差异性传播引导块稀疏正则的图拉普拉斯嵌入  

Graph Laplacian Embedding Based on Dissimilarity Propagation-guided Block Sparse Regularization

作　　者：邓秀勤[1] 刘威[1] 辜方清[1] 张晓明[2] DENG Xiuqin;LIU Wei;GU Fangqing;CHEUNG Yiuming(School of Mathematics and Statistics,Guangdong University of Technology,Guangzhou 510000,China;Faculty of Science,Hong Kong Baptist University,Hong Kong 999077,China)

机构地区：[1]广东工业大学数学与统计学院,广东广州510520 [2]香港浸会大学理学院,中国香港999077

出　　处：《控制工程》2023年第8期1458-1466,共9页Control Engineering of China

基　　金：广东省研究生教育创新计划项目(2021SFKC030);广东省自然科学基金资助项目(2021A1515011839)。

摘　　要：图拉普拉斯嵌入(graph Laplacian embedding,GLE)作为传统的无监督降维方法在处理非线性流行数据上有着广泛的应用,但是它忽视了数据本身所携带的有限的弱监督信息,同时仅学习样本空间的结构,无法有效区分具有高度相似的不同类簇的样本。鉴于此,提出了一种差异性传播引导块稀疏正则的图拉普拉斯嵌入(dissimilarity propagation-guided block sparse GLE,DPBS-GLE)方法。首先,引入约束谱正则聚类(constrained clustering via spectral regularization,CCSR)模型,结合弱监督信息生成的成对约束,将原样本映射到高维的类判别空间,增强类簇之间的差异性;然后,通过图正则化方式,获取高维空间的邻接结构;最后,使用样本的“勿连”约束构造不相似矩阵引导一个稀疏正则项,用来增强数据低维嵌入的块对角表示能力,进而提高样本间的差异性。提出的算法与其他5个对比算法在6个标准数据集上进行比较,实验结果表明,提出的算法具有更高的聚类性能。Graph Laplacian embedding,a traditional unsupervised dimensionality reduction method,has been widely used in dealing with non-linear manifold data.However,graph Laplacian embedding ignores the limited weak supervision information carried by the data and only studies the structure of sample space.The algorithm cannot effectively distinguish samples of different clusters with high similarity.Therefore,a graph Laplacian embedding based on dissimilarity propagation-guided block sparse regularization is proposed.Firstly,the CCSR model is introduced to combine with the pairwise constraints generated by the weak supervisory information.The original samples are mapped into a high-dimensional category discriminant space to enhance the difference between clusters.Secondly,the adjacency structure of the high-dimensional space is captured by graph regularization.Finally,a sparse regularization is introduced by a dissimilarity matrix constructed by the cannot-link constraints to enhance block diagonal representation of low-embedding.We compare the proposed algorithm with its counterparts on six data sets.The experimental results show the proposed algorithm has a higher clustering performance.

关 键 词：图拉普拉斯嵌入 降维 成对约束 约束聚类 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]