A review on outlier/anomaly detection in time series data <s> Univariate detection techniques. Each variable of the multivariate time series can contain subsequence outliers <s> We present a new algorithm for detecting anomalies in realvalued multidimensional time series. Our algorithm uses an exemplar-based model that is used to detect anomalies in single dimensions of the time series and a function that predicts one dimension from a related one to detect anomalies in multiple dimensions. The algorithm is shown to work on a variety of dierent types of time series as well as to detect a variety of dierent types of anomalies. We compare our algorithm to other algorithms for both one-dimensional and multidimensional time series and demonstrate that it improves over the state-of-the-art. <s> BIB001 </s> A review on outlier/anomaly detection in time series data <s> Univariate detection techniques. Each variable of the multivariate time series can contain subsequence outliers <s> We investigate algorithms for efficiently detecting anomalies in real-valued one-dimensional time series. Past work has shown that a simple brute force algorithm that uses as an anomaly score the Euclidean distance between nearest neighbors of subsequences from a testing time series and a training time series is one of the most effective anomaly detectors. We investigate a very efficient implementation of this method and show that it is still too slow for most real world applications. Next, we present a new method based on summarizing the training time series with a small set of exemplars. The exemplars we use are feature vectors that capture both the high frequency and low frequency information in sets of similar subsequences of the time series. We show that this exemplar-based method is both much faster than the efficient brute force method as well as a prediction-based method and also handles a wider range of anomalies. We compare our algorithm across a large variety of publicly available time series and encourage others to do the same. Our exemplar-based algorithm is able to process time series in minutes that would take other methods days to process. <s> BIB002 </s> A review on outlier/anomaly detection in time series data <s> Univariate detection techniques. Each variable of the multivariate time series can contain subsequence outliers <s> The problem of anomaly detection in time series has received a lot of attention in the past two decades. However, existing techniques cannot locate where the anomalies are within anomalous time series, or they require users to provide the length of potential anomalies. To address these limitations, we propose a self-learning online anomaly detection algorithm that automatically identifies anomalous time series, as well as the exact locations where the anomalies occur in the detected time series. In addition, for multivariate time series, it is difficult to detect anomalies due to the following challenges. First, anomalies may occur in only a subset of dimensions (variables). Second, the locations and lengths of anomalous subsequences may be different in different dimensions. Third, some anomalies may look normal in each individual dimension but different with combinations of dimensions. To mitigate these problems, we introduce a multivariate anomaly detection algorithm which detects anomalies and identifies the dimensions and locations of the anomalous subsequences. We evaluate our approaches on several real-world datasets, including two CPU manufacturing data from Intel. We demonstrate that our approach can successfully detect the correct anomalies without requiring any prior knowledge about the data. <s> BIB003 </s> A review on outlier/anomaly detection in time series data <s> Univariate detection techniques. Each variable of the multivariate time series can contain subsequence outliers <s> Abstract Discord search is an important technique for time series analysis, especially for anomaly detection. In recent years, many computational approaches of discord search were studied; however, limitation exists while only the problems with univariate time series data can be well addressed. In this study, we proposed a novel computational framework to identify discords from multivariate time series (MTS) data, namely, LRRDS (Local Recurrence Rate based Discord Search). LRRDS accurately identifies the discords by analyzing a recurrence plot, which is transformed from the original time series data. An innovative strategy was employed to improve the efficiency for pair-wise distance comparison of two subsequences. In the experimental simulations, LRRDS was applied to an extensive number of MTS datasets. Results show that the proposed approach is more efficient than existing methods, such as GDS. In conclusion, the LRRDS approach solves the adaptability problem of discord sequences in multi-dimensional space and guarantees the computational effectiveness and efficiency. <s> BIB004
that are independent of other variables. The identification of those subsequences may be carried out by applying the univariate techniques discussed in Section 4.1 to each time-dependent variable. In particular, BIB001 BIB002 apply the exemplar-based method to each variable of the multivariate input time series, using an external time series as the reference of normality and without considering the correlation that may exist between variables. Recall that omitting this correlation can lead to a loss of information. Intending to simplify the multivariate task but without completely ignoring the correlation between the variables, some methods reduce the dimensionality of the input series before applying a univariate detection technique. For example, BIB003 extend their method for univariate subsequences by applying clustering to a simplified series to detect variable-length subsequence outliers (see equation (7)). 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 t h 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 BIB004 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 BIB003 identify multivariate batch outliers, the variable-length subsequence outliers that are then identified within those batches affect a single variable. Finally, none of the analyzed techniques detect periodic subsequence outliers. reviewed in this section deal with multiple time-dependent variables simultaneously and typically detect temporally aligned outliers that affect multiple variables. As shown in Fig. 19 , these techniques are divided into two main groups. However, the philosophy behind some of them is repeated because they are an extension of simpler techniques introduced in previous sections.