Robust simultaneous low rank approximation of tensors

Abstract

We propose simultaneous low rank approximation of tensors (SLRAT) for the dimensionality reduction of tensors and modify it to the robust one, i.e., the robust SLRAT. For both the SLRAT and the robust SLRAT, we propose iterative algorithms for solving them. It is experimentally shown that the robust SLRAT achieves lower reconstruction error than the SLRAT when a dataset contains noise data. We also propose a method for classifying sets of tensors and call it the subspace matching, where both training data and testing data are represented by their subspaces, and each testing datum is classified on the basis of the similarity between subspaces. It is experimentally verified that the robust SLRAT achieves higher recognition rate than the SLRAT when the testing data contain noise data. © 2009 Springer Berlin Heidelberg.