Research On New Methods Of Linear Discriminant Analysis And Their Applications

Fisher linear discriminant analysis (FLDA, or for short, LDA) is a very popular and effective feature extraction approach, and has obtained extensive and successful applications in the fields of dimensionality reduction, data analysis and pattern classification, etc. In this thesis, a series of researches on LDA are developed. Firstly, kernel-based Multi-feature LDA (kMFLDA) is proposed to enhance MFLDA's classification accuracy, in order to deal with the linearly non-separable problem. Secondly, a modified Fisher linear discriminant analysis (FLDA) is presented to improve the classification performance of FLDA by modifying the original discriminant criterion, which aims at not only overcome the rank limitation of FLDA, but also relax singularity of the within-class scatter matrix. Experiments on nine publicly available datasets and one artificial dataset show that the above two proposed methods have better or comparable performance on all the datasets than conventional FLDA. Finally, a new LDA criterion is developed to gray image binarization. The criterion implicitly assumes that an object in a gray image generally has uniform or homogeneous gray value distribution while its background is generally disorderly and unsystematic. Through optimization of the criterion, the best threshold can be obtained. Experiments results on five images show that the proposed method has not only visually better segmentation effect but also stronger noise removal ability than those of Otsu, Huang&Wang and Kwon.