Worst-Case Linear Discriminant Analysis as Scalable Semidefinite Feasibility Problems

In this paper, we propose an efficient semidefinite programming (SDP) approach to worst-case linear discriminant analysis (WLDA). Compared with the traditional LDA, WLDA considers the dimensionality reduction problem from the worst-case viewpoint, which is in general more robust for classification. However, the original problem of WLDA is non-convex and difficult to optimize. In this paper, we reformulate the optimization problem of WLDA into a sequence of semidefinite feasibility problems. To efficiently solve the semidefinite feasibility problems, we design a new scalable optimization method with quasi-Newton methods and eigen-decomposition being the core components. The proposed method is orders of magnitude faster than standard interior-point based SDP solvers. Experiments on a variety of classification problems demonstrate that our approach achieves better performance than standard LDA. Our method is also much faster and more scalable than standard interior-point SDP solvers based WLDA. The computational complexity for an SDP with $m$ constraints and matrices of size $d$ by $d$ is roughly reduced from $\mathcal{O}(m^3+md^3+m^2d^2)$ to $\mathcal{O}(d^3)$ ($m>d$ in our case).Comment: 14 page

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-based nonlinear discriminant analysis using minimum squared errors criterion for multiclass and undersampled problems

It is well known that there exist two fundamental limitations in the linear discriminant analysis (LDA). One is that it cannot be applied when the within-class scatter matrix is singular, which is caused by the undersampled problem. The other is that it lacks the capability to capture the nonlinearly clustered structure of the data due to its linear nature. In this paper, a new kernel-based nonlinear discriminant analysis algorithm using minimum squared errors criterion (KDA-MSE) is proposed to solve these two problems. After mapping the original data into a higher-dimensional feature space using kernel function, the MSE criterion is used as the discriminant rule and the corresponding dimension reducing transformation is derived. Since the MSE solution does not require the scatter matrices to be nonsingular, the proposed KDA-MSE algorithm is applicable to the undersampled problem. Moreover, the new KDA-MSE algorithm can be applied to multiclass problem, whereas the existing MSE-based kernel discriminant methods are limited to handle twoclass data only. Extensive experiments, including object recognition and face recognition on three benchmark databases, are performed and the results demonstrate that our algorithm is competitive in comparison with other kernel-based discriminant techniques in terms of recognition accuracy. (C) 2009 Elsevier B.V. All rights reserved.National Natural Science Foundation of China [60672046, 60675002]; Fujian Province Science and Technology Foundation [2008H0036]; Specialized Research Fund for the Doctorol Program of Higher Educatio

Robust Face Representation and Recognition Under Low Resolution and Difficult Lighting Conditions

This dissertation focuses on different aspects of face image analysis for accurate face recognition under low resolution and poor lighting conditions. A novel resolution enhancement technique is proposed for enhancing a low resolution face image into a high resolution image for better visualization and improved feature extraction, especially in a video surveillance environment. This method performs kernel regression and component feature learning in local neighborhood of the face images. It uses directional Fourier phase feature component to adaptively lean the regression kernel based on local covariance to estimate the high resolution image. For each patch in the neighborhood, four directional variances are estimated to adapt the interpolated pixels. A Modified Local Binary Pattern (MLBP) methodology for feature extraction is proposed to obtain robust face recognition under varying lighting conditions. Original LBP operator compares pixels in a local neighborhood with the center pixel and converts the resultant binary string to 8-bit integer value. So, it is less effective under difficult lighting conditions where variation between pixels is negligible. The proposed MLBP uses a two stage encoding procedure which is more robust in detecting this variation in a local patch. A novel dimensionality reduction technique called Marginality Preserving Embedding (MPE) is also proposed for enhancing the face recognition accuracy. Unlike Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA), which project data in a global sense, MPE seeks for a local structure in the manifold. This is similar to other subspace learning techniques but the difference with other manifold learning is that MPE preserves marginality in local reconstruction. Hence it provides better representation in low dimensional space and achieves lower error rates in face recognition. Two new concepts for robust face recognition are also presented in this dissertation. In the first approach, a neural network is used for training the system where input vectors are created by measuring distance from each input to its class mean. In the second approach, half-face symmetry is used, realizing the fact that the face images may contain various expressions such as open/close eye, open/close mouth etc., and classify the top half and bottom half separately and finally fuse the two results. By performing experiments on several standard face datasets, improved results were observed in all the new proposed methodologies. Research is progressing in developing a unified approach for the extraction of features suitable for accurate face recognition in a long range video sequence in complex environments