非随机性数据缺失的结构化稀疏子空间聚类研究

This proposal mainly concerns data clustering with nonrandom missing entries. There are two key points in this proposal. One is how to effectively measure the similarity between data with nonrandom missing entries. And the other is how to construct the clustering similarity graph for data with nonrandom missing entries. The two points are closely related. Sparse representation can measure the sparse similarity between data with random missing entries. However, when missing entries is not at random, sparse representation can not measure the non-sparse similarity between data. In this case, partial similarity may debase the connectivity of clustering similarity graph, where points in the same cluster form multiple components, so that it can not generate effective clustering. Motivated by this critical problem, in this proposal we will conduct the following study. Firstly, structured sparse optimization platform with neighborhood constraint is studied for complex structure data with nonrandom missing entries, so as to get the sparse representation and its corresponding coefficients, and form the partial clustering similarity graph between data. Then, the latent non-sparse similarity between data with nonrandom missing entries is gotten by the link-based refinement approach according to the above sparse similarity, which can form the complete clustering similarity graph between data. In the complete clustering similarity graph, points in the same subspace lie in one component, so that it can generate effective clustering. The proposed research aims to study how to forms effective structured sparse subspace clustering for data with nonrandom missing entries. Expected outcomes of the proposed research will provide solution for the critical problem underlying structured sparse subspace clustering with nonrandom missing entries, so that the proposed research can be more and more popular in the application of data clustering with missing entries.

本项目拟重点研究非随机性数据缺失聚类，涉及两个关键问题：相似性度量以及连通的聚类相似图的构建。稀疏表示能够提取随机性数据缺失的稀疏相似性信息，却无法提取非随机性数据缺失的非稀疏相似性信息。依据不完整的稀疏相似性信息，聚类相似图的连通性较差，使得同一子空间内的数据位于多个连通分量，无法形成有效的聚类。针对这一问题，首先研究邻域约束的结构化稀疏平台，提取具有复杂结构的非随机性数据缺失的稀疏表示及其系数，初步建立聚类相似图；然后，在此基础上研究基于链接分析的信息优化方法，提取非随机性数据缺失隐含的非稀疏相似性，完善聚类相似图，使得同一子空间内的数据位于同一连通分量内，从而形成有效的聚类。项目旨在揭示非随机性数据缺失对结构化稀疏子空间聚类的影响，提出非随机性数据缺失结构化稀疏子空间聚类关键问题的解决方案，使得该研究在数据缺失聚类中具有广泛的应用空间。

随着聚类分析应用领域的扩展和深入，噪音和缺失数据聚类成为当前研究的热点。如何有效度量噪音和缺失数据的相似性是聚类分析的关键点。子空间聚类从数据中提取低秩表示，并计算数据的相似性矩阵，通过谱聚类得到聚类结果。但是，当数据存在噪音和缺失，子空间聚类无法正确提取数据的低秩表示，相似性矩阵的块状性能无法保证，从而无法形成有效的聚类。.本项目开展以下研究：（i）基于低秩表示的健壮回归算法，低秩表示获取数据的低维子空间结构，但是却忽略了邻域信息。在低秩表示获取干净数据集的基础上，回归误差可以准确获取数据的邻域信息。二者将全局和局部信息结合，减少噪音和缺失的影响，探测数据内部的真实结构。（ii）基于块状约束的健壮子空间聚类算法研究，针对噪声和缺失数据设计自适应误差权重，极小化加权的块状约束数据的重构误差，直接获取较好块状性能的相似性矩阵，使得同一子空间数据位于同一连通分量内，从而形成有效的聚类。.项目旨在揭示噪声和缺失对子空间聚类的影响，提出噪声和缺失数据的子空间聚类关键问题和的解决方案，使得该研究在噪声和缺失数据聚类中具有广泛的应用空间。