| The color face image recognition problem is common in daily production and life.This problem has the characteristics of mutually interrelated color channels,large scale and high complexity.It has become one of the hardest problems in modern information science.As one of the important features of color images,color information can help humans to accurately identify,compress or reconstruct color images.However,color images require more storage space than grey images,and generate larger-scale color data,which brings huge challenges to the modeling and solution of color face image recognition.If the two-dimensional principal component analysis method in the real field is directly applied to handle the color face image recognition problem,the coupling between color channels cannot be effectively preserved.The color face image recognition rate falls short of the expected goal.In addition,the existing quaternion matrix principal component analysis methods are difficult to effectively handle more complicated color face image recognition problem.In view of this,this thesis proposes four bilateral quaternion matrix principal component analysis methods for color face image recognition in different scenarios,and applies them to practical color face image recognition.Firstly,since the single-direction quaternion matrix principal component analysis method has a low rate of color face image recognition,a bilateral quaternion matrix principal component analysis method is proposed.This method extracts principal components from both row and column directions simultaneously,which reduces the dimension of the extracted features and improves the recognition performance;In order to further improve the recognition rate,a class-weighted bilateral quaternion matrix principle component analysis method is proposed.This method uses the label information to generate the weight of each class of training samples,and the training sample class who has large variance is emphasized.The proposed method is applied to handle the color face image recognition problem and compared with three classical algorithms.The experimental results indicate that the proposed method has a better recognition performance.Secondly,in order to overcome the week anti-noise defect of bilateral quaternion matrix principal component analysis method,a relaxed bilateral quaternion matrix principal component analysis method is proposed.This method integrates supervised and unsupervised methods to improve the performance of anti-noise and face recogniton;In order to improve the speed of calculating principle components,a Lanczos bidiagonalization based algorithm is presented;In order to further improve the color face recognition rate of the proposed method,a principal component weighting strategy is designed,which emphasizes principal components on which the projections of training samples have large divergence and reduces the effect of principal components with small divergence.The proposed method is applied to handle the color face image recognition problem and compared with two bilateral quaternion matrix principal component analysis methods proposed above.The experimental results indicate that the proposed method has higher face recognition rate and anti-noise performance.Next,in order to solve the problem of losing principal component sparseness caused by L2-norm constraint,a generalized bilateral quaternion matrix principal component analysis method with Lp-norm constraint is proposed.In this method,the orthogonality constraint of principal components is added to the optimization model,and the shrinkage technique and minimum-maximization framework are applied to design a quaternion optimization algorithm.A new method is presented to calculate the weighting vector of principle components.The proposed method is applied to color face image recognition and reconstruction,and compared with two typical methods.The experimental results show that the generalized bilateral quaternion matrix principal component analysis method is superior to the contrast methods in terms of recognition rate and image reconstruction ratio.Finally,in order to improve the weak anti-noise ability of the generalized bilateral quaternion matrix principal component analysis method,a generalized relaxed bilateral quaternion matrix principal component analysis method is proposed.This method uses relaxation technology to integrate supervised and unsupervised learning methods and improves the recognition and anti-noise performance;In order to solve the problem of weighting method selection in color face image recognition,a data-driven principle component weight vector optimization strategy is designed.For the problem of model parameter selection,an optimal parameter selection strategy in alternating directions is proposed.The proposed method is applied to handle the color face image recognition problem,and compared with seven classical two-dimensional principal component analysis methods and nine neural network methods.The experimental results indicate that the generalized relaxed bilateral quaternion matrix principal component analysis method has higher recognition and anti-noise performance.The proposed methods enrich the theory of quaternion matrix principal component analysis,improve the performance of the principal component analysis method,solve the color face image recognition problem well,and provide a reference for other color image recognition and reconstruction problems,and thus,have important theoretical significance and practical value.This thesis has a total of 27 figures,26 tables,and 132 references. |
