论文标题
通过光谱嵌入连接进行超图建模：超图切割，加权内核$ k $ -MEANS和热核
Hypergraph Modeling via Spectral Embedding Connection: Hypergraph Cut, Weighted Kernel $k$-means, and Heat Kernel
论文作者
论文摘要
我们提出了一个多路相似性的理论框架，该框架与将实值数据建模为通过光谱嵌入聚类的超图。对于基于图形的光谱群集，通常，通过使用内核函数对成对相似性进行建模，将实价数据模拟为图。这是因为内核函数与图形切割具有理论连接。对于使用多路相似性比成对相似性更合适的问题，自然地将模型作为超图（即图）的概括。但是，尽管剪切幅度进行了充分研究，但尚未建立基于HyperGraph Cut的框架来建模多路相似性。在本文中，我们通过利用内核函数的理论基础来制定多路相似性。我们展示了我们的配方和超图之间的理论联系，以两种方式削减了加权内核$ k $ -MEANS和热核，我们证明了我们的配方合理。我们还为光谱聚类提供了快速算法。与现有图和其他启发式建模方法相比，我们的算法在经验上显示出更好的性能。
We propose a theoretical framework of multi-way similarity to model real-valued data into hypergraphs for clustering via spectral embedding. For graph cut based spectral clustering, it is common to model real-valued data into graph by modeling pairwise similarities using kernel function. This is because the kernel function has a theoretical connection to the graph cut. For problems where using multi-way similarities are more suitable than pairwise ones, it is natural to model as a hypergraph, which is generalization of a graph. However, although the hypergraph cut is well-studied, there is not yet established a hypergraph cut based framework to model multi-way similarity. In this paper, we formulate multi-way similarities by exploiting the theoretical foundation of kernel function. We show a theoretical connection between our formulation and hypergraph cut in two ways, generalizing both weighted kernel $k$-means and the heat kernel, by which we justify our formulation. We also provide a fast algorithm for spectral clustering. Our algorithm empirically shows better performance than existing graph and other heuristic modeling methods.
