Signed Graph Laplacian for Semi-Supervised Anomaly Detection

Anomaly detection is a cutting-edge technology in the fields of healthcare and machine failure detection. It is well known that the performance of anomaly detection can be improved with more labeled data. However, it is common to predict anomalous and normal data in where are large unlabeled data and small labeled data. Generally, using a large amount of labeled data can lead to high accuracy prediction. However, the cost of labeling data is expensive, which can lead to challenges in anomaly detection. To achieve high prediction rate of anomaly detection, it is required to utilize a large amount of unlabeled data. The only way to achieve high rates of anomaly detection using both unlabeled data and labeled data is to use semi-supervised learning. However, if semi-supervised learning is used without data preprocessing, there is a limitation to obtain high detection rates. To perform effectively preprocess, we propose a scheme that leverages graph theory and semi-supervised learning to address the limitation. The proposed scheme uses graph Laplacian to get high accuracy in situations where there is little labeled data and a lot of unlabeled data. We further extend our scheme by considering friendly-antagonistic interactions into graph Laplacian, which is called signed graph Laplacian. We show that using signed graph Laplacian can improve the performance of our anomaly detection scheme. Furthermore, we evaluate our proposed scheme on a variety of validated datasets and show that it outperforms state-of-the-art semi-supervised anomaly detection methods.