Research On Cutting Plane Algorithm For Support Tensor Machine

Support vector machine gained a lot of attractive features and promising performance for data classification and regression analysis of small sample size, high-dimensional problems which was solved using the dual formulation of the primal quadratic optimization problem. So-called decomposition techniques as chunking or SMO are able to handle classification problems with larger datasets by exploiting the special structure of the SVM problem. The key idea of decomposition is to solve a sequence of constant-size subproblems instead of the dual problem. However with the increase in the size of datasets, the number of subproblems in decomposition techniques to be solved is also increasing. When the data volumes become larger and larger, the method becomes computationally intractable. Later the Cutting Plane Algorithm(CPA) based method which focused on solving the unconstrained SVM primal problem were proposed. The performance of support vector machine to solve classification problem of large-scale datasets has been significantly improved.Many applications in IT-Security and Text-Classification usually come with huge amounts of multi linear data points such as matrices or higher-order tensors. Although tensor objects can be reshaped into vectors beforehand to comply with the input requirements of traditional SVM algorithms, several studies have indicated that this direct reshaping breaks the natural structure and correlation in the original data and leads to the curse of dimensionality.For the wide spread of massive tensor datasets and the disadvantage of traditional vectors models, in this paper, we present a novel Cutting Plane Algorithm for Linear Support High-Order Tensor Machine(CPA-SHTM) to solve problems of tensor classification with large-scale datasets. In order to retain more structural information and obtain computationally efficient method capable of dealing with tensor datasets, this algorithm used tensor as input and integrated tensor rank-one decomposition algorithm to construct Linear Support Higher-Order Tensor Machine(SHTM).Then Cutting Plane Algorithm was applied in SHTM by approximating the risk function in primal optimization problem by a piece-wise linear function defined as the maximum over a set of linear under-estimators.A set of experiments are conducted on twelve datasets of face recognition, gait recognition and digit written recognition to illustrate the average training time and average fitting precision of the proposed CPA-SHTM comparing with Optimized Cutting Plane Algorithm for SVMs(OCA-T).The experimental results show that compared with OCA-T,CPA-SHTM provides significant performance gain in terms of average test accuracy and average training speed. At the end of the experience we investigate how computational time and test accuracy scales with the number of the rank R of a tensor.