稀疏相似性度量的模糊鉴别分析方法  

Fuzzy Discriminant Analysis Based on Sparse Similarity Measurement

作　　者：宋晓宁[1,2,3] 徐勇[4] 

机构地区：[1]江苏科技大学计算机科学与工程学院,镇江212003 [2]江南大学物联网工程学院,无锡214122 [3]南京理工大学计算机科学与技术学院,南京210094 [4]哈尔滨工业大学深圳研究生院生物计算研究中心,深圳518055

出　　处：《模式识别与人工智能》2014年第3期199-205,共7页Pattern Recognition and Artificial Intelligence

基　　金：国家自然科学基金项目(No.61100116);中国博士后科学基金项目(No.2011M500926);江苏省自然科学基金项目(No.BK2012700);江苏省博士后科学基金项目(No.1102063C);人工智能四川省重点实验室开放基金项目(No.2012RZY02);浙江大学CAD&CG国家重点实验室开放课题项目(No.A1418)资助

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.

关 键 词：稀疏表示 模糊鉴别分析 系数重构 图像识别 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]