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

VeST: Very Sparse Tucker Factorization of Large-Scale Tensors