Research On Centered Weight Based Principal Component Analysis

In the fields of data analysis,pattern recognition,machine learning,etc.,principal component analysis is one of the classic feature extraction algorithms.Whether it is one-dimensional principal component analysis or two-dimensional principal component analysis,they all use the square of the Euclidean distance as a measure of similarity.As a result,more information is learned from farther distances and algorithms are less robust.Although most existing robust principal component analysis and two-dimensional principal component analysis methods based on F-norm can alleviate the sensitivity to outliers in the field of image analysis and pattern recognition.However,the existing methods not only do not retain the data structure information in the optimization target,nor do they have the robustness of generalized performance.In order to solve the above problems,this paper proposes two new models based on centered weights,namely centered principal component analysis(C-PCA)and generalized centered two-dimensional principal component analysis(GC-2DPCA).In view of the fact that the existing principal component analysis method does not make full use of the structural information of the data,this paper proposes a principal component analysis based on the centered weight,namely C-PCA.The algorithm utilizes the idea of linear kernel principal component analysis(L-KPCA),and uses the centered weight to measure the similarity,which can better preserve the structure of the data.Meanwhile,the algorithm is the optimization model based on l₂-norm to maximize the covariance between samples.The singular value decomposition method is used to obtain the reconstruction weight matrix of C-PCA,and then the centered matrix is used to obtain the recognition weight matrix of C-PCA.Experiments on the Extended Yale B,CMU-PIE,and AR face databases with noise show the efficiency of the algorithm.C-PCA does improve classification performance compared to the existing class of principal component analysis methods,but it still retains a weight matrix that is not robust enough to reconstruct errors.Aiming at the defects of C-PCA,this paper proposes a two-dimensional principal component analysis model based on l_2,p-norm,which has robust generalization performance,still retains rotation invariance,and adopts a new non-greedy iterative algorithm.Solving the model,the optimization time will be shorter,the convergence speed will be faster,and the better objective function value will be obtained.The GC-2DPCA still retains the characteristics that the C-PCA using similar information to learn the internal structure of the data,and also obtains two different and closely related weight matrices.On this basis,GC-2DPCA will make full use of the advantages of l_2,p-norm,and further explore the connection between internal data to achieve a more robust generalization model.By applying GC-2DPCA to the extended Yale B,CMU-PIE,and AR face database with noise for image reconstruction task and image recognition task,it can be concluded that the recognition efficiency of the algorithm is relatively improved by 4.9%and the reconstruction error is relatively low by 5.8%.