Factorization of Multiple Tensors for Supervised Feature Extraction

Tensors are effective representations for complex and time-varying networks. The factorization of a tensor provides a high-quality low-rank compact basis for each dimension of the tensor, which facilitates the interpretation of important structures of the represented data. Many existing tensor factorization (TF) methods assume there is one tensor that needs to be decomposed to low-rank factors. However in practice, data are usually generated from different time periods or by different class labels, which are represented by a sequence of multiple tensors associated with different labels. When one needs to analyse and compare multiple tensors, existing TF methods are unsuitable for discovering all potentially useful patterns, as they usually fail to discover either common or unique factors among the tensors: 1) if each tensor is factorized separately, the factor matrices will fail to explicitly capture the common information shared by different tensors, and 2) if tensors are concatenated together to form a larger “overall” tensor and then factorize this concatenated tensor, the intrinsic unique subspaces that are specific to each tensor will be lost. The cause of such an issue is mainly from the fact that existing tensor factorization methods handle data observations in an unsupervised way, considering only features but not labels of the data. To tackle this problem, we design a novel probabilistic tensor factorization model that takes both features and class labels of tensors into account, and produces informative common and unique factors of all tensors simultaneously. Experiment results on feature extraction in classification problems demonstrate the effectiveness of the factors discovered by our method.