The linear discriminant analysis (LDA) is a very popular linear feature extraction approach. The algorithms of LDA usually perform well under the following two assumptions. The first assumption is that the global data structure is consistent with the local data structure. The second assumption is that the input data classes are Gaussian distributions. However, in real-world applications, these assumptions are not always satisfied. In this paper, we propose an improved LDA framework, the local LDA (LLDA), which can perform well without needing to satisfy the above two assumptions. Our LLDA framework can effectively capture the local structure of samples. According to different types of local data structure, our LLDA framework incorporates several different forms of linear feature extraction approaches, such as the classical LDA and principal component analysis. The proposed framework includes two LLDA algorithms: a vector-based LLDA algorithm and a matrix-based LLDA (MLLDA) algorithm. MLLDA is directly applicable to image recognition, such as face recognition. Our algorithms need to train only a small portion of the whole training set before testing a sample. They are suitable for learning large-scale databases especially when the input data dimensions are very high and can achieve high classification accuracy. Extensive experiments show that the proposed algorithms can obtain good classification results.

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