Query-Based Evolutionary Graph Cuboid Outlier Detection

Graph-OLAP is an online analytical framework which allows us to obtain various projections of a graph, each of which helps us view the graph along multiple dimensions and multiple levels. Given a series of snapshots of a temporal heterogeneous graph, we aim to find interesting projections of the graph which have anomalous evolutionary behavior. Detecting anomalous projections in a series of such snapshots can be helpful for an analyst to understand the regions of interest from the temporal graph. Identifying such semantically related regions in the graph allows the analyst to derive insights from temporal graphs which enables her in making decisions. While most of the work on temporal outlier detection is performed on nodes, subgraphs and communities, we are the first to propose detection of evolutionary graph cuboid outliers. Further, we perform this detection in a query sensitive manner. Thus, an evolutionary graph cuboid outlier is a projection (or cuboid) of a snapshot of the temporal graph such that it contains an unexpected number of matches for the query with respect to other cuboids both in the same snapshot as well as in the other snapshots. Identifying such outliers is challenging because (1) the number of cuboids per snapshot could be large, and (2) number of snapshots could itself be large. We model the problem by predicting the outlier score for each cuboid in each snapshot. We propose to build subspace ensemble regression models to learn (a) the behavior of a cuboid across different snapshots, and (b) the behavior of all the cuboids in a given snapshot. Experimental results on both synthetic and real datasets show the effectiveness of the proposed algorithm in discovering evolutionary graph cuboid outliers.