J-Distance Discord: An Improved Time Series Discord Definition and Discovery Method

A time series discord is a subsequence that is maximally different to all the rest subsequences of a longer time series. Classic discord discovery has been used for detecting anomalous or interesting pattern, which usually represents the most unusual subsequences within a time series. However, an anomalous or interesting pattern may happen twice or more times so that any instance of this pattern is not distinct enough to be a top discord. To mitigate the issue, we propose an improved definition named J-distance discord (JDD), which incorporates the methodologies of KNN (k nearest neighbor) algorithm. JDD measures the similarity between a subsequence and its Jth most similar subsequence and ranks discords according to the similarity. We also propose a JDD discovery method to reduce the extra computational requirements brought by JDD definition. Experiments on synthetic and real world datasets show that JDD captures more de-facto anomalous and interesting patterns compared to the results of the original definition of discord. Besides, the JDD discovery method is as fast as the classic discord discovery method in terms of computational efficiency.