Clustering is a fundamental task in data analysis, and spectral clustering has been recognized as a promising approach to it. Given a graph describing the relationship between data, spectral clustering explores the underlying cluster structure in two stages. The first stage embeds the nodes of the graph in real space, and the second stage groups the embedded nodes into several clusters. The use of the k-means method in the grouping stage is currently standard practice. We present a spectral clustering algorithm that uses convex programming in the grouping stage and study how well it works. This algorithm is designed based on the following observation. If a graph is well-clustered, then the nodes with the largest degree in each cluster can be found by computing an enclosing ellipsoid of the nodes embedded in real space, and the clusters can be identified by using those nodes. We show that, for well-clustered graphs, the algorithm can find clusters of nodes with minimal conductance. We also give an experimental assessment of the algorithm’s performance.

聚类是数据分析中的一项基本任务，光谱聚类已被认为是一种有前途的方法。给定一个描述数据之间关系的图表，频谱聚类分两个阶段探索了潜在的聚类结构。第一阶段将图的节点嵌入到真实空间中，第二阶段将嵌入式节点分组为几个群集。k的使用分组阶段的-means方法是目前的标准做法。我们提出了一种光谱聚类算法，该算法在分组阶段使用凸规划，并研究其工作原理。该算法是基于以下观察而设计的。如果对图进行了很好的聚类，则可以通过计算嵌入在真实空间中的节点的封闭椭圆形来找到每个聚类中度数最大的节点，然后可以使用这些节点来识别聚类。我们表明，对于聚类良好的图，该算法可以找到电导最小的节点簇。我们还对算法的性能进行了实验评估。