Abstract:

This paper proposes a novel sparse subspace clustering model which is based on the constraints of fractional function in order to overcome the shortcoming of sparse subspace clustering algorithm that the coefficient matrix obtained by this algorithm cannot reflect the sparsity of data distribution in high-dimensional space accurately and solves this model by applying the alternating direction iteration method. It is proved that the coefficient matrix obtained by this method has block diagonal structure without any noise, which provides a theoretical guarantee to acquire its data structure accurately. Under the condition of noise, the fractional function constraint is also used as the regular term for outlier noise to improve the robustness of the model. Experimental results on artificial data sets, Extended Yale B database and Hopkins155 data set show that the sparse subspace clustering method based on fractional function constraint not only improves the accuracy of clustering results and also improves the robustness to outlier noise.

Key words: fractional function, sparse representation, block diagonal structure, subspace clustering, spectral clustering

摘要：

针对现有稀疏子空间聚类算法获取的系数矩阵不能准确反应高维空间中数据分布的稀疏性的不足，提出一种分式函数约束的稀疏子空间聚类模型，并利用交替方向迭代方法给出该模型的解。在无噪声情形下，证明了该方法获取的系数矩阵具有块对角结构，这为其准确获取数据结构提供了理论保证；在含噪声情形下，对异常点噪声同样采用分式函数约束作为正则项，提高了模型的鲁棒性。在人工数据集、Extended Yale B库和Hopkins155数据集上的实验结果表明，基于分式函数约束的稀疏子空间聚类方法不仅提高了聚类结果的准确率，而且对异常点噪声具有更好的鲁棒性。

关键词: 分式函数, 稀疏表示, 块对角结构, 子空间聚类, 谱聚类