Large-scale tucker Tensor factorization for sparse and accurate decomposition

Abstract

How can we generate sparse tensor decomposition results for better interpretability? Typical tensor decomposition results are dense. Dense results require additional postprocessing for data interpretation, especially when the data are large. Thus, we present a large-scale Tucker factorization method for sparse and accurate tensor decomposition, which we call the Very Sparse Tucker factorization (VeST) method. The proposed VeST outputs highly sparse decomposition results from a large-scale partially observable tensor data. The approach starts by decomposing the input tensor data, then iteratively determining unimportant elements, removing them, and updating the remaining elements until a terminal state is reached. We define 'responsibility' of each element on the reconstruction error to determine unimportant elements in the decomposition results. The decomposition results are updated iteratively in parallel using carefully constructed coordinate descent rules for scalable computation. Furthermore, the suggested method automatically looks for the optimal sparsity ratio, resulting in a balanced sparsity-accuracy trade-off. Extensive experiments using real-world datasets showed that our method produces more accurate results than that of the competitors. Experiments further showed that the proposed method is scalable in terms of the input dimensionality, the number of observable entries, and the thread count.