Non-negative Matrix Semi-Tensor Factorization For Image Recognition

In recent years,with the rapid development of computer technology,multimedia technology,artificial intelligence technology and many other technologies,image recog-nition technology has been applied more widely.The difficulty of image recognition is that the image data itself has a high dimension.In order to achieve image recognition,it is necessary to reduce the dimension of the data to complete the mapping from the model space to low-dimensional class space.Non-negative Matrix Factorization(NMF)is a clas-sical method of data dimensionality reduction.The image data dimension is reduced by the product of two non-negative low-dimensional matrices,and the features extracted by NMF have good physical meaning.Semi-Tensor Product of matrices(STP)is novel operation of matrix multiplication.It is a generalization of the conventional matrix product.It is well defined for matching dimension condition,factor dimension condition and general dimension condition.Semi-Tensor Product of Matrices can effectively manage the level of high-dimensional data and it is a powerful tool for processing high-dimensional data.In this paper,we propose a new non-negative matrix factorization method Non-negative Matrix Semi-Tensor Factorization(NMSTF)by combining the theory of STP with the method of NMF.The number of feature images extracted by this method is consistent with the traditional non-negative matrix method,and the size of the feature image is much smaller than the traditional non-negative matrix method.At the same time,the NMSTF method produces more coefficients than NMF.An image corresponds to several points in the low-dimensional space.Several points' co-determination of one image's classification is helpful to eliminate the influence of errors,so as to improve the accuracy of clustering and recognition.We theoretically analyze the solution of the NMSTF problem and derive the itera-tive formula.The theoretical analysis shows that the model is a non-convex optimization problem.The iterative formula is derived theoretically using the Lagrangian multiplier method and KKT condition.The objective function value decreases with the growth of iteration,and finally converges to the convergence value.It is proved that the iterative formula obtained in this paper is correct and effective.We design a NMSTF image clustering algorithm and a large number of experiments has been done.Compared with the traditional NMF algorithm,the convergence rate of the two methods is consistent,but the objective function value of NMSTF is smaller,that is,image loss error is smaller;in the feature extraction,The feature image extracted by NMSTF is smaller,more independent and local,with good physical meaning;in the clustering accuracy,this method has a certain degree of improvement.Furthermore,we realize the application of image recognition on the robot.Based on the design of the above image clustering algorithm,combined with ROS robot operating system and openCV and other open source software packages,we use Kinect vision sensor to take images and realize the robot image recognition by analyzing the image coefficient vector and learning image coefficient vector Clustering.