Traditional machine learning methods characterize data observations by feature vectors, where an entry of a vector denotes a scalar feature value of a data instance. While this data representation facilitates the application of conventional machine learning algorithms, in many cases it is not the best way of extracting all useful information from the data observations. In this paper we relax the (often unstated) assumption of vectorizing features of data instances, and allow a more natural representation of the data in a tensor format. Tensors are multi-mode (aka multi-way) arrays, of whom vectors (i.e., one-mode tensors) and matrices (i.e., two-mode tensors) are special cases. We show that the tensor representation captures useful information that is difficult to provide in the conventional vector format. More importantly, to effectively utilize the rich information contained in tensors, we propose a novel semi-naive Bayesian tensor classification method (which we call Bat) that builds predictive models directly on data in tensor form (instead of on their vectorizations). We apply Bat to supervised learning problems, and perform comprehensive experiments on classifying text documents and graphs, which demonstrate (1) the advantage of the tensor representation over conventional feature-vectorization approaches, and (2) the superiority of the proposed Bat tensor classifier over other existing learners.
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