Research And Application Of Machine Learning Algorithm Based Tensor Representation

In the traditional research for machine learning, most of the classical learning algorithms are based on the vector space model. But many objects are naturally represented by tensors in computer vision research. In prevenient research, the tensor was always scanned into vector, thus leading to the data structure destroyed. It discarded a great deal of useful structural information, such as spatial information and temporal information. Recently, the advantages of tensorial algorithms have attracted significant interest from the research community. Compared with vector representation, tensor representation is helpful to overcome the over fitting problem in vector-based learning and the tensor learning algorithms specially suited for small-sample-size problems. Therefore tensor representation and tensor learning have become a new research hotspot at present.In this paper, the reaserch of tensor learning method is based on optimization method, especially focus on the establishment of the new model, new algorithm and its applications. Support Vector Machine (SVM) is a powerful tool of data mining and pattern recognition. In this paper, SVM algorithms have been extended to deal with tensors. The new tensor models and algrithms are presented. Specifically, the main achievement of this paper is as follows:1. The new tensor learning framework, low rank Support Tensor Machine, is presented:Based on statistical learning theory, the paper discussed the limitation of classical Support Vector Machine (SVM) and Support Tensor Machine (STM). The Rank-One limitation of the formulation of weight parameters tensor is broken, a novel low rank tensor projection has been discussed. At last, the new tensor learning framework, low rank Support Tensor Machine (LR-STM), has been presented.2. Two novel tensorial algorithms has been designed to sovle the proposed LR-STM:Tensor gradient descent algorithm calculated the descent direction for LR-STM by some smoothing operations. It avoids the alternating process which existed in traditional tensor algorithm and gets the optimal solution directly and fast.Tensor two-step algorithm divided the primal problem of LR-STM into two sub-problems. By skillful combining the two solutions from the sub-problems, Tensor two-step algorithm can find an approximate solution for the LR-STM model.3. LS-TNPPC algorithm is presented to deal with imbalance tensor data classification problem:Based on the idea of low rank projection, the classical Twin-SVM algorithm has been extended to solve imbalance tensor data classification problem. In this paper, a novel LS-TNPPC algorithm has been presented. The new method can get better prediction accuracy in standard test data. It proved the idea of low rank projection can help the extending of traditional tensor algorithm to handle tensor data. 4. Tensor kernel method and multi-label kernel support tensor machine:Based the theory of kernel method, this paper discussed the application of kernel learning in tensor learning. In this paper, a tensor kernel method has been presented. By the new tensor kernel method, a novel multi-label kernel support tensor machine is presented. Experiments on some real applications suggest the efficiency and the effectiveness of this method.