Detecting Localized Categorical Attributes on Graphs

TL;DR

This paper introduces statistical methods for detecting localized categorical attributes on graphs, applicable to social networks, recommender systems, and cyber-physical systems, validated through simulations and real-world data.

Contribution

It proposes two novel graph-based statistics, the graph wavelet and scan statistics, with proven effectiveness for identifying localized attributes.

Findings

Effective detection of localized attributes in simulated data

Successful application to air pollution and keyword ranking data

Proven robustness and efficiency of the proposed methods

Abstract

Do users from Carnegie Mellon University form social communities on Facebook? Do signal processing researchers from tightly collaborate with each other? Do Chinese restaurants in Manhattan cluster together? These seemingly different problems share a common structure: an attribute that may be localized on a graph. In other words, nodes activated by an attribute form a subgraph that can be easily separated from other nodes. In this paper, we thus focus on the task of detecting localized attributes on a graph. We are particularly interested in categorical attributes such as attributes in online social networks, ratings in recommender systems and viruses in cyber-physical systems because they are widely used in numerous data mining applications. To solve the task, we formulate a statistical hypothesis testing problem to decide whether a given attribute is localized or not. We propose two statistics: graph wavelet statistic and graph scan statistic, both of which are provably effective in detecting localized attributes. We validate the robustness of the proposed statistics on both simulated data and two real-world applications: high air-pollution detection and keyword ranking in a co-authorship network collected from IEEE Xplore. Experimental results show that the proposed graph wavelet statistic and graph scan statistic are effective and efficient.