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.
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Huang, K., Zhang, L. (2013). Optimal Calculation of Tensor Learning Approaches. In: Guo, C., Hou, ZG., Zeng, Z. (eds) Advances in Neural Networks – ISNN 2013. ISNN 2013. Lecture Notes in Computer Science, vol 7951. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39065-4_40
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DOI: https://doi.org/10.1007/978-3-642-39065-4_40
Publisher Name: Springer, Berlin, Heidelberg
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