| The ability to mine data represented as a graph has become important in several domains for detecting various structural patterns, but less work has been done in terms of detecting anomalies in graph-based data. Also, time-series of graphs are becoming more and more common, for example, communication graphs, social networks, etc., and methods for statistical inferences are demanding. While there has been some previous work that used statistical metrics and conditional entropy measurements, the results have been limited to certain types of anomalies and specific domains.;Moreover, most anomaly-detection methods use a supervised approach, which requires some sort of baseline of information from which comparisons or training can be performed. In general, if one has an idea what is normal behavior, deviations from that behavior could constitute an anomaly. However, the issue with those approaches is that one has to train the system, and the data has to already be labeled. It is also known that no single graph feature is uniformly most powerful.;This research introduced a theory of scan statistics on time series of graphs and hypergraphs to investigate an effectiveness on anomaly/change point detection problem. The primary research hypothesis of this work is that scan statistic is capable of detecting certain types of anomalies that are not apparent by using other techniques. Also, by combining multiple graph features, the performance of statistical inference can be improved compared to a method that only uses an individual feature separately.;The result shows that the proposed statistics on time series of graphs and hypergraphs outperforms on certain anomalies. It is further demonstrated that a fusion statistic can provide superior inference compared to individual features alone.;The major contributions of this work are the introduction of a new graph feature on detecting anomaly in time series of graphs and hypergraphs, and the confirmation of adaptive weighting as a mechanism for combination of features. |
