# VeST: Very Sparse Tucker Factorization of Large-Scale Tensors

## TL;DR

VeST is a novel tensor factorization method that produces highly sparse and accurate decompositions of large-scale, partially observable tensors, improving interpretability and scalability over existing approaches.

## Contribution

We introduce VeST, a scalable tensor factorization technique that yields very sparse core tensors and factor matrices without sacrificing accuracy.

## Key findings

- VeST achieves at least 2.2 times more sparsity than competitors.
- VeST is at least 2.8 times more accurate than existing methods.
- The method scales well with input size and observable entries.

## Abstract

Given a large tensor, how can we decompose it to sparse core tensor and factor matrices such that it is easier to interpret the results? How can we do this without reducing the accuracy? Existing approaches either output dense results or give low accuracy. In this paper, we propose VeST, a tensor factorization method for partially observable data to output a very sparse core tensor and factor matrices. VeST performs initial decomposition, determines unimportant entries in the decomposition results, removes the unimportant entries, and carefully updates the remaining entries. To determine unimportant entries, we define and use entry-wise 'responsibility' for the decomposed results. The entries are updated iteratively in a coordinate descent manner in parallel for scalable computation. Extensive experiments show that our method VeST is at least 2.2 times more sparse and at least 2.8 times more accurate compared to competitors. Moreover, VeST is scalable in terms of input order, dimension, and the number of observable entries. Thanks to VeST, we successfully interpret the result of real-world tensor data based on the sparsity pattern of the resulting factor matrices.