Abstract:

In order to obtain a more reasonable affine matrix, a sparse subspace clustering algorithm based on [k]-nearest neighbor and local similarity is proposed. The algorithm first calculates the [k]-nearest neighbor of each point and linearly represents it with [k]-nearest neighbor data points, so that the affine matrix can guarantee a strong local linear relationship in the case of overall sparseness. At the same time, based on the knowledge of graph theory, the affine matrix is constrained by the actual distribution of the data, so that the affine matrix is further reasonably equivalent to the similarity matrix to be spectrally clustered. Experiments are carried out on artificial datasets, randomly generated subspace datasets, image datasets and real datasets. The experimental results show that the algorithm is effective.

Key words: [k]-nearest neighbor, subspace clustering method, sparse, similarity matrix

摘要：

为了获得结构更加合理的仿射矩阵，提出了一种基于[k]-近邻与局部相似度的稀疏子空间聚类算法。该算法首先计算每个点的[k]-近邻，并对其用[k]-近邻数据点进行线性表示，使仿射矩阵在整体稀疏的情况下保证局部的强线性关系。基于图论知识，利用数据的实际分布情况对仿射矩阵进行约束，使仿射矩阵进一步合理地等价于待进行谱聚类的相似矩阵。在人造数据集、随机生成的子空间数据集、图像数据集以及真实数据集上进行了实验，结果表明该算法是有效的。

关键词: [k]-近邻, 子空间聚类方法, 稀疏, 相似矩阵