Methods And Application Of Classification Based On Tensor Data

Data representation is an important problem in machine learning. In the current research, tensor data were always scanned into vectors, thus discarding a great deal of useful structural information. Tensor data can preserve the structure information, and is more in line with the actual situation. Now, machine learning based on tensor data has been widely researched and applied, it has become a new research direction in the field of data mining, theoretical research and practical application of it is in fast development. The optimization method is one of the main tools.This paper is based on the machine learning methods of vector data, and studies the learning methods based on tensor data from the optimization points, it pays special attention to design new models of tensor data and their optimization algorithms. The research contents of this paper are as following:1. Through the analysis of the existing models, the relationship between tensor-learning method and vector-learning method is determined, and then explains support tensor machine from the perspective of geometry. According to discuss the particular weight tensor of support tensor machine, several methods to keep the tensor structure information are obtained, and then a new model of tensor learning---Rk-Constraint Support Tensor Machine, is established. Numerical experiments show that this method not only can achieve the desired classification results, but also avoid the alternating iterative algorithm and save a large amount of computation time.2. In order to maintain the relevance of vector-factor, a new kernel function based on tensor data is constructed, this kernel function can maintain the tensor structure information effectively. Combining this kernel function and the dual problem of support tensor machine, a new method for nonlinear classification based on tensor data is obtained—Krnel based Support Tensor Machine.3. Since the Euclidean distance is based on the orthogonal hypothesis, it is unreasonable to measure the distance between matrix data. By introducing the spatial relationship between the quantity-factor of matrix, a new matrix distance is obtained. This new matrix distance not only considered the relation between the quantity-factor, but also can reasonably measure the distance between matrix data. The new matrix distance can be applied to dimensionality reduction, classification, regression and clustering of matrix data.4. Based on the new matrix distance and multilinear discriminant subspace analysis, we propose a new dimension reduction method of matrix. By introducing L2, norm which can reflect the sparsity of the matrix, a model of Sparsity-Support Tensor Machine is established, this method not only can reduce the dimensionality of data, but also can predict the category. Through the extensive numerical experiments, it shows that the two methods of dimensionality reduction are feasible and effective.5. Through the comprehensive summary of the machine learning methods based on tensor data, we propose a framework of tensor learning method. The framework indicates that researching tensor learning method is essentially searching for an ideal tensor distance metric.