Anomaly Detection Based on Wavelet Domain GARCH Random Field Modeling

Abstract

One-dimensional Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model is widely used for modeling financial time series. Extending the GARCH model to multiple dimensions yields a novel clutter model which is capable of taking into account important characteristics of a wavelet-based multiscale feature space, namely heavy-tailed distributions and innovations clustering as well as spatial and scale correlations. We show that the multidimensional GARCH model generalizes the casual Gauss Markov random field (GMRF) model, and we develop a multiscale matched subspace detector (MSD) for detecting anomalies in GARCH clutter. Experimental results demonstrate that by using a multiscale MSD under GARCH clutter modeling, rather than GMRF clutter modeling, a reduced false-alarm rate can be achieved without compromising the detection rate