余弦度量的多流形最大间距鉴别保持嵌入

Multi-manifold Maximal Margin Discriminant Preserving Embedding Based on Cosine Measure

针对LMMDE算法存在的缺陷,提出了余弦度量的多流形最大间距鉴别保持嵌入算法(Multi-manifold Maximal Margin Discriminant Preserving Embedding based on Cosine M easure,CM M M M DPE).该算法首先利用多流形思想将原始样本集中的每个样本分成若干个局部小块样本,形成一个多流形的样本空间.在为流形内的每个局部小块样本确定类间邻域和类内邻域时,采用余弦距离代替欧式距离的度量方式.定义了加权的类间邻域散布矩阵和类内散布矩阵,来描述整个多流形空间中样本之间的相似度,通过相应的准则函数为每个样本流形找到最优投影矩阵,对每个样本流形降维到更低维流形空间中,最后通过计算测试样本流形与训练样本流形的距离来判定测试样本的类别归属.通过在多个人脸库上的实验,验证了本文方法的有效性.

Aiming at the defects existing in LMMDE algorithm,a new algorithm called multi-manifold maximal margin discriminant preserving embedding based on cosine measure is proposed （CMMMMDPE）.In this algorithm,each sample of the original sample set is divided into a number of local small samples by the idea of manifold,then the multi-manifold sample space was reconstructed.During determining the inter-class neighborhood and intra-class neighborhood for each local small sample in the multi-manifold sample space,the cosine distance is used instead of the euclidean distance.In order to describe the similarity between the sample of the whole multi-manifold space,the weighted scatter matrix of inter-class neighborhood and the weighted scatter matrix of intra-class neighborhood are defined,then each sample manifold is reduced to a lower dimensional manifold space by finding the optimal projection matrix for each sample manifold through the criterion function,finally the categories of the test sample is got by calculating the distance between the test sample manifold and the training sample manifold.The experimental results on various face databases verify the effectiveness of the method which is put forward in this paper.