# CADDeLaG: Framework for distributed anomaly detection in large dense graph sequences

Random walk based distance measures for graphs such as commute-time distance are useful in a variety of graph algorithms, such as clustering, anomaly detection, and creating low dimensional embeddings. Since such measures hinge on the spectral decomposition of the graph, the computation becomes a bottleneck for large graphs and do not scale easily to graphs that cannot be loaded in memory. Most existing graph mining libraries for large graphs either resort to sampling or exploit the sparsity structure of such graphs for spectral analysis. However, such methods do not work for dense graphs constructed for studying pairwise relationships among entities in a data set. Examples of such studies include analyzing pairwise locations in gridded climate data for discovering long distance climate phenomena. These graphs representations are fully connected by construction and cannot be sparsified without loss of meaningful information. In this paper we describe CADDeLaG, a framework for scalable computation of commute-time distance based anomaly detection in large dense graphs without the need to load the entire graph in memory. The framework relies on Apache Spark's memory-centric cluster-computing infrastructure and consists of two building blocks: a decomposable algorithm for commute time distance computation and a distributed linear system solver. We illustrate the scalability of CADDeLaG and its dependency on various factors using both synthetic and real world data sets. We demonstrate the usefulness of CADDeLaG in identifying anomalies in a climate graph sequence, that have been historically missed due to ad hoc graph sparsification and on an election donation data set.

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