二重カーネル化スコアリングと行列カーネルを用いた異常検知

抄録

We consider the task of simultaneous anomaly detection in a system and its elements by comparing a pair of multivariate data sets. This task corresponds to simultaneously conducting anomaly detection and localization. For solving this task, we estimate scores which represent anomalousness of a whole system and its elements. This scoring is difficult for the following reasons. First, it is not trivial how to estimate the scores by taking into account changes of relationships between the elements, which strongly correlate with each other. Second, it is required that scores of the system and its elements are estimated from a single framework. Otherwise, the relation between the scores is not clear and thus localization becomes difficult. We propose a solution, which is a single framework to simultaneously estimate anomalousness of a system and its elements. The key ideas of the method are the following two. First, we introduce doubly kernelized scores. We construct a score by using difference between kernel matrices defined between elements. Then we represent the difference by using a kernel defined between matrices. Second, we construct matrix kernels, which are defined between different dimensional matrices. This method has the following properties: (1) the method can be applied to any data sets where a kernel can be defined between the elements, (2)can estimate scores of element group of any number, and (3)can be applied to a pair of data sets whose numbers of elements are different. Especially, the second and the third properties are realized by introducing matrix kernels. We demonstrate the effectiveness of the proposed method through the experimental results using three data sets.