Logistic Regression Image Classification Algorithm Based on Tensor Decomposition

• 1、School of Computer Science and Technology, Tianjin University, Tianjin, 300350
• 2、Department of Mathematics and Computer Science, Hengshui University, Hengshui, 053000

Abstract：Image classification has become an important research content in the image processing field. Traditional vector-based image classification algorithm needs to vectorize the images. Vectorization process results in the loss of image spatial information and generation of high-dimensional vector data. In order to solve the problems brought by the vectorization, as a natural expression of the image, tensor becomes a research hotspot for image classification issue. Based on the two forms of tensor decomposition, namely CP (CANDECOMP/PARAFAC) decomposition and Tucker decomposition, this paper proposes two tensor logistic regression classification models for direct classification operation of tensor image data. In addition, are introduced in both models separately structured sparse term L(2,1)-norm and matrix regularization term LF-norm. The former is called the logistic tensor regression with rank selection, which can automatically select CP decomposition rank in the model parameters training process, and obtain accurate tensor decomposition expression form. The latter is called a logic Tucker regression model, and by using Tucker decomposition, it can obtain the effective principal components of the tensor, and also can achieve the purpose of dimensionality reduction of high dimensional data. The classification experiments on two second-order grayscale graph data set and two third-order motion graph data set verifies that, as to the image classification accuracy rate, the proposed method is not only higher than vector-based classification algorithm, but also better than the currently popular tensor classification algorithm.

Keywords： Image classification CP (CANDECOMP/PARAFAC) decomposition Tucker decomposition L(2,1)-norm LF-norm