The critical point for the successes of spectral-type subspace clustering algorithms is to seek reconstruction coefficient matrices which can faithfully reveal the subspace structures of data sets. An ideal reconstruction coefficient matrix should have two properties: 1) it is block diagonal with each block indicating a subspace; 2) each block is fully connected. Though there are various spectral-type subspace clustering algorithms have been proposed, some defects still exist in the reconstruction coefficient matrices constructed by these algorithms. We find that a normalized membership matrix naturally satisfies the above two conditions. Therefore, in this paper, we devise an idempotent representation (IDR) algorithm to pursue reconstruction coefficient matrices approximating normalized membership matrices. IDR designs a new idempotent constraint for reconstruction coefficient matrices. And by combining the doubly stochastic constraints, the coefficient matrices which are closed to normalized membership matrices could be directly achieved. We present the optimization algorithm for solving IDR problem and analyze its computation burden as well as convergence. The comparisons between IDR and related algorithms show the superiority of IDR. Plentiful experiments conducted on both synthetic and real world datasets prove that IDR is an effective and efficient subspace clustering algorithm.
翻译:光谱类子空间群集算的成功的关键点是寻求能够忠实地揭示数据集的子空间结构的重建系数矩阵。理想的重建系数矩阵应该有两个属性:1)它是每个区块的块对角,表明一个子空间;2)每个区是完全相连的。虽然提出了各种光谱类子空间分组算法,但这些算法所构建的重建系数矩阵中仍然存在一些缺陷。我们发现,一个正常的会籍矩阵自然满足上述两个条件。因此,在本文件中,我们设计了一种极好的代表算法(IDR)算法,以追求重建系数矩阵对正常成员基体的接近度。IDR设计了对重建系数基体的新的副作用限制。通过将二元制组合,可以直接达到对正常的会籍矩阵封闭的系数矩阵。我们介绍了解决IDR问题和分析其计算负担的优化算法以及趋同性。在IDR和相关的算法之间的比较表明IDR的优越性。在合成和真实的世界数据基体上进行的宽实验证明,有效的次基体是有效的IDR。