稀疏相似性度量的模糊鉴别分析方法

摘要

稀疏表示的数学本质就是稀疏正则化约束下的信号分解。提出一种稀疏相似性的模糊鉴别分析方法。首先，各高维图像样本划分成若干相同大小的局部块并以脊波序列表示，其次通过一种新型稀疏学习算法获得系数分解和对应的稀疏相似性度量，由此构造出稀疏相似度嵌入的模糊鉴别分析准则。该方法利用新型稀疏监督学习作为特征提取工具，克服了传统鉴别分析方法缺乏样本间结构知识的缺点，可有效解决高维非线性小样本问题。在ORL和FERET人脸数据库上的实验结果验证了算法的有效性。%The mathematic essence of sparse representation is signal decomposition under the constraint of sparsity regularization. A fuzzy discriminant analysis based on sparse similarity measurement is proposed in this paper. Each high dimensional image sample is firstly partitioned into several local blocks with equal size by the proposed algorithm, and these local blocks are combined to represent the samples as a Ridgelet sequence. Then, a new sparse learning algorithm is presented for coefficient decomposition and the corresponding sparse similarity measurement, and the fuzzy discriminant analysis criterion is subsequently developed by embedding the sparse similarity. The proposed algorithm successfully utilizes the novel sparse supervised learning algorithm as a feature extraction tool. Meanwhile, it overcomes the shortcomings of traditional discriminant analysis method derived from the lack of structure knowledge between samples, especially in the case of high dimensional nonlinear small sample sizes. The experimental results on the ORL and FERET face images show the effectiveness of the proposed method.