通过局部正则化构建更符合数据几何结构的稀疏图，提升聚类效果。
Locally Regularized Sparse Graph by Fast Proximal Gradient Descent
- 引入支持正则项，使邻近点在图中保持局部平滑性。
- 提出快速近端梯度法求解非凸优化，收敛速度达最优阶。
- 在多个真实数据集上优于现有聚类方法，适合高维数据聚类。
由稀疏表示构建的稀疏图在高维数据聚类中已被证明有效。尽管表现优异，但原始稀疏图忽略数据的几何结构，对每个样本独立进行稀疏表示。为获得与数据局部几何结构一致的稀疏图，本文提出一种新的支持正则化稀疏图（SRSG），通过定义良好的支持正则项，促使邻近数据点在其邻域内保持局部平滑性。针对SRSG的非凸优化问题，提出一种快速近端梯度下降法，其收敛速度匹配光滑凸目标函数在Lipschitz连续梯度下的Nesterov最优一阶方法收敛率。在多个真实数据集上的大量实验表明，SRSG在聚类性能上优于其他竞争方法。
原文摘要 · Abstract (English)
Sparse graphs built by sparse representation has been demonstrated to be effective in clustering high-dimensional data. Albeit the compelling empirical performance, the vanilla sparse graph ignores the geometric information of the data by performing sparse representation for each datum separately. In order to obtain a sparse graph aligned with the local geometric structure of data, we propose a novel Support Regularized Sparse Graph, abbreviated as SRSG, for data clustering. SRSG encourages local smoothness on the neighborhoods of nearby data points by a well-defined support regularization term. We propose a fast proximal gradient descent method to solve the non-convex optimization problem of SRSG with the convergence matching the Nesterov's optimal convergence rate of first-order methods on smooth and convex objective function with Lipschitz continuous gradient. Extensive experimental results on various real data sets demonstrate the superiority of SRSG over other competing clustering methods.
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