Abstract :
Attributed graphs are widely used for the representation of social networks, gene and protein interactions, communication networks, or product co-purchase in web stores. Each object is represented by its relationships to other objects (edge structure) and its individual properties (node attributes). For instance, social networks store friendship relations as edges and age, income, and other properties as attributes. These relationships and properties seem to be dependent on each other and exploiting these dependencies is beneficial, e.g. for community detection and community outlier mining. However, state-of-the-art techniques highly rely on this dependency assumption. In particular, community outlier mining is able to detect an outlier node if and only if connected nodes have similar values in all attributes. Such assumptions are generally known as homophily and are widely used. However, looking at multivariate spaces, one can observe that not all given attributes have high dependencies with the graph structure. For example, social properties such as income or age have strong dependencies with the graph structure of social networks. In contrast, properties such as gender are rather independent from it. Consequently, recent graph mining algorithms degenerate for multivariate attribute spaces that lack dependency with the graph structure in some of the attributes.
