ALID

Abstract

Detecting dominant clusters is important in many analytic applications. The state-of-the-art methods find dense subgraphs on the affinity graph as dominant clusters. However, the time and space complexities of those methods are dominated by the construction of affinity graph, which is quadratic with respect to the number of data points, and thus are impractical on large data sets. To tackle the challenge, in this paper, we apply Evolutionary Game Theory (EGT) and develop a scalable algorithm, Approximate Localized Infection Immunization Dynamics (ALID). The major idea is to perform Localized Infection Immunization Dynamics (LID) to find dense subgraphs within local ranges of the affinity graph. LID is further scaled up with guaranteed high efficiency and detection quality by an estimated Region of Interest (ROI) and a Candidate Infective Vertex Search method (CIVS). ALID only constructs small local affinity graphs and has time complexity O ( C ( a * + δ ) n ) and space complexity O ( a * ( a * + δ )), where a * is the size of the largest dominant cluster, and C « n and δ « n are small constants. We demonstrate by extensive experiments on both synthetic data and real world data that ALID achieves the state-of-the-art detection quality with much lower time and space cost on single machine. We also demonstrate the encouraging parallelization performance of ALID by implementing the Parallel ALID (PALID) on Apache Spark. PALID processes 50 million SIFT data points in 2.29 hours, achieving a speedup ratio of 7.51 with 8 executors.