Support vector machine based on low-rank tensor train decomposition for big data applications

Tensor representation plays a very important role in high-dimensional problems, like in the emerging big data applications. The numerical treatment of high-dimensional problems is difficult because of the curse of dimensionality, i.e., the number of elements and the computational complexity increase exponentially with the data dimension. To break the curse of dimensionality, finding a low-dimensional representations of the original data is always important in practical applications, especially in big data applications. Tensor representation and decomposition are emerging and promising tools for big data analysis and data mining. In this paper, we exploit the technique of tensor train decomposition which is one of the most effective and stable representations of high dimensional tensors to learn a low-dimensional representation of original data. By combining tensor train decomposition with the support vector machine, we proposed a support vector machine based on low-rank tensor decomposition for big data applications. The proposed method possesses high classification performance and has significantly reduced computational complexity.