亲和矩阵图卷积子空间聚类

Affinity Matrix Graph Convolution Subspace Clustering

摘要: 子空间聚类是聚类来源于底层子空间的数据的一个高效的方法。在近些年，基于谱聚类的方法成为了最受欢迎的子空间聚类方法之一。新近提出的自适应图卷积子空间聚类方法受图卷积网络的启发，使用图卷积技术去设计了新的特征提取的方法和系数矩阵的约束，取得了优异的效果。但其需要重构系数矩阵满足对称和非负的条件，这会限制重构系数矩阵的表示能力。为了克服这一缺陷，本文改为直接约束由重构系数矩阵生成的亲和矩阵，亲和矩阵天然具有对称和非负的性质，进而设计了亲和矩阵图卷积子空间聚类算法。不仅克服了求解模型的困难之处，还进行了对比实验在四个基准数据集上以此论证本文方法的有效性。

Abstract: Subspace clustering is an efficient method for clustering data derived from the bottom level subspace. In recent years, spectral clustering based methods have become one of the most popular subspace clustering methods. The recently proposed adaptive graph convolution subspace clustering method is inspired by graph convolutional networks and uses graph convolution techniques to design new feature extraction methods and constraints on coefficient matrices, achieving excellent results. But it requires the reconstruction coefficient matrix to satisfy symmetric and non negative conditions, which limits the representational power of the reconstructed coefficient matrix. To overcome this limitation, this paper proposes to directly constrain the affinity matrix generated from the reconstructed coefficient matrix, which naturally has symmetric and non negative properties. Therefore, an affinity matrix graph convolution subspace clustering algorithm is designed. Not only did it overcome the difficulties in solving the model, but it also conducted comparative experiments on four benchmark datasets to demonstrate the effectiveness of the proposed method.