Synergistic coding by cortical neural ensembles
IEEE Transactions on Information Theory - Special issue on information theory in molecular biology and neuroscience
Fraud Detection: Methods of Analysis for Hypergraph Data
ASONAM '12 Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012)
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This paper addresses the problem of detecting anomalous multivariate co-occurrences using a limited number of unlabeled training observations. A novel method based on using a hypergraph representation of the data is proposed to deal with this very high-dimensional problem. Hypergraphs constitute an important extension of graphs which allow edges to connect more than two vertices simultaneously. A variational Expectation-Maximization algorithm for detecting anomalies directly on the hypergraph domain without any feature selection or dimensionality reduction is presented. The resulting estimate can be used to calculate a measure of anomalousness based on the False Discovery Rate. The algorithm has $O(np)$ computational complexity, where $n$ is the number of training observations and $p$ is the number of potential participants in each co-occurrence event. This efficiency makes the method ideally suited for very high-dimensional settings, and requires no tuning, bandwidth or regularization parameters. The proposed approach is validated on both high-dimensional synthetic data and the Enron email database, where $p 75,000$, and it is shown that it can outperform other state-of-the-art methods.