Learning a reliable affinity matrix is the key to achieving good performance for graph-based clustering methods. However, most of the current work usually directly constructs the affinity matrix from the raw data. It may seriously affect the clustering performance since the original data usually contain noises, even redundant features. On the other hand, although integrating manifold regularization into the framework of clustering algorithms can improve clustering results, some entries of the pre-computed affinity matrix on the original data may not reflect the true similarities between data points. To address the above issues, we propose a novel subspace clustering method to simultaneously learn the similarities between data points and conduct feature selection in a unified optimization framework. Specifically, we learn a high-quality graph under the guidance of a low-dimensional space of the original data such that the obtained affinity matrix can reflect the true similarities between data points as much as possible. A new algorithm based on augmented Lagrangian multiplier is designed to find the optimal solution to the problem effectively. Extensive experiments are conducted on benchmark datasets to demonstrate that our proposed method performs better against the state-of-the-art clustering methods.

学习可靠的亲和力矩阵是基于图的聚类方法获得良好性能的关键。但是，大多数当前工作通常直接从原始数据构建亲和力矩阵。由于原始数据通常包含噪声甚至冗余功能，因此可能会严重影响聚类性能。另一方面，尽管将流形正则化集成到聚类算法的框架中可以改善聚类结果，但是原始数据上预先计算的亲和力矩阵的某些条目可能无法反映数据点之间的真实相似性。为了解决上述问题，我们提出了一种新颖的子空间聚类方法，可以在统一优化框架中同时学习数据点之间的相似性并进行特征选择。特别，我们在原始数据的低维空间的指导下学习了一个高质量的图，这样获得的亲和度矩阵就可以尽可能反映数据点之间的真实相似性。设计了一种基于增强拉格朗日乘子的新算法，可以有效地找到问题的最优解。在基准数据集上进行了广泛的实验，以证明我们提出的方法相对于最新的聚类方法表现更好。