Kernel-based Angle 2DPCA For Face Recognition

With the development of science and technology,face recognition is playing a more and more important role in national defense,business application and daily life.Face recognition is extracting image features and classifying images,and the most important step is feature extraction.Principal component analysis(PCA)as a classical feature extraction method has been successfully applied in the field of face recognition.Nonlinear two-dimensional principal component analysis(K2DPCA)is able to depict the nonlinear features of the image,and retain the two-dimensional data structure and domain information of the original image.However,K2DPCA has some shortcomings: on the one hand,it overemphasizes the data that is farther away because of using the square of the Euclidean distance to measure the similarity between the data,resulting in the method is more sensitive to outliers(occlusion of images,noise,etc.);on the other hand,since the size of the kernel matrix is determined by samples in nonlinear space.The size of the kernel matrix increases exponentially when the sample size is large,which makes K2DPCA difficult to solve.Aiming at these problems,this paper conducts an in-depth study on the robustness and computational complexity of K2DPCA,which is summarized as follows:Aiming at the problem that nonlinear 2DPCA is sensitive to outliers,this paper proposes nonlinear angle 2DPCA(Sin-K2DPCA),which is a non-linear extension of the angle 2DPCA.It maintains the rotational invariance,and improves the robustness to outliers.Sin-K2DPCA uses the F norm as a metric and considers the linear relationship between the reconstruction error and the sample.After mapping the data into a high-dimensional nonlinear space,we minimize sample's relative reconstruction error to obtain a projection matrix.The low-dimensional projection obtained in this way can describe the face information more accurately and overcome the influence of noise to a certain extent.The experimental results on the face database ORL and CUM PIE also prove that this method significantly improves the robustness of K2DPCA.When Sin-K2DPCA is applied to large-scale data,the calculation complexity will be too high and the storage space will be too large due to the large size of the kernel matrix,so that data dimensionality reduction cannot be effectively achieved.In order to further optimize the computational complexity of Sin-K2DPCA,we propose an optimization algorithm based on Cholesky decomposition method called Chol+ Sin K2DPCA.It is an improvement to Sin-K2DPCA,which is not only robust,but also saves computing time and storage space.This method uses the Cholesky decomposition technique of selecting principal elements to approximate the low-rank of large-scale kernel matrix,which avoids the calculation of the entire kernel matrix,reduces the calculation complexity and saves the storage space.The experimental results on small and medium-sized database show that Chol + Sin K2DPCA can reduce the algorithm's sensitivity to noise in the process of selecting the principal element.Meanwhile,the experimental results on large-scale face database show that this method overcomes the problem that the classical K2DPCA method cannot be effectively implemented due to the large size of the core matrix.