Linear Discriminant Analysis Based On Non-Euclidean Framework

With the information age’ arrival, it is inevitable to encounter numbers of high-dimensional data in many practical applications. The high-dimensional data burdens the computational requirement and brings “the curse of dimensionality” when doing researches. Therefore, if we want to get the intrinsic structures of information hidden in the data and avoid the curse of dimensionality problem, dimensionality reduction is essential to high-dimensional data. It plays a vital role in related scientific recognition as a way of dealing with the he curse of dimensionality”, which is the important topic for researchers.The thesis focuses on the theories and method of dimensionality reduction for high-dimensional data and it’s applications in face recognition. In the paper, some current techniques of dimensionality reduction are reviewed, such as Principal Component Analysis, Fisher Discriminat Analysis, dimensionality reduction method based on kernel function and dimensionality reduction method based on 2D data. A new method, i.e. Adaptive Regularization based Kernel Two Dimensional Discriminant Analysis(ARKTDDA) is presented. Due to the manifold regularization is defined on the original feature space in typical semi-supervised dimension reduction techniques. However, the regularization construction involved in these methods is not contributed to subsequent classification. Therefore, the method is proposed. Firstly, each image matrix is transformed as the product of two orthogonal matrices and a diagonal matrix by using the Singular Value Decomposition method, in which the column vectors of two orthogonal matrices are transformed into high dimensional space by two kernel map functions. Then, the adaptive regularization is defined on the low-dimensional feature space, which is integrated with two dimensional matrix nonlinear method into one single objective function. By altering iterative optimization, the discriminating information in two kernel subspaces is extracted.ARKTDDA algorithm makes experiments on the Extended YaleB and CMU PIE face database. Experimental results on two face data sets demonstrate that the proposed algorithm obtains considerable improvement in discrimination accuracy.