An Application of Weighted Kernel Fuzzy Discriminant Analysis
In this paper, a new method for feature extraction and recognition called based on QR decomposition weighted kernel fuzzy discriminant analysis (WKFDA/QR) is proposed to deal with nonlinear separable problem. Since QR decomposition on a small size matrix is adopted. A superiority of the proposed methods is its computational efficiency and can avoid the singularity. In the proposed method, the membership degree is incorporated into the definition of between-class and within-class scatter matrixes to get fuzzy between-class and within-class scatter matrixes. Under different distances and different kernel functions, we compare WKFDA/QR, kernel discriminant analysis (KDA) and fuzzy discriminant analysis (FDA) three algorithms by means of the classification rate. In addition, we also compare WKFDA/QR with KDA and FDA under the parameters of weighted function and kernel function. Experiments on ORL and FERET two real-world data sets are performed to test and evaluate the effectiveness of the proposed algorithms and the effect of weights on classification accuracy. The results show that the effect of weighted schemes is very significantly.
Weighted kernel fuzzy discriminant analysis; fuzzy membership; QR decomposition; weighting function; small sample size problem(S3); classification accuracy
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