Optimal calculation of tensor learning approaches

Authors:
Kai Huang;Liqing Zhang
Affiliations:
MOE-Microsoft Key Laboratory for Intelligent Computing and Intelligent Systems, Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China;MOE-Microsoft Key Laboratory for Intelligent Computing and Intelligent Systems, Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China
Venue:
ISNN'13 Proceedings of the 10th international conference on Advances in Neural Networks - Volume Part I
Year:
2013

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Abstract

Most algorithms have been extended to the tensor space to create algorithm versions with direct tensor inputs. However, very unfortunately basically all objective functions of algorithms in the tensor space are non-convex. However, sub-problems constructed by fixing all the modes but one are often convex and very easy to solve. However, this method may lead to difficulty converging; iterative algorithms sometimes get stuck in a local minimum and have difficulty converging to the global solution. Here, we propose a computational framework for constrained and unconstrained tensor methods. Using our methods, the algorithm convergence situation can be improved to some extent and better solutions obtained. We applied our technique to Uncorrelated Multilinear Principal Component Analysis (UMPCA), Tensor Rank one Discriminant Analysis (TR1DA) and Support Tensor Machines (STM); Experiment results show the effectiveness of our method.