Universal Consistency of Support Tensor Machine

Tensor (multidimensional array) classification problem has become popular in modern applications such as computer vision and spatial-temporal data analysis. The Support Tensor Machine (STM) classifier, which is extended from support vector machine, takes tensor type data as predictors to predict the labels of the data. The distribution-free property of STM highlights its potential in handling different types of data applications. In this work, we provide a theoretical result for the universal consistency of STM. This result guarantees the solid generalization ability of STM with universal tensor based kernel functions. In addition, we give out a way of constructing universal kernel functions for tensor data, which may be helpful for other types of tensor based kernel methods.