Feature Extraction Based On Correlation Projection Analysis And Its Application To Image Recognition

Feature extraction is one of the most basic problems of pattern recognition. For image recognition tasks, extracting the effective image feature is a crucial step. As the classical and popular technique for feature extraction, linear and nonlinear projection analysis methods have been deeply researched and are verified to be effective in the application of image recognition. However, the linear and linear projection analysis methods are processing mainly on one feature set of the patterns. It is unsuitable to apply it to directly fuse and extract the features of multi-view data. Correlation projection analysis, including canonical correlation analysis (CCA) and partial least squares (PLS), has been widely employed in multiple feature fusion and extraction. It has obtained good recognition results in the application of image classification. In this dissertation, we focus on researching the correlation projection analysis and its variants, in order to increase the discriminative ability of extracted features. Our work mainly includes the following parts:(1) For using locality preserving canonical correlation analysis (LPCCA) to pattern classification and acquiring good results, a supervised LPCCA (SLPCCA) is proposed to incorporate the class label information. Through maximizing the weighted correlation between corresponding samples and their near neighbors belonged to the same class, it effectively utilizes the class label information and improves the stabilization and effectiveness of the algorithm. In addition, the proposed algorithm can effectively fuse the discrimination information of DCCA without the restriction of total class numbers. Besides, based on the kernel trick, a kernel SLPCCA (KSLPCCA) is also proposed in order to extract nonlinear features of the data.(2) CCA has been extensively researched and aims at extracting statistically uncorrelated features via conjugate orthonormalization constraints of the projection directions. However, there exist two problems. First, the formulated directions under conjugate orthonormalization are not reliable when the training samples are few and the covariance matrix is not exactly estimated. Secondly, this widely pursued property is focused on data representation rather than task discrimination. It is not suited for classification problems when the samples that belong to different classes do not share the same distribution type. An orthogonal regularized CCA (ORCCA) is proposed to avoid the above questions and extract more discriminative features via orthogonal constraints and regularization parameters.(3) Sparsity preserving projections (SPP) aim to preserve the sparse reconstructive relationship of the data, and contain natural discriminating information even without class labels. Enlightened by this, we propose a sparsity preserving canonical correlation analysis (SPCCA). It can not only fuse the discriminative information of two feature sets efficiently but also constrain the sparse reconstructive relationship among each feature set in order to increase the representational power and have good discrimination capability of the features extracted by SPCCA. Based on SPCCA, sparsity regularized discriminant canonical correlation analysis (SrDCCA) is proposed through semi-supervised learning on partly labeled samples. Extensive experiments on both handwritten numerals classification and face recognition demonstrate that the proposed methods can effectively enhance the recognition performance.(4) Multiple component analysis (MCA) is proposed for feature extraction of the multi-view data. CCA and PLS are always used as fusing two feature sets. How to extend them to fuse multiple features in a generalized way is still an unsolved problem. In this paper, a novel feature fusion method called MCA is proposed. By constructing a higher-order tensor, all kinds of information are fused into the covariance tensor. Then orthogonal subspaces corresponding to each feature set are learned through tensor singular value decomposition (SVD) that couples dimension reduction and feature fusion together. Compared with multiple feature fusion by subspace learning (MFFSL), our method has the ability to represent fused data more efficiently and discriminatively in very few components. And it is shown that PCA (principle component analysis) and PLS are special cases of our method when there are only one set and two sets of features respectively. Extensive experiments on both handwritten numerals classification and face recognition demonstrate the effectiveness and robustness of the proposed method.(5) Two-dimensional mutual subspace method (2DMSM) and multiple principle angles embedding (2DMPE) are proposed for image set classification. Based on two-dimensional principle component analysis,2DMSM is proposed to retain the underlying data structure of images which has been broken by vectorizing the image matrix into a high dimensional vector in the application of image set classification. Additionally,2DMPE is also proposed which jointly considers both’local’and’global’canonical correlations by iteratively learning a global discriminative subspace, on wich the angle among multiple subspaces of the same class is minimized while that of different classes is maximized. It can not only enhance the discriminative ability of subspaces, but also decrease the space storages and the time costing of classifying the newly test samples.