一种基于松弛条件的改进模糊线性鉴别分析算法

Improved Fuzzy Discriminant Analysis Algorithm Based on the Relaxed Condition

对模糊线性鉴别分析算法进行了本质研究。通过采用模糊k近邻(FKNN)方法得到相应的样本分布隶属度信息,同时考虑到离群样本对整个分类结果的不利影响,提出了一种松弛的归一化条件,将每一个样本的隶属度根据它对散布矩阵重定义所做的贡献按照松弛条件融入到特征抽取的过程中,从而得到完整有效的模糊样本特征向量集。该算法同传统模糊线性鉴别分析方法相比有效地解决了小样本和离群样本问题,在ORL和NUST603人脸数据库上的实验结果验证了它的有效性。

A study was made on the essence of fuzzy Fisher discriminant analysis （FLDA） algorithm in this paper. A reformative FLDA algorithm based on the fuzzy k-nearest neighbor （FKNN） was implemented to achieve the distribution information of every original sample represented with fuzzy membership degree and was incorporated into the redefinition of the scatter matrices. Furthermore, considering the fact that the outlier samples have some adverse influence to the classification result, a relaxed normalized condition in the fuzzy membership degrees was proposed simultaneously, therefore, the limitation from the outlier samples was overcome. Unlike the conventional FLDA algorithm, the proposed method computes its discriminant vectors with fuzzy membership degree from every training sample, which is theoretically effective to address the small size sample and outlier samples problems. Extensive experimental studies conducted on the ORL and NUST603 face images show the effectiveness of the proposed algorithrn.