arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2209.02513cs.LG
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基于动态图结构学习的半监督聚类

Semi-Supervised Clustering via Dynamic Graph Structure Learning

Yau Mathematical Sciences Center, Tsinghua University(清华大学丘成桐数学科学中心);Yanqi Lake Beijing Institute of Mathematical Sciences and Applications(北京雁栖湖应用数学研究院)

Huaming Ling, Chenglong Bao, Xin Liang, Zuoqiang Shi

摘要:

大多数现有的基于半监督图的聚类方法通过细化亲和矩阵或直接约束数据点的低维表示来利用监督信息。亲和矩阵表示图的结构,对基于图的半监督聚类的性能至关重要。然而,现有的方法采用静态的亲和矩阵来学习数据点的低维表示,并且在学习过程中没有优化亲和矩阵。本文提出了一种新的动态图结构学习方法用于半监督聚类。在这种方法中,我们同时优化亲和矩阵和低维表示的数据点,利用给定的成对约束。此外,我们提出了一个交替的最小化方法,证明了收敛性来解决所提出的非凸模型。在迭代过程中,我们的方法循环更新数据点的低维表示,并细化亲和矩阵,从而产生动态亲和矩阵(图结构)。具体来说,对于亲和度矩阵的更新,我们强制具有显著不同的低维表示的数据点具有亲和度值0。此外,我们构造的初始亲和矩阵,通过集成的局部距离和整体的自我表示的数据点之间。在不同设置下的8个基准数据集上的实验结果表明了该方法的优越性。

英文摘要:

Most existing semi-supervised graph-based clustering methods exploit the supervisory information by either refining the affinity matrix or directly constraining the low-dimensional representations of data points. The affinity matrix represents the graph structure and is vital to the performance of semi-supervised graph-based clustering. However, existing methods adopt a static affinity matrix to learn the low-dimensional representations of data points and do not optimize the affinity matrix during the learning process. In this paper, we propose a novel dynamic graph structure learning method for semi-supervised clustering. In this method, we simultaneously optimize the affinity matrix and the low-dimensional representations of data points by leveraging the given pairwise constraints. Moreover, we propose an alternating minimization approach with proven convergence to solve the proposed nonconvex model. During the iteration process, our method cyclically updates the low-dimensional representations of data points and refines the affinity matrix, leading to a dynamic affinity matrix (graph structure). Specifically, for the update of the affinity matrix, we enforce the data points with remarkably different low-dimensional representations to have an affinity value of 0. Furthermore, we construct the initial affinity matrix by integrating the local distance and global self-representation among data points. Experimental results on eight benchmark datasets under different settings show the advantages of the proposed approach.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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