Theoretical Research And Application Of Fuzzy Support Tensor Machine

Traditionally, most of machine learning algorithms are based on vector, the input data are vectors, the data for input are points in a high dimensional vector space, and the goal of an algorithm is to search a linear or nonlinear function for classification or prediction. But in our real life there are many samples of tensor. For example, photographs can be regarded as a second order tensor, a video clip may be considered as a third order tensor. Support Tensor Machine (STM) was developed from Support vector machine (SVM) by X. F. He. It uses tensor for input, to find a separating hyperplane for classification. But Support Tensor Machine is only a linear method it can only solve linearly separable problems. It's difficult for it to solve the nonlinear data. Also it can not used for n-order (n>2) tensor data. In this dissertation, first we make STM can solve nonlinear data; second STM not only be used for classification but also used for function regression; third it can deal with n-order (n>2) tensor data. Concretely, this dissertation contains these parts as follows:1. We propose a new kernel function for tensors. So we can use kernel method for mapping original data into a high dimension feature space by a nonlinear function. In this space we can use a linear classifier to reach a good recognition rate. Combining kernel method with support tensor machine, we propose a new algorithm named kernel support tensor machine (KSTM) which has a better generalization performance than traditional support vector machine according to the results of experiments.2. To solve multiclass problems we propose a Fuzzy Kernel Support Tensor Machine (FKSTM). If we use support vector machine and support tensor machine for multiclass problems, unclassifiable regions exist. In order to solve the problem Shigeo Abe et al. developed 1-against-1 (1-a-1) and 1-against-rest (1-a-r) fuzzy classification methods and proposed 1-a-1 and 1-a-r fuzzy support vector machine. Using the decision function obtained from binary two class support vector machine to construct a membership function, unclassifiable regions are resolved. We combine our kernel support tensor machine with 1-a-1 and 1-a-r fuzzy classification methods, and propose 1-a-1 and 1-a-r fuzzy kernel support tensor machines. We evaluate the generalization performance of our methods on iris and wine data sets.3. We propose Kernel Support Tensor Regression algorithm (KSTR). Support vector machine not only can be used for classification, can also be applied to regression problems by the introduction of an alternative loss function. Usingε-insensitive loss function we propose the algorithm namedε-insensitive kernel support tensor regression method. Five different data sets are used to evaluate the performance of the proposed KSTR algorithm.4. We propose Generalized Support Tensor Machine (GSTM). The algorithms of kernel support tensor machine and kernel support tensor regression can only use on second order tensor while GSTM can be used for dealing with n-order (n>2) tensor data. And we also evaluate the classification performance with UCI data sets.