoiding data filling.

Successful application to diverse real-world datasets.

Abstract

Information is extracted from large and sparse data sets organized as 3-mode tensors. Two methods are described, based on best rank-(2,2,2) and rank-(2,2,1) approximation of the tensor. The first method can be considered as a generalization of spectral graph partitioning to tensors, and it gives a reordering of the tensor that clusters the information. The second method gives an expansion of the tensor in sparse rank-(2,2,1) terms, where the terms correspond to graphs. The low-rank approximations are computed using an efficient Krylov-Schur type algorithm that avoids filling in the sparse data. The methods are applied to topic search in news text, a tensor representing conference author-terms-years, and network traffic logs.