Parameter rating by diffusion gradient

Anomaly detection is a central task in high-dimensional data analysis. It can be performed by using dimensionality reduction methods to obtain a low-dimensional representation of the data, which reveals the geometry and the patterns that exist and govern it. Usually, anomaly detection methods classify highdimensional vectors that represent data points as either normal or abnormal. Revealing the parameters (i.e., features) that cause detected abnormal behaviors is critical in many applications. However, this problem is not addressed by recent anomalydetection methods and, specifically, by nonparametric methods, which are based on feature-free analysis of the data. In this chapter, we provide an algorithm that rates (i.e., ranks) the parameters that cause an abnormal behavior to occur.We assume that the anomalies have already been detected by other anomaly detection methods and they are treated in this chapter as prior knowledge. Our algorithm is based on the underlying potential of the diffusion process that is used in DiffusionMaps (DM) for dimensionality reduction. We show that the gradient of this potential indicates the direction from an anomalous data point to a cluster that represents a normal behavior. We use this direction to rate the parameters that cause the abnormal behavior to occur. The algorithm was applied successfully to rate the measured parameters from process control and networking applications.