Local community detection by seed expansion: from conductance to weighted kernel 1-mean optimization

In local community detection by seed expansion a single cluster concentrated around few given query nodes in a graph is discovered in a localized way. Conductance is a popular objective function used in many algorithms for local community detection. Algorithms that directly optimize conductance usually add or remove one node at a time to find a local optimum. This amounts to fix a specific neighborhood structure over clusters. A natural way to avoid the problem of choosing a specific neighborhood structure is to use a continuous relaxation of conductance. This paper studies such a continuous relaxation of conductance. We show that in this setting all strict local optima are discrete, thus continuous optimization leads to hard clusters. We investigate the relation of conductance with weighted kernel

• Type: Journal
• Year: 2016
• Where: CORR
• Authors: Twan van Laarhoven, Elena Marchiori
• Keywords: CORR 2016, Education