A Support Tensor Train Machine

There has been growing interest in extending traditional vector-based machine learning techniques to their tensor forms. An example is the support tensor machine (STM) that utilizes a rank-one tensor to capture the data structure, thereby alleviating the overfitting and curse of dimensionality problems in the conventional support vector machine (SVM). However, the expressive power of a rank-one tensor is restrictive for many real-world data. To overcome this limitation, we introduce a support tensor train machine (STTM) by replacing the rank-one tensor in an STM with a tensor train. Experiments validate and confirm the superiority of an STTM over the SVM and STM. 1 Introduction Classification algorithm design has been a popular topic in machine learning, pattern recognition and computer vision for decades. One of the most representative and successful classification algorithms is the support vector machines (SVM) [ V apnik, 2013], which achieves an enormous success in pattern classification by minimizing the V apnik-Chervonenkis dimensions and structural risk. However, a standard SVM model is based on vector inputs and cannot directly deal with matrices or higher dimensional data structures, namely, tensors, which are very common in real-life applications.