Generalized Higher-Order Tensor Decomposition via Parallel ADMM

Authors

  • Fanhua Shang The Chinese University of Hong Kong
  • Yuanyuan Liu The Chinese University of Hong Kong
  • James Cheng The Chinese University of Hong Kong

Abstract

Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting, gross corruptions and computational efficiency. To address these problems, we first propose a parallel trace norm regularized tensor decomposition method, and formulate it as a convex optimization problem. This mehtod does not require the rank of each mode to be specified beforehand, and can automaticaly determine the number of factors in each mode through our optimization scheme. By considering the low-rank structure of the observed tensor, we analyze the equivalent relationship of the trace norm between a low-rank tensor and its core tensor. Then, we cast a non-convex tensor decomposition model into a weighted combination of multiple much smaller-scale matrix trace norm minimization. Finally, we develop two parallel alternating direction methods of multipliers (ADMM) to solve our problems. Experimental results verify that our regularized formulation is effective, and our methods are robust to noise or outliers.

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Published

2014-06-21

How to Cite

Shang, F., Liu, Y., & Cheng, J. (2014). Generalized Higher-Order Tensor Decomposition via Parallel ADMM. Proceedings of the AAAI Conference on Artificial Intelligence, 28(1). Retrieved from https://ojs.aaai.org/index.php/AAAI/article/view/8913

Issue

Section

Main Track: Machine Learning Applications