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

2020/12/14 by Lars Eldén, Eldén, L., Maryam Dehghan +1
Computer Science · Engineering · Mathematics · #05C50 (Primary) 15A69 #65F15 (Secondary) #Algorithms and Data Compression #FOS: Mathematics #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2012.07754

openalex publication_date 2020/12/14 · openalex created_date 2020/12/21 · openalex updated_date 2026/07/28

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.

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