The Research Of Linear Discriminant Analysis Based On Subspace

Linear Discriminant Analysis (LDA) is one of the effective method for feature extraction and dimensionality reduction in most linear classification problems, such as face recognition, fingerprint recognition and financial data analysis. However, the recognition performance of traditional LDA is poor on some samples with incomplete feature information or small size data. Besides, the singular matrix caused by Small Size Sample(SSS) problem in image recognition cannot be eliminated, and the optimal projection cannot be computed directly using traditional LDA. The researcher has proposed a two stage linear discrimination analysis (TSLDA), which is based on linear subspace, to solve this problem. But TSLDA still has high time complexity and cannot discard the noise information in projection space. For these problems, the main works are as following:1 . We present a probabilistic method of linear discriminant analysis with randomized input (PLDA-R). As feature information of sample is incomplete or small size training samples, PLDA-R generates a randomized space to enlarge feature information of samples,where samples are projected onto this space. Moreover, probabilistic generative model is introduced as a classifier to give a probabilistic discrimination result.2. We proposes an improved two stage linear discriminant analysis (Improved TSLDA). It eliminates the singular matrix using an approximate matrix method to reduce the time complexity, which approximately computes the inverse of original eigenvalue matrix with a reverse eigenvalue matrix. Meanwhile, the Improve TSLDA proposes a selection method to extract superior feature vectors and discard noise information in the four subspace, which defines a single feature Fisher criterion to measure the importance of single feature vector.This paper presents comparative experiments on UCI dataset to analyze classification performance of the LDA+KNN, LDA+Bayes, Randomization LDA and PLDA-R in various dimension and number of training samples. Meanwhile, the paper also presents comparative experiments on five face recognition databases to validate the effectiveness of the Improved TSLDA. The experiments confirm the effectiveness of PLDA-R and Improved TSLDA in solving related problems.