A C Library for Tensor Decomposition In this paper, we develop a new library TenDeC for tensor decompositions in C. TenDeC supports popular tensor decomposition functions including Canonical Polyadic, Tucker, tensortrain, and tSVD, assisting C programmers to shorten the development cycle of deep learning applications. Compared with the resourceintensive Python and MATLAB, C has the nature advantages on fast running time and high compatibility. To further explore potentials of C, we propose a novel underlying technology PointerDefomer leveraging the unique pointer. Since the transformation between tensor and sizespecific matrix is indispensable in tensor decompositions, PointerDefomer can virtually achieve such a transformation by controlling the movement of pointer in memory address. As a result, the conventional transformation steps can be skipped to accelerate the decomposition process and there is no memory needed for saving the intermediate results of tensor transformation. In our experiment, TenDeC reduces decomposition time and support larger size of tensor compared with the classic Tensorly in Python and TensorLab in MATLAB, respectively.

Shape Constrained Tensor Decompositions We propose a new lowrank tensor factorization where one mode is coded as a sparse linear combination of elements from an overcomplete library. Our method, Shape Constrained Tensor Decomposition (SCTD) is based upon the CANDECOMPPARAFAC (CP) decomposition which produces rrank approximations of data tensors via outer products of vectors in each dimension of the data. The SCTD model can leverage prior knowledge about the shape of factors along a given mode, for example in tensor data where one mode represents time. By constraining the vector in the temporal dimension to known analytic forms which are selected from a large set of candidate functions, more readily interpretable decompositions are achieved and analytic time dependencies discovered. The SCTD method circumvents traditional flattening techniques where an Nway array is reshaped into a matrix in order to perform a singular value decomposition. A clear advantage of the SCTD algorithm is its ability to extract transient and intermittent phenomena which is often difficult for SVDbased methods. We motivate the SCTD method using several intuitively appealing results before applying it on a realworld data set to illustrate the efficiency of the algorithm in extracting interpretable spatiotemporal modes. With the rise of datadriven discovery methods, the decomposition proposed provides a viable technique for analyzing multitudes of data in a more comprehensible fashion.