A family of algorithms using spectral clustering and DBSCAN

Recent attention in studies of clustering is focused upon generation of clusters on the basis of graph structures. Nodes and edges with weights are given and clusters with dense groups of nodes should be found. Several algorithms have been proposed for this purpose, among which the method of spectral clustering and DBSCAN have frequently been used. The former uses eigenvalue analysis while the latter is based on density seeking using the concept of core points. This study aims at combining the two algorithms to reduce computation and at the same time using advantages of the both methods. Relations of a family of algorithms including these two uncovers the nature of the algorithms and gives a methodological perspective including these algorithms as well as other traditional algorithms. As a result we propose an efficient algorithm combining the ideas of this family of algorithms. The effectiveness and efficiency of the proposed algorithm are shown theoretically and by numerical examples.