Establishing the community structure of signed interconnected graph in data

Graph communities can be an efficient and robust way to identify the clustering structure of data. A common scenario is the case that data matrix can be represented by graphs from instance and attribute. How to associate the consistent community structure in the two data matrices from instance and attribute respectively are important for understanding the data. We propose a novel and simple method to construct a interconnected network, by combining the instance and attribute graphs of the data as the interconnections between them, which unlike the bipartite graph cluster or the bicluster approaches. The community structure can be detected with an extended Q-modularity algorithm that also takes negative weighted edges into consideration, where each community can contain both instances and attributes that provide the association. Toy models are provided to illustrate the efficiency of the method. Real data of waste water treatment plants are treated by this method and the consistent community structure associated with day/measurements can be found.