Abstract:

The purpose of subspace clustering is to segment data from different subspaces into the corresponding low-dimensional subspaces which the data essentially belong to. The existing methods based on data self-representation and spectral clustering divide this problem into two consecutive stages： first， the affinity matrix of the data was learned from the high-dimensional data， and then the cluster membership of the data was inferred by applying spectral clustering to the learned affinity matrix. A new data adaptive sparse regularization term was defined and combined with Structural Sparse Subspace Clustering （SSSC） model and improved Sparse Spectral Clustering （SSpeC） model， and a new unified optimization model was proposed. In the new model， by using the mutual guidance of data similarity and clustering indicators， the blindness of SSpeC sparsity penalty was overcome and the similarity was made to be discriminative， which was conducive to dividing the data from different subspaces into different classes， and the defect that the SSSC model only forces the data from the same subspace to have the same labels was made up. Experimental results on common datasets show that the proposed model enhances the ability of clustering discrimination and is superior to some classical two-stage methods and SSSC model.

Key words: subspace clustering, affinity matrix, sparse regularity, spectral clustering, clustering indicator matrix

摘要：

子空间聚类的目的是将来自不同子空间的数据分割到其本质上所属的低维子空间。现有的基于数据的自我表示和谱聚类的子空间聚类算法将该问题分为两个连续的阶段：首先从高维数据中学习数据的相似性矩阵，然后通过将谱聚类应用于所学相似性矩阵来推断数据的聚类隶属。通过定义一种新的数据自适应稀疏正则项，并将其与结构稀疏子空间聚类（SSSC）模型和改进的稀疏谱聚类（SSpeC）模型相结合，给出了一个新的统一优化模型。新模型利用数据的相似度和聚类指标的相互引导克服了SSpeC稀疏性惩罚的盲目性，并使得相似度具有了判别性，这有利于将不同子空间的数据分为不同类，弥补了SSSC模型只强制来自相同子空间的数据具有相同标签的缺陷。常用数据集上的实验结果表明，所提模型增强了聚类判别的能力，优于一些经典的两阶段法和SSSC模型。

关键词: 子空间聚类, 相似度矩阵, 稀疏正则性, 谱聚类, 聚类指标矩阵