Abstract In this paper an effective graph learning method is proposed for clustering based on adaptive graph regularizations. Many graph learning methods focus on optimizing a global constraint on sparsity, low-rankness or weighted pair-wise distances, but they often fail to consider local connectivities. We demonstrate the importance of locality by generalizing the Locality-constrained Linear Coding (LLC) for unsupervised learning. Each data sample is expressed as a representation of its nearest neighbors, which naturally leads to a combination of distance regularized features and a Locally Linear Embedding (LLE) decomposition. The representation enforces a locally sparse connection on the data graph that exhibits high discrimination power and is easy to optimize. To improve the learned graph structure and incorporate cluster information, a rank constraint is further imposed on the Laplacian matrix of the data graph so that the connected components match the class number. The obtained representations are smoothed via manifold regularizations on a predefined graph which serves as a prior for graph learning. Finally, we utilize unsupervised Extreme Learning Machine (US-ELM) to learn a flexible and discriminative data embedding. Extensive evaluations show that the proposed algorithm outperforms graph learning counterpart methods on a wide range of benchmark datasets.

中文翻译：

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通过自适应和局部约束图学习和无监督 ELM 进行聚类

摘要 本文提出了一种基于自适应图正则化的有效图学习方法进行聚类。许多图学习方法专注于优化对稀疏性、低秩或加权成对距离的全局约束，但它们通常无法考虑局部连通性。我们通过推广无监督学习的局部约束线性编码（LLC）来证明局部性的重要性。每个数据样本都表示为其最近邻居的表示，这自然会导致距离正则化特征和局部线性嵌入 (LLE) 分解的组合。该表示在数据图上强制执行局部稀疏连接，该连接具有高辨别力且易于优化。为了改进学习的图结构并合并集群信息，对数据图的拉普拉斯矩阵进一步施加秩约束，以便连接的组件与类号匹配。获得的表示通过在预定义图上的流形正则化进行平滑，该图用作图学习的先验。最后，我们利用无监督的极限学习机 (US-ELM) 来学习灵活且有判别力的数据嵌入。广泛的评估表明，所提出的算法在广泛的基准数据集上优于图学习对应方法。我们利用无监督的极限学习机 (US-ELM) 来学习灵活且有判别力的数据嵌入。广泛的评估表明，所提出的算法在广泛的基准数据集上优于图学习对应方法。我们利用无监督的极限学习机 (US-ELM) 来学习灵活且有判别力的数据嵌入。广泛的评估表明，所提出的算法在广泛的基准数据集上优于图学习对应方法。