A review on outlier/anomaly detection in time series data

The simplified series is obtained by first applying their univariate technique to each of the variables independently; that is, each univariate batch of data is separated into variable-length subsequences, and the obtained subsequences are then clustered as explained in Section 4.1. With this process, a set of representative univariate subsequences is obtained for each variable. Each new multivariate batch of data is then represented by a vector of distances, (d 1,d 2,...,d l), where d j represents the Euclidean distance between the j th variable-length subsequence of the new batch and its corresponding representative subsequence. As with their univariate technique, the reference of normality that is considered by this method is the same time series. The technique proposed by Hu et al. [2019] is also based on reducing the dimensionality of the time series and allows us to detect variable-length discords, while using the same time series as the reference of normality. This is based on the fact that the most unusual subsequences tend to have local regions with significantly different densities (points that are similar) in comparison to the other subsequences in the series. Each point in the new univariate time series describes the density of a local region of the input multivariate time series obtained by a sliding window. This series is also used to obtain the variable-length subsequences. Discords are identified using the Euclidean and Bhattacharyya distances simultaneously.