Cyclizing Clusters via Zeta Function of a Graph

Detecting underlying clusters from large-scale data plays a central role in machine learning research. In this paper, we attempt to tackle clustering problems for complex data of multiple distributions and large multi-scales. To this end, we develop an algorithm named Zeta $l$-links, or Zell which consists of two parts: Zeta merging with a similarity graph and an initial set of small clusters derived from local $l$-links of the graph. More specifically, we propose to structurize a cluster using cycles in the associated subgraph. A mathematical tool, Zeta function of a graph, is introduced for the integration of all cycles, leading to a structural descriptor of the cluster in determinantal form.