Relaxed 2-D Principal Component Analysis by LpL_p Norm for Face Recognition

A relaxed two dimensional principal component analysis (R2DPCA) approach is proposed for face recognition. Different to the 2DPCA, 2DPCA-$L_1$ and G2DPCA, the R2DPCA utilizes the label information (if known) of training samples to calculate a relaxation vector and presents a weight to each subset of training data. A new relaxed scatter matrix is defined and the computed projection axes are able to increase the accuracy of face recognition. The optimal $L_p$-norms are selected in a reasonable range. Numerical experiments on practical face databased indicate that the R2DPCA has high generalization ability and can achieve a higher recognition rate than state-of-the-art methods.Comment: 19 pages, 11 figure

Kernel Multivariate Analysis Framework for Supervised Subspace Learning: A Tutorial on Linear and Kernel Multivariate Methods

Feature extraction and dimensionality reduction are important tasks in many fields of science dealing with signal processing and analysis. The relevance of these techniques is increasing as current sensory devices are developed with ever higher resolution, and problems involving multimodal data sources become more common. A plethora of feature extraction methods are available in the literature collectively grouped under the field of Multivariate Analysis (MVA). This paper provides a uniform treatment of several methods: Principal Component Analysis (PCA), Partial Least Squares (PLS), Canonical Correlation Analysis (CCA) and Orthonormalized PLS (OPLS), as well as their non-linear extensions derived by means of the theory of reproducing kernel Hilbert spaces. We also review their connections to other methods for classification and statistical dependence estimation, and introduce some recent developments to deal with the extreme cases of large-scale and low-sized problems. To illustrate the wide applicability of these methods in both classification and regression problems, we analyze their performance in a benchmark of publicly available data sets, and pay special attention to specific real applications involving audio processing for music genre prediction and hyperspectral satellite images for Earth and climate monitoring

Generalized Two-Dimensional Quaternion Principal Component Analysis with Weighting for Color Image Recognition

A generalized two-dimensional quaternion principal component analysis (G2DQPCA) approach with weighting is presented for color image analysis. As a general framework of 2DQPCA, G2DQPCA is flexible to adapt different constraints or requirements by imposing $L_{p}$ norms both on the constraint function and the objective function. The gradient operator of quaternion vector functions is redefined by the structure-preserving gradient operator of real vector function. Under the framework of minorization-maximization (MM), an iterative algorithm is developed to obtain the optimal closed-form solution of G2DQPCA. The projection vectors generated by the deflating scheme are required to be orthogonal to each other. A weighting matrix is defined to magnify the effect of main features. The weighted projection bases remain the accuracy of face recognition unchanged or moving in a tight range as the number of features increases. The numerical results based on the real face databases validate that the newly proposed method performs better than the state-of-the-art algorithms.Comment: 15 pages, 15 figure