Research On Principal Component Analysis Based On L21 Norm

With the development of technology,big data era is coming,and people's lives are full of information processing.Dealing with huge data quickly is an urgent problem we need to face.Feature extraction is an effective solution to handle massive information.Many scholars have carried out wide-ranging and in-depth research on feature extraction.These studies are of great value in practice and also have many challenges.After introducing the research status of the existing feature extraction algorithms,this paper focuses on the principal component analysis algorithm(PCA),and studies the L21norm-based PCA algorithm with good robustness.Traditional machine learning algorithms commonly use L2 norm to measure the sample distance.The advantage of using the L21 norm is that it retains rotation invariance same as using the L2 norm,and it is robus.The algorithm is not sensitive to deviation in input samples.Based on this idea,we combine it with other algorithms,and the following aspects are studied:For the 2DPCA algorithm,an improved 2DPCA based on Frobenius norm is studied.A new objective function is proposed in 2DPCA,and a solution to the generalized optimization problem is introduced.It is applied to the solution process of the new objective function,and an iterative algorithm is obtained to solve the problem based on Frobenius norm.This algorithm is directly based on the image matrix operation compared to L21 PCA,skipping the vectorization with image matrix,thus can reduce the amount of calculation and speed up the algorithm.The algorithm with good robustness is implemented in several common data sets and the effectiveness of the algorithm is verified.For the GPCA algorithm,an improved GPCA based on Frobenius norm is studied.We adjust the objective function in the optimization problem.Specifically the square of the Frobenius norm obtained from image matrix is removed,so that the algorithm is not sensitive to the deviation in the sample.GPCA based on Frobenius norm take use of the 2DPCA algorithm based on Frobenius norm.Compared with GPCA algorithm,the decision condition in algorithm convergence is changed.Detailed theoretical derivation is used to illustrate the selection of decision conditions.In common face database ORL,YALE and FERET,the GPCA algorithm based on Frobenius norm was compared with the GPCA algorithm.The nearest classifier is selected and the Euclidean distance is chosen to measure the sample distance.The proposed algorithm shows better performance in recognition.Based on a kernelization framework,the kernel L21 PCA was studied.A general framework of learning algorithm is introduced combining the kernel function method.As long as the algorithm satisfies several specific conditions,the framework can be directly applied to obtain the kernel method of the learning algorithm.Combined with the previous L21 PCA algorithm,the input data is first preprocessed using full rank KPCA,and the data obtained is used as the input of L21 PCA algorithm.Then the nearest neighbor classifier is used to identify the test samples.The feasibility of the kernel method is verified by experiments.