Semi-Supervised Anomaly Detection Based on Quadratic Multiform Separation

In this paper we propose a novel method for semi-supervised anomaly detection (SSAD). Our classifier is named QMS22 as its inception was dated 2022 upon the framework of quadratic multiform separation (QMS), a recently introduced classification model. QMS22 tackles SSAD by solving a multi-class classification problem involving both the training set and the test set of the original problem. The classification problem intentionally includes classes with overlapping samples. One of the classes contains mixture of normal samples and outliers, and all other classes contain only normal samples. An outlier score is then calculated for every sample in the test set using the outcome of the classification problem. We also include performance evaluation of QMS22 against top performing classifiers using ninety-five benchmark imbalanced datasets from the KEEL repository. These classifiers are BRM (Bagging-Random Miner), OCKRA (One-Class K-means with Randomly-projected features Algorithm), ISOF (Isolation Forest), and ocSVM (One-Class Support Vector Machine). It is shown by using the area under the curve of the receiver operating characteristic curve as the performance measure, QMS22 significantly outperforms ISOF and ocSVM. Moreover, the Wilcoxon signed-rank tests reveal that there is no statistically significant difference when testing QMS22 against BRM nor QMS22 against OCKRA.