Kernel Support Tensor Regression

Support vector machine (SVM) not only can be used for classification, can also be applied to regression problems by the introduction of an alternative loss function. Now most of the regress algorithms are based on vector as input, but in many real cases input samples are tensors, support tensor machine (STM) by Cai and He is a typical learning machine for second order tensors. In this paper, we propose an algorithm named kernel support tensor regression (KSTR) using tensors as input for function regression. In this algorithm, after mapping the each row of every original tensor or of every tensor converted from original vector into a high dimensional space, we can get associated points in a new high dimensional feature space, and then compute the regression function. We compare the results of KSTR with the traditional SVR algorithm, and find that KSTR is more effective according to the analysis of the experimental results. (C) 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Harbin University of Science and Technology.