  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.
