一种谱分解降维的模糊有监督局部保持投影策略

提出一种谱分解降维的模糊有监督局部保持投影策略。首先针对监督局部保持投影SLPP存在过学习和不能较好地保持图像空间的差异信息等问题,通过最小化局部离散度和最大化差异离散度准则提取投影方向,找到一种线性鉴别分析的等价形式。其次,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,提出一种模糊化方法,根据样本的隶属度对样本分布矩阵重定义所做的贡献,将每个样本的隶属度融入到SLPP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,有效解决了小样本问题的特征抽取问题。第三,提出一种谱分解的矩阵分析方法,在SLPP投影准则下,对散布矩阵实现降维。在ORL和NUST603人脸库上的实验结果验证了该方法的有效性。

A Strategy of Spectra Factorization Dimensional Reduction on Fuzzy Supervised Locality Preserving Projection

Classification of nonlinear high-dimensional data is usually not amenable to standard pattern recognition techniques because of an underlying small sample size conditions. To address the problem, a novel Supervised Locality Preserving Projection (SLPP) learning algorithm combined with a fuzzy feature extraction strategy and spectra factorization is developed in this paper. First, according to the problem that SLPP has the over-learning problem and does not preserve the diversity information of data which is also useful for data recognition, a concise transformation of feature extraction criterion is raised by minimizing the local scatter, which efficiently preserves the local structure and simultaneously maximize the diversity scatter, however, an equivalent form of linear discriminant analysis is obtained. Secondly, a reformative fuzzy algorithm based on the fuzzy k-nearest neighbor (FKNN) is implemented to achieve the distribution information of each original sample represented with fuzzy membership degree and is incorporated into the redefinition of the scatter matrices of SLPP. Thirdly, a matrix decomposition is proposed on the basis of matrix analysis theory in this paper, under the SLPP criterion, the technology of spectra factorization is utilized in order to reduce the dimension of samples. Experimental results conducts on the ORL and NUST603 face database demonstrate the effectiveness of the proposed method.