Generalized Higher-Order Tensor Decomposition via Parallel ADMM
This work addresses tensor decomposition problems for applications in computer vision, social network analysis, data mining, and neuroscience, representing an incremental improvement with a novel method for a known bottleneck.
The paper tackles challenges in higher-order tensor decomposition, including model selection, gross corruptions, and computational efficiency, by proposing a parallel trace norm regularized method that automatically determines factor numbers and achieves robustness to noise or outliers.
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 method does not require the rank of each mode to be specified beforehand, and can automatically 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.