Entropy-Based Anomaly Detection for Gaussian Mixture Modeling

Gaussian mixture modeling is a generative probabilistic model that assumes that the observed data are generated from a mixture of multiple Gaussian distributions. This mixture model provides a flexible approach to model complex distributions that may not be easily represented by a single Gaussian distribution. The Gaussian mixture model with a noise component refers to a finite mixture that includes an additional noise component to model the background noise or outliers in the data. This additional noise component helps to take into account the presence of anomalies or outliers in the data. This latter aspect is crucial for anomaly detection in situations where a clear, early warning of an abnormal condition is required. This paper proposes a novel entropy-based procedure for initializing the noise component in Gaussian mixture models. Our approach is shown to be easy to implement and effective for anomaly detection. We successfully identify anomalies in both simulated and real-world datasets, even in the presence of significant levels of noise and outliers. We provide a step-by-step description of the proposed data analysis process, along with the corresponding R code, which is publicly available in a GitHub repository.