Gabe Chandler (Pomona College)

Title: Graphical Anomaly Detection for High Dimensional and Object Data

Abstract: Anomaly detection is an important task in data analysis, though an agreed upon definition of what constitutes an outlier does not exist.  Accordingly, a graphical tool that can highlight interesting observations in a data set that the scientist can then investigate with domain specific knowledge would be of value.  The depth quantile function (DQF), a recently introduced feature map that takes data of arbitrary dimension to a function of a single variable while encoding certain geometric information, will provide such a tool.  After introducing the DQF, we will discuss adaptations that make it particularly suited to the problem of anomaly detection, particularly the case where the non-anomalous data is living on a lower dimensional manifold in the data space.  The DQF is also kernelizable, allowing applications to non-Euclidean data, as will be demonstrated via several examples.