Feature Extraction Based On Locality Preserving Subspace Analysis With Its Application In Face Recognition

As one fundamental problem in pattern recognition, extracting the effective features is of paramount importance for face recognition. Among all the algorithms, due to the characteristic of low computation and desirable performance, subspace algorithms have dominated this filed. Principal Component Analysis and Linear Discriminant Analysis are the first two classical algorithms and achieved great success. But some researchers suggest that the face images may reside in nonlinear manifolds, and Principal Component Analysis and Linear Discriminant Analysis that are based on Euclidean space can not explain the nonlinear manifold structure, thus the feature extracted are not optimal for classification. Locality Preserving Projection is a linear approximation of one manifold learning called Laplacian Eigenmap, and can preserve the manifold structure. Based on locality preserving projections, some work are carried out from the perspective of statistics, nonlinear feature extraction, two-dimensional image feature extraction and the small sample size problem, to be specific, they are:1) Due to the fact that Locality Preserving Projection is an unsupervised method, that is, it does not consider the class information, and the features extracted have redundancy, Uncorrelated Discriminant Locality Preserving Projection is proposed. LPP only considers the locality and does not take the class information into account; also the correlation of features is ignored. Some methods have utilized the class information, but mostly the inter-class information is not considered. The proposed algorithm preserves the locality like LPP, and the class information is taken into account, also an uncorrelated constraint is imposed so as to makes the features uncorrelated, hence the redundancy is greatly reduced, all these ensures that the proposed algorithm have more discriminant power.2) Locality Preserving Projection is a linear method in nature, and only considers the locality but the differences of samples are ignored, what's more, the features extracted are not orthogonal. To solve these problems, Kernel Orthogonal Discriminant Locality Preserving Difference Maximization Analysis is proposed, which first map the samples into one high dimensional space by kernel trick so as to make the samples in that high dimensional space linearly separatable, and then the locality and differences of samples are taken into account, lastly an orthogonal constraint is imposed to help the reconstruction of samples.3) The original Locality Preserving Projection is based on vectors, which means that it has to convert the image matrix into a vector, during which, the pixel structure will be destroyed and it will result in the small sample size problem, both of which are not beneficial for classification. To solve these problems, unitary-subspace based 2D Discriminant Locality Preserving Projection is proposed, which takes the class information into account and it is based on the image matrix to extract the features horizontally and vertically. Then a complex matrix is constructed in the unitary space. At last the features are obtained by linear discriminant analysis. As can be seen that it avoids the small sample size problem and the pixel structure is preserved, both of which are beneficial for classification.4) In face recognition, due to the fact that the dimension of samples is much greater than the number of samples, small sample size problem is a universal problem for subspace algorithms. To better discovering the low dimensional manifolds and solving the small sample size problem, Null Space Locality Preserving Discriminant Intrinsicfaces and Supervised Laplacian Discriminant Analysis are proposed. The former makes full use of intrapersonal differences and individual differences and employs the idea of manifold learning so that the similarity in the intra-class is preserved while the separability of samples from different classes is enlarged by discriminant criterion. The optimal feature vectors are extracted from the null space of intrapersonal locality preserving difference scatter matrix, which avoids the singularity and the small sample size problem is solved. The latter is to minimize the intra-class Laplacian scatter while maximize the inter-class Laplacian scatter. The null space of total Laplacian scatter matrix is discarded firstly, then the intra-class Laplacian scatter matrix is projected onto the range space of the total Laplacian scatter matrix, and then the solution is reduced to the eigen-problem in that space. On one hand, it only operates on one smaller matrix and thus it is efficient for computation; on the other hand, the small sample size problem is artfully avoided while there is no information loss, both of which improve the efficiency and recognition rate.Finally, the conclusions are drawn and some future works are pointed out.