  This paper presents a new approach, based on polynomial optimization and the
method of moments, to the problem of anomaly detection. The proposed technique
only requires information about the statistical moments of the normal-state
distribution of the features of interest and compares favorably with existing
approaches (such as Parzen windows and 1-class SVM). In addition, it provides a
succinct description of the normal state. Thus, it leads to a substantial
simplification of the the anomaly detection problem when working with higher
dimensional datasets.
