TensorD: A tensor decomposition library in TensorFlow

Abstract The TensorD toolbox is a Python tensor library built on TensorFlow. It provides tensor decomposition methods as well as basic tensor operations. In addition, other features of TensorD include GPU compatibility, high modularity of structure, and open source. It facilitate the practice of tensor methods in computer vision, deep learning and other related research fields. The TensorD toolbox is available at https://github.com/Large-Scale-Tensor-Decomposition/tensorD .

[1]  Zenglin Xu,et al.  Bayesian Nonparametric Models for Multiway Data Analysis , 2015, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  L. Tucker,et al.  Some mathematical notes on three-mode factor analysis , 1966, Psychometrika.

[3]  Zenglin Xu,et al.  Simple and efficient parallelization for probabilistic temporal tensor factorization , 2017, 2017 International Joint Conference on Neural Networks (IJCNN).

[4]  T. Kolda.  Multilinear operators for higher-order decompositions , 2006 .

[5]  Seungjin Choi,et al.  Nonnegative Tucker Decomposition , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[6]  Paolo Bientinesi,et al.  HPTT: a high-performance tensor transposition C++ library , 2017, ARRAY@PLDI.

[7]  J. Chang,et al.  Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition , 1970 .

[8]  F. L. Hitchcock.  The Expression of a Tensor or a Polyadic as a Sum of Products , 1927 .

[9]  Zenglin Xu,et al.  Robust graph regularized nonnegative matrix factorization for clustering , 2017, Data Mining and Knowledge Discovery.

[10]  Zenglin Xu,et al.  Adaptive local structure learning for document co-clustering , 2018, Knowl. Based Syst..

[11]  Wotao Yin,et al.  A Block Coordinate Descent Method for Regularized Multiconvex Optimization with Applications to Nonnegative Tensor Factorization and Completion , 2013, SIAM J. Imaging Sci..

[12]  Yuan Yu,et al.  TensorFlow: A system for large-scale machine learning , 2016, OSDI.

[13]  H. Kiers.  Towards a standardized notation and terminology in multiway analysis , 2000 .

[14]  Lieven De Lathauwer,et al.  Decompositions of a Higher-Order Tensor in Block Terms - Part II: Definitions and Uniqueness , 2008, SIAM J. Matrix Anal. Appl..

[15]  Zenglin Xu,et al.  Exact and Stable Recovery of Pairwise Interaction Tensors , 2013, NIPS.

[16]  C. Eckart,et al.  The approximation of one matrix by another of lower rank , 1936 .

[17]  Grazia Lotti,et al.  O(n2.7799) Complexity for n*n Approximate Matrix Multiplication , 1979, Inf. Process. Lett..

[18]  Zenglin Xu,et al.  Learning Compact Recurrent Neural Networks with Block-Term Tensor Decomposition , 2017, 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition.

[19]  Zenglin Xu,et al.  Robust multi-view data clustering with multi-view capped-norm K-means , 2018, Neurocomputing.

[20]  Jieping Ye,et al.  Tensor Completion for Estimating Missing Values in Visual Data , 2013, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  Tamara G. Kolda,et al.  Parallel Tensor Compression for Large-Scale Scientific Data , 2015, 2016 IEEE International Parallel and Distributed Processing Symposium (IPDPS).

[22]  Ivan Oseledets,et al.  Tensor-Train Decomposition , 2011, SIAM J. Sci. Comput..

[23]  Zenglin Xu,et al.  Infinite Tucker Decomposition: Nonparametric Bayesian Models for Multiway Data Analysis , 2011, ICML.

[24]  Joos Vandewalle,et al.  On the Best Rank-1 and Rank-(R1 , R2, ... , RN) Approximation of Higher-Order Tensors , 2000, SIAM J. Matrix Anal. Appl..

[25]  P. Paatero.  A weighted non-negative least squares algorithm for three-way ‘PARAFAC’ factor analysis , 1997 .

[26]  M. V. Van Benthem,et al.  Fast algorithm for the solution of large‐scale non‐negativity‐constrained least squares problems , 2004 .

[27]  Nuria Oliver,et al.  Multiverse recommendation: n-dimensional tensor factorization for context-aware collaborative filtering , 2010, RecSys '10.

[28]  Tamir Hazan,et al.  Non-negative tensor factorization with applications to statistics and computer vision , 2005, ICML.

[29]  H. Sebastian Seung,et al.  Algorithms for Non-negative Matrix Factorization , 2000, NIPS.

[30]  J. Mocks,et al.  Topographic components model for event-related potentials and some biophysical considerations , 1988, IEEE Transactions on Biomedical Engineering.