Abstract
Linear Discriminant Analysis (LDA) is a well-known scheme for feature extraction and dimension. It has been used widely in many applications involving high-dimensional data, such as face recognition, image retrieval, etc. An intrinsic limitation of classical LDA is the so-called singularity problem, that is, it fails when all scatter matrices are singular. A well-known approach to deal with the singularity problem is to apply an intermediate dimension reduction stage using Principal Component Analysis (PCA) before LDA. The algorithm, called PCA + LDA, is used widely in face recognition. However, PCA + LDA have high costs in time and space, due to the need for an eigen-decomposition involving the scatter matrices. Also, Two Dimensional Linear Discriminant Analysis (2DLDA) implicitly overcomes the singular- ity problem, while achieving efficiency. The difference between 2DLDA and classical LDA lies in the model for data representation. Classical LDA works with vectorized representation of data, while the 2DLDA algorithm works with data in matrix representation. To deal with the singularity problem we propose a new technique coined as the Weighted Scatter-Difference-Based Two Dimensional Discriminant Analysis (WSD2DDA). The algorithm is applied on face recognition and compared with PCA + LDA and 2DLDA. Experiments show that WSD2DDA achieve competitive recognition accuracy, while being much more efficient.
Highlights
Linear Discriminant Analysis [1,2,3,4,5] is a well-known method which projects the data onto a lower-dimensional vector space such that the ratio of between-class distance to the within-class distance is maximized, achieving maximum discrimination
Classical Linear Discriminant Analysis (LDA) works with vectorized representation of data, while the 2-dimensional LDA (2DLDA) algorithm works with data in matrix representation
For the comparison of cup time(s) for feature extraction of ORL databases, it can be seen from Table 2, 2DLDA, 2DPCA and WSD2DDA takes little time than Principal Component Analysis (PCA) + LDA, because the size of the covariance matrix in 2DLDA is ( Nx N y ) and the size of covariance matrix in PCA + LDA is (P × P) where P is size ( Nx N y )
Summary
Linear Discriminant Analysis [1,2,3,4,5] is a well-known method which projects the data onto a lower-dimensional vector space such that the ratio of between-class distance to the within-class distance is maximized, achieving maximum discrimination. All scatter matrices in question can be singular since the data is drawn from a very high-dimensional space, and in general, the dimension exceeds the number of data points This is known as the under sampled or singularity problem [6]. The within-class scatter matrix is always singular, making the direct implementation of the LDA algorithm an intractable task To overcome these problems, a new technique called 2-dimensional LDA (2DLDA) was recently proposed. A new technique called 2-dimensional LDA (2DLDA) was recently proposed This method directly computes the eigenvectors of the scatter matrices without conversion a matrix into a vector. Tang et al [13] have introduced a weighting scheme to estimate the within-class scatter matrix using a so called relevance weights This technique was used in face recognition by Chougdali and all [14]
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