Maximum Margin Multisurface Support Tensor Machines with application to image classification and segmentation

Virtually all previous classifier models take vectors as inputs, performing directly based on the vector patterns. But it is highly necessary to consider images as matrices in real applications. In this paper, we represent images as second order tensors or matrices. We then propose two novel tensor algorithms, which are referred to as Maximum Margin Multisurface Proximal Support Tensor Machine (M³PSTM) and Maximum Margin Multi-weight Vector Projection Support Tensor Machine (M³VSTM), for classifying and segmenting the images. M³PSTM and M³VSTM operate in tensor space and aim at computing two proximal tensor planes for multisurface learning. To avoid the singularity problem, maximum margin criterion is used for formulating the optimization problems. Thus the proposed tensor classifiers have an analytic form of projection axes and can achieve the maximum margin representations for classification. With tensor representation, the number of estimated parameters is significantly reduced, which makes M³PSTM and M³VSTM more computationally efficient when handing the high-dimensional datasets than applying the vector representations based methods. Thorough image classification and segmentation simulations on the benchmark UCI and real datasets verify the efficiency and validity of our approaches. The visual and numerical results show M³PSTM and M³VSTM deliver comparable or even better performance than some state-of-the-art classification algorithms.