Adjoint dynamical kernel density for anomaly detection

Abstract

Anomalies affect data quality and lead to unexpected analysis results in data mining. Although techniques to handle anomalies do exist, they can fail in considering density changes of object along with incremental neighbors. This paper proposes an outlier factor based on the change of adjoint dynamical kernel density (ADD) to represent the degree of the object being an anomaly. The factor is equal to the ratios of the adjoint dynamical kernel density fluctuation (ADDF) of the object and the average ADDF of its neighborhood. ADDF is estimated by the difference of ADD, which describes the difference of every two consecutive adjoint kernel densities (AKD) of the object. AKD indicates kernel densities of the object while its neighbors are added one by one. Importantly, the kernel function is adopted to measure the distance between objects where the kernel trick improves discriminability between objects and reduces the computational burden of the algorithm. The experiments are performed on eight datasets to evaluate the effectiveness of the proposed method with different kernel functions. The experimental results have shown that the proposed method with the Gaussian kernel function has better performance of anomalies recognition and higher adaption of the parameter k of k-nearest neighbors over some other anomaly detection methods.