Anomaly Detection Methods for Nonparametric Fitting Gaussian Mixture Distributions for Data Features

In the realm of unsupervised anomaly detection, the increasing scale of datasets, escalating dimensionality, and growing complexity of features have given rise to a host of challenges, such as high computational costs, intricate hyperparameter tuning, limited model interpretability, and difficulties in analyzing data features. To address these issues, we propose an anomaly detection method that non-parametrically fits a Gaussian mixture distribution of data features (NGMDAD), which utilizes the cumulative probability fluctuations of the cumulative probability distribution to non-parametrically fit the Gaussian mixture distribution of data features. NGMDAD first selects feature perturbations for each dimension using the moving average absolute deviation method and then applies them to the data set. Nonparametric estimation of the cumulative probability fluctuations of each feature before and after perturbation by means of an empirical cumulative distribution function reveals the Gaussian mixture distribution properties of the data features. These fluctuations can be used to measure the normality and degree of anomaly of the features under the mixed Gaussian distribution. Finally, the cumulative probability fluctuations of all features for each data point are aggregated to produce an anomaly score. Comparing this score to a predefined threshold allows the data points to be categorized as normal or abnormal. Experiments conducted on eight different real datasets show that NGMDAD outperforms the three benchmark methods in terms of AUC and Precision.