Study Of L21-norm Based Feature Extraction

PCA and LDA are two classical feature extraction algorithms for pattern recognition and machine learning.However,when applying the above two methods to the image data,it is necessary to transform the image data represented by the image matrix into the corresponding image vector form,which will result in the loss of data structure information.In order to address these problems,2DPCA and 2DLDA are proposed.However,2DPCA and 2DLDA all employs the square Euclidean distance to measure the similarity between the images,thus making these two algorithms sensitive to the presence of noise and occlusion.In view of the above problems,this paper starts from the similarity measurement of the sample,and implements L21 norm based 2DPCA and L21 norm based 2DLDA.The main contents of the thesis include:Aiming at the shortcomings of 2DPCA sensitive to outliers,a L21 norm based two-dimensional principal component analysis is proposed,which employs L21 norm to measure the similarity between data samples and thus can maintain the geometry structure of the data.In this paper,the problem is transformed into the optimization problem of the matrix trace.Using the singular value decomposition of the matrix,we employs a non-greedy iterative algorithm to obtain the local optimal solution of the model.Experimental results on Extended Yale B,PIE,LFWcrop and AR face database show that the algorithm can obtain more robust feature,shorter run time,better experimental results and local convergence.For the defect of 2DLDA being obviously degenerated on noisy images,we propose L21-norm based two-dimensional linear discriminant analysis,which employs L21-norm to measure interclass and intra-class scattered distance and thus can well preserve the geometric structure and the non-greedy iterative algorithm can maximize the objective function value.Through constructing an auxiliary function and combined with the projection sub-gradient method to optimize the projection matrix in a whole and thus obtaining a more optimal objective value.Experimental results on Extended Yale B,PIE and AR face database show that the algorithm proposed in this paper can obtain more robust discriminant features,better experimental results and better convergence.