Incremental Sorting Algorithm -
Issam Dagher International Journal of Biometrics and Bioinformatics (IJBB), Volume (4): Issue (2) 86 Incremental PCA-LDA Algorithm Issam Dagher email@example.com Department Of Computer Engineering University of Balamand POBOX 100,Elkoura,Lebanon Abstract In this paper a recursive algorithm of calculating the discriminant features of the PCA-LDA procedure is introduced. This algorithm computes the principal components of a sequence of vectors incrementally without estimating the covariance matrix (so covariance-free) and at the same time computing the linear discriminant directions along which the classes are well separated. Two major techniques are used sequentially in a real time fashion in order to obtain the most efficient and linearly discriminative components. This procedure is done by merging the runs of two algorithms based on principal component analysis (PCA) and linear discriminant analysis (LDA) running sequentially. This algorithm is applied to face recognition problem. Simulation results on different databases showed high average success rate of this algorithm compared to PCA and LDA algorithms. The advantage of the incremental property of this algorithm compared to the batch PCA-LDA is also shown. Keywords: Recursive PCA-LDA, principal component analysis (PCA), linear discriminant analysis (LDA), face recognition. 1. INTRODUCTION A large number of face recognition techniques use face representations found by unsupervised statistical methods. Typically, these methods find a set of basis images and represent faces as a linear combination of those images. For the same purpose, this paper merges sequentially two techniques based on principal component analysis and linear discriminant analysis. The first technique is called incremental principal component analysis (IPCA) which is an incremental version of the popular unsupervised principal component technique. The traditional PCA algorithm  computes eigenvectors and eigenvalues for a sample covariance matrix derived from a well known given image data matrix, by solving an eigenvalue system problem. Also, this algorithm requires that the image data matrix be available before solving the problem (batch method). The incremental principal component method updates the eigenvectors each time a new image is introduced. The second technique is called linear discriminant analysis (LDA) . LDA is a data separation technique. The objective of LDA is to find the directions that will well separate the different classes of the data once projected upon. The set of human faces is represented as a data matrix X where each row corresponds to a different human face. Each image x, represented by a (n,m) matrix of pixels, will be represented by a high dimensional vector of nxm pixels. Turk and Pentland  were among the first who used this representation for face recognition.