Jieping Ye, Ravi Janardan, Qi Li
Linear Discriminant Analysis (LDA) is a well-known scheme for feature extraction and dimension reduction. It has been used widely in many ap- plications involving high-dimensional data, such as face recognition and image retrieval. An intrinsic limitation of classical LDA is the so-called singularity problem, that is, it fails when all scatter matrices are singu- lar. A well-known approach to deal with the singularity problem is to apply an intermediate dimension reduction stage using Principal Com- ponent Analysis (PCA) before LDA. The algorithm, called PCA+LDA, is used widely in face recognition. However, PCA+LDA has high costs in time and space, due to the need for an eigen-decomposition involving the scatter matrices. In this paper, we propose a novel LDA algorithm, namely 2DLDA, which stands for 2-Dimensional Linear Discriminant Analysis. 2DLDA over- comes the singularity problem implicitly, while achieving efﬁciency. The key difference between 2DLDA and classical LDA lies in the model for data representation. Classical LDA works with vectorized representa- tions of data, while the 2DLDA algorithm works with data in matrix representation. To further reduce the dimension by 2DLDA, the combi- nation of 2DLDA and classical LDA, namely 2DLDA+LDA, is studied, where LDA is preceded by 2DLDA. The proposed algorithms are ap- plied on face recognition and compared with PCA+LDA. Experiments show that 2DLDA and 2DLDA+LDA achieve competitive recognition accuracy, while being much more efﬁcient.