Fuzzy kkNN Entropy and its Anomaly Detection

With the successful application of granular computing in anomaly detection, a variety of tools including fuzzy information entropy can achieve superior detection results. However, fuzzy information entropy calculates fuzzy similarity through a global strategy, ignoring the local information in the data. To address this deficiency, this paper constructs a fuzzykNN entropy theory and applies it to identify anomalies. Firstly, fuzzyk-similarity and fuzzykNN are defined, andkNN entropy theory and the related information-theoretic metrics are proposed. Then, the relevant definitions and propositions of fuzzykNN entropy, fuzzyk-joint entropy, fuzzyk-conditional information entropy, as well as fuzzyk-mutual information are elaborated. Based on the proposed theory, an anomaly detection model is constructed. At first, the fuzzyk-similarity relation matrix is constructed based on the fuzzyk-similarity in the proposed theory, and the relative fuzzykNN entropy is calculated. Based on the relative fuzzykNN entropy, the fuzzyk-relation anomaly degree is defined to characterize the anomaly intensity of fuzzykNN information granules. Then, the anomaly factor based on fuzzykNN entropy is built to represent the anomaly degree of data objects. Finally, the corresponding FuzzykNN Entropy-based Anomaly Detection algorithm (FkEAD) is designed. Comparative experiments are conducted with 11 state-of-the-art anomaly detection methods on thirty public datasets. The results reveal that the proposed method achieves better performance.