Learning on Hypergraphs With Sparsity
Learning on Hypergraphs With Sparsity
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DOI：
10.1109/tpami.2020.2974746
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发表时间：
2018-04
影响因子：
23.6
通讯作者：
Canh Hao Nguyen;Hiroshi Mamitsuka
中科院分区：
文献类型：
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作者：
Canh Hao Nguyen;Hiroshi Mamitsuka
超图是表示对象集合上的高阶关系的一般方法。它是图的一个推广，其中只能表示两两关系。它在观察到两个以上对象的关系的各种领域中找到应用。在超图上，作为图的推广，人们希望学习关于其拓扑的光滑函数。一个基本的问题是找到合适的光滑性措施的功能的节点上的图/超图。我们展示了一个一般框架，概括了以前提出的平滑措施，并产生新的。为了解决不相关或噪声数据的问题，我们希望将稀疏学习框架引入超图的学习中。我们提出了稀疏光滑的配方，学习光滑的功能，并在超边和节点水平上的超图诱导稀疏。我们展示了它们的属性和稀疏支持恢复结果。我们进行的实验表明，我们的稀疏平滑模型是有益的学习无关的和嘈杂的数据，通常给出类似的或改进的性能相比，密集的模型。
Hypergraph is a general way of representing high-order relations on a set of objects. It is a generalization of graph, in which only pairwise relations can be represented. It finds applications in various domains where relationships of more than two objects are observed. On a hypergraph, as a generalization of graph, one wishes to learn a smooth function with respect to its topology. A fundamental issue is to find suitable smoothness measures of functions on the nodes of a graph/hypergraph. We show a general framework that generalizes previously proposed smoothness measures and also generates new ones. To address the problem of irrelevant or noisy data, we wish to incorporate sparse learning framework into learning on hypergraphs. We propose sparsely smooth formulations that learn smooth functions and induce sparsity on hypergraphs at both hyperedge and node levels. We show their properties and sparse support recovery results. We conduct experiments to show that our sparsely smooth models are beneficial to learning irrelevant and noisy data, and usually give similar or improved performances compared to dense models.