Research Of Feature Extraction And Recognition Theory Based On Subspace Learning

With the popularization of smart phones and monitoring systems,massive data is being generated in real life.How to extract the required knowledge from these high-dimensional data becomes more and more important.Subspace learning can effectively analyze and utilize this data,and it has been widely used in various data mining and computer vision tasks.However,traditional linear subspace learning is vector based method,which produces very high-dimensional vectors when dealing with high-order tensors,leading to the estimation of a large number of parameters.Multilinear subspace learning is a higher-order generalization of linear subspace learning,it directly maps high-dimensional tensors to low-dimensional spaces without vectorization,which can improve the computational efficiency and preserve the original spatial structure of the data.But unfortunately,the current research on multilinear subspace learning is not sufficient.How to further enrich the theory of multilinear subspace learning and apply it to different classification tasks has become a research difficulty in the field of pattern recognition.Single image based pattern recognition methods are sensitive to various interference and degradation factors,and they require to ensure high imaging quality and resolu-tion.While image set data contains various kinds of images of an object in different expressions,different postures and different illumination conditions,it can provide vari-ous properties of the pattern,thereby overcoming the influence of different factors such as imaging quality,illumination and so on.In recent years,pattern recognition based on image set has become a new research hotspot and difficulty.Generally speaking,im-age set data often lies in a high-dimensional space,it contains many redundant features,and there exist correlations between different images.Therefore,it is significant to learn the latent low-dimensional embedding of image set data,which contributes to improving the classification effect and reducing the complexity of the model.Based on the above consideration,this thesis focuses on subspace learning,and the two aspects of high-order data dimensionality reduction and image set classification are deeply studied.By incor-porating multiple rank multi-linear,manifold learning,sparse representation,localization and multi-kernel learning techniques,we explore the application of subspace learning in different tasks.The main contributions of this thesis are as follows:(1)The existing two-directional two-dimensional canonical correlation analysis method((2D)~2CCA)assumes that the rank of the projection matrix is 1,but this assump-tion is generally not true in real-world scenarios.This paper intends to study a more common image low-dimensional embedding technology,i.e.,the projection matrix is a general multi-rank matrix,and then the multiple rank multi-linear canonical correlation analysis(MRCCA)is developed.MRCCA assumes that the rank of the projection matrix is k,then by performing singular value decomposition to the pro-jection matrices,k pairs left transforms and k pairs right transforms are obtained.In order to jointly solve these transformation vectors,the idea of canonical correla-tion analysis(CCA)is used to construct objective function,that is,the transformed data is required to have the maximum correlation in the low-dimensional embedded space.At the same time,through the theoretical analysis,we find that the rank kof the projection matrix can be seen as a balance parameter between the calculation time and the recognition accuracy.If k becomes larger,the classification accuracy will increase,the corresponding calculation time will also increase,and vice ver-sa.The feasibility in feature extraction and recognition of the proposed method is verified by the experimental results on multiple real life data sets.(2)The traditional CCA and(2D)~2CCA algorithms are unsupervised multiple feature extraction methods.Hence,introducing the supervised information of samples into these methods should be able to promote the classification performance.In this paper,a novel method is proposed to carry out the multiple feature extraction for classification,called two-directional two-dimensional supervised canonical cor-relation analysis((2D)~2SCCA),in which the supervised information is added to the criterion function.Then,by analyzing the relationship between generalized canonical correlation analysis(GCCA)and(2D)~2SCCA,another feature extraction method called multiple rank multi-linear supervised canonical correlation analysis (MSCCA)is also developed.The convergence behavior and computational com-plexity of the algorithms are analyzed.(2D)~2SCCA is a special case of MSCCA,and MSCCA can also be seen as a supervised generalization of MRCCA.The 1-NN method is used to classify the images,after obtaining the optimal low-dimensional embedding.A large number of experimental results on object recognition and face recognition show that the proposed method achieves good recognition results.(3)Two-dimensional canonical correlation analysis(2DCCA)directly takes the image matrix as input instead of vectorizing it,which can effectively maintain the spatial information of the image,reduce the computational cost and avoid the problem of “curse of dimensionality”.However,2DCCA is a linear method,it fails to effec-tively extract nonlinear features of images.Therefore,this paper first develops a nonlinear two-dimensional canonical correlation analysis method based on the idea of locality,which is called two dimensional locality preserving canonical correlation analysis(2DLPCCA).Based on the equivalent formulation of 2DCCA,2DLPCCA uses local neighbor information to discover the internal structure of the data.In addition,because the sparse reconstruction coefficient has natural discriminative ability,from the perspective of the similarity matrix construction,this paper fur-ther proposes a two dimensional sparsity preserving canonical correlation analysis (2DSPCCA)framework.Finally,the effectiveness of the proposed algorithms is verified on different real life databases.(4)Traditional image set classification methods usually use a single model to represent image sets,such as linear subspaces,convex hulls,etc.These methods can only extract discriminant information from one aspect of the image set,while ignoring other complementary information.Therefore,in order to integrate the information from different modeling methods,a novel image set classification method,termed as multi-model fusion metric learning(MMFML),is proposed.MMFML uses the mean vector,linear subspace,and covariance matrix to jointly represent an image set,such that the complementary discriminant information can be used to improve the classification accuracy.Since the above three representation methods lie on different spaces,it is difficult to measure the distance between them.In order to reduce the dissimilarity between the heterogeneous spaces,we first embed them into the high dimensional Hilbert spaces using the corresponding kernel function-s.After embedding,the final objective function is then learned from the Hilbert space to a shared Euclidean subspace,and sequentially we can get three two-model fusion Modes.Finally,the image set is classified in the low-dimensional shared subspace.The experimental results on Honda,ETH-80 and Youtube Celebrities three databases verify the effectiveness of the proposed algorithm.