Color Image Recognition Based On Quaternion Principal Component Analysis

In recent years,the application of quaternion and quaternion matrix in quaternion method has become a key research topic in the field of image recognition,which is of great significance to artificial intelligence and engineering computing.Based on the detailed understanding of the algebraic basic principle of quaternion matrix,its eigenvalue theory is an important concept to solve the various applications based on quaternion.In fact,there are many ways to solve eigenvalue problems with conventional matrices,but it is often more complicated to solve eigenvalue problems with quaternion matrices.Starting from the basic theory knowledge of quaternion,this paper expounds three kinds of principal component analysis methods based on quaternion theory system.In the process of applying the feature decomposition of quaternion matrix to color face image recognition,QPCA,Q2 DPCA and QBDPCA methods are formed.Based on the Schatten-P norm two-way two-dimensional principal component analysis model,an iterative algorithm is proposed to solve the Schatten-P norm two-way two-dimensional principal component analysis model optimization scheme.In the process of image recognition and classification,the combination effect of color image recognition based on quaternion representation model and three kinds of classifiers(nearest neighbor classifier,support vector machine classifier and generalized regression neural network classifier)is explored.In addition,a series of comparison experiments were carried out between two-dimensional principal component analysis model and bilateral two-dimensional principal component analysis model based on Frobenius norm,Nuclear norm and Schatten-p norm,and the optimal color image recognition rate was obtained by combining the difference comparison experiments of image recognition of various classifiers.The characteristics of three kinds of classifiers are summarized.In terms of computation time,the nearest neighbor classifier takes longer time than the other two classifiers.In terms of recognition accuracy,SVM classifier has the best performance.In terms of stability,the generalized neural network classifier has the best robustness.Thus,the optimal color image recognition rate based on different norms is obtained,and its validity and feasibility are verified.