The success of Linear Discriminant Analysis (LDA) is due in part to the simplicity of its formulation, which reduces to a simultaneous diagonalization of two symmetric matrices A and B. However, a fundamental drawback of this approach is that it cannot be efficiently applied wherever the matrix A is singular or when some of the smallest variances in A are due to noise. In this paper, we present a factorization of A −1 B and a correlation-based criterion that can be readily employed to solve these problems. We provide detailed derivations for the linear and non-linear classification problems. The usefulness of the proposed approach is demonstrated thoroughly using a large variety of databases.

Abstract—When the feature dimension is larger than the number of samples the small sample-size problem occurs. There is great concern about it within the face recognition community. We point out that optimizing the Fisher index in linear discriminant analysis does not necessarily give the best performance for a face recognition system. We propose a new regularization scheme. The proposed method is evaluated using the Olivetti Research Laboratory database, the Yale database, and the Feret database. Index Terms—Face recognition, optimization, regularized discriminant analysis (RDA), small sample-size problem. I.

This paper proposes a novel pipeline to develop a Face Recognition System robust to illumination variation. We consider the case when only one single image per person is available during the training phase. In order to utilize the superiority of Linear Discriminant Analysis (LDA) over Principal Component Analysis (PCA) in regard to variable illumination, a number of new images illuminated from different directions are synthesized from a single image by means of the Quotient Image. Furthermore, during the testing phase, an iterative algorithm is used for the restoration of frontal illumination of a face illuminated from any arbitrary angle. Experimental results on the YaleB database show that our approach can achieve a top recognition rate compared to existing methods and can be integrated into real time face recognition system.

Abstract—Pose problem is a big challenge for applying face recognition technology under real world conditions. In this paper, appearance based approach was proposed to recognize face across front and non-frontal view images by reconstructing frontal view features. Statistical learning method based on sample images is applied to find transformation matrix which encapsulated general knowledge of pose transition in feature subspace, therefore, different view feature vectors constituted linear equations and transformation matrix can be solved from the equations by least square (LS) approach. Experimental results on popular FERET and CMU databases showed that the proposed method could cope with the head rotation roughly within half profile view. Compared with model based approaches, this method is not dependent on heavy computation and has merit of easy implementing in live conditions. Index Terms—face recognition, feature reconstruction, statistical learning, subspace transformation, pose problem. I.

This study is a result of a successful joint-venture with my adviser Prof. Dr. Muhittin Gökmen. I am thankful to him for his continuous assistance on preparing this project. Special thanks to the assistants of the Computer Vision Laboratory for their steady support and help in many topics related with the project.

journal homepage: www.elsevier.com/locate/patrec Improved direct LDA and its application to DNA microarray gene expression data

Linear subspace learning (LSL) is a popular approach to image recognition and it aims to reveal the essential features of high dimensional data, e.g., facial images, in a lower dimensional space by linear projection. Most LSL methods compute directly the statistics of original training samples to learn the subspace. However, these methods do not effectively exploit the different contributions of different image components to image recognition. We propose a novel LSL approach by sparse coding and feature grouping. A dictionary is learned from the training dataset, and it is used to sparsely decompose the training samples. The decomposed image components are grouped into a more discriminative part (MDP) and a less discriminative part (LDP). An unsupervised criterion and a supervised criterion are then proposed to learn the desired subspace, where the MDP is preserved and the LDP is suppressed simultaneously. The experimental results on benchmark face image databases validated that the proposed methods outperform many state-of-the-art LSL schemes. 1.