Time series discords are a useful primitive for time series anomaly detection, and the matrix profile is capable of capturing discord effectively. There exist many research efforts to improve the scalability of discord discovery with respect to the length of time series. However, there is surprisingly little work focused on reducing the time complexity of matrix profile computation associated with dimensionality of a multidimensional time series. In this work, we propose a sketch for discord mining among multi-dimensional time series. After an initial pre-processing of the sketch as fast as reading the data, the discord mining has runtime independent of the dimensionality of the original data. On several real world examples from water treatment and transportation, the proposed algorithm improves the throughput by at least an order of magnitude (50X) and only has minimal impact on the quality of the approximated solution. Additionally, the proposed method can handle the dynamic addition or deletion of dimensions inconsequential overhead. This allows a data analyst to consider "what-if" scenarios in real time while exploring the data.

Time series classification is a widely studied problem in the field of time series data mining. Previous research has predominantly focused on scenarios where relevant or foreground subsequences have already been extracted, with each subsequence corresponding to a single label. However, real-world time series data often contain foreground subsequences that are intertwined with background subsequences. Successfully classifying these relevant subsequences requires not only distinguishing between different classes but also accurately identifying the foreground subsequences amidst the background. To address this challenge, we propose a novel subsequence classification method that represents each subsequence as an ego-network, providing crucial nearest neighbor information to the model. The ego-networks of all subsequences collectively form a time series subsequence graph, and we introduce an algorithm to efficiently construct this graph. Furthermore, we have demonstrated the significance of enforcing temporal consistency in the prediction of adjacent subsequences for the subsequence classification problem. To evaluate the effectiveness of our approach, we conducted experiments using 128 univariate and 30 multivariate time series datasets. The experimental results demonstrate the superior performance of our method compared to alternative approaches. Specifically, our method outperforms the baseline on 104 out of 158 datasets.

The matrix profile is an effective data mining tool that provides similarity join functionality for time series data. Users of the matrix profile can either join a time series with itself using intra-similarity join (i.e., self-join) or join a time series with another time series using inter-similarity join. By invoking either or both types of joins, the matrix profile can help users discover both conserved and anomalous structures in the data. Since the introduction of the matrix profile five years ago, multiple efforts have been made to speed up the computation with approximate joins; however, the majority of these efforts only focus on self-joins. In this work, we show that it is possible to efficiently perform approximate inter-time series similarity joins with error bounded guarantees by creating a compact "dictionary" representation of time series. Using the dictionary representation instead of the original time series, we are able to improve the throughput of an anomaly mining system by at least 20X, with essentially no decrease in accuracy. As a side effect, the dictionaries also summarize the time series in a semantically meaningful way and can provide intuitive and actionable insights. We demonstrate the utility of our dictionary-based inter-time series similarity joins on domains as diverse as medicine and transportation.

Publishing and sharing data is crucial for the data mining community, allowing collaboration and driving open innovation. However, many researchers cannot release their data due to privacy regulations or fear of leaking confidential business information. To alleviate such issues, we propose the Time Series Synthesis Using the Matrix Profile (TSSUMP) method, where synthesized time series can be released in lieu of the original data. The TSSUMP method synthesizes time series by preserving similarity join information (i.e., Matrix Profile) while reducing the correlation between the synthesized and the original time series. As a result, neither the values for the individual time steps nor the local patterns (or shapes) from the original data can be recovered, yet the resulting data can be used for downstream tasks that data analysts are interested in. We concentrate on similarity joins because they are one of the most widely applied time series data mining routines across different data mining tasks. We test our method on a case study of ECG and gender masking prediction. In this case study, the gender information is not only removed from the synthesized time series, but the synthesized time series also preserves enough information from the original time series. As a result, unmodified data mining tools can obtain near-identical performance on the synthesized time series as on the original time series.

The most useful data mining primitives are distance measures. With an effective distance measure, it is possible to perform classification, clustering, anomaly detection, segmentation, etc. For single-event time series Euclidean Distance and Dynamic Time Warping distance are known to be extremely effective. However, for time series containing cyclical behaviors, the semantic meaningfulness of such comparisons is less clear. For example, on two separate days the telemetry from an athlete workout routine might be very similar. The second day may change the order in of performing push-ups and squats, adding repetitions of pull-ups, or completely omitting dumbbell curls. Any of these minor changes would defeat existing time series distance measures. Some bag-of-features methods have been proposed to address this problem, but we argue that in many cases, similarity is intimately tied to the shapes of subsequences within these longer time series. In such cases, summative features will lack discrimination ability. In this work we introduce PRCIS, which stands for Pattern Representation Comparison in Series. PRCIS is a distance measure for long time series, which exploits recent progress in our ability to summarize time series with dictionaries. We will demonstrate the utility of our ideas on diverse tasks and datasets.

Over the last decade, time series motif discovery has emerged as a useful primitive for many downstream analytical tasks, including clustering, classification, rule discovery, segmentation, and summarization. In parallel, there has been an increased understanding that Dynamic Time Warping (DTW) is the best time series similarity measure in a host of settings. Surprisingly however, there has been virtually no work on using DTW to discover motifs. The most obvious explanation of this is the fact that both motif discovery and the use of DTW can be computationally challenging, and the current best mechanisms to address their lethargy are mutually incompatible. In this work, we present the first scalable exact method to discover time series motifs under DTW. Our method automatically performs the best trade-off between time-to-compute and tightness-of-lower-bounds for a novel hierarchy of lower bounds representation we introduce. We show that under realistic settings, our algorithm can admissibly prune up to 99.99% of the DTW computations.

Noname manuscript No. (will be inserted by the editor)Time series classification for varying length series Chang Wei Tan · Fran cois Petitjean· Eamonn Keogh · Geoffrey I. Webb the date of receipt and acceptance should be inserted later Abstract Research into time series classification has tended to focus on the case of series of uniform length. However, it is common for real-world time series data to have unequal lengths. Differing time series lengths may arise from a number of fundamentally different mechanisms. In this work, we identify and evaluate two classes of such mechanisms - variations in sampling rate relative to the relevant signal and variations between the start and end points of one time series relative to one another. We investigate how time series generated by each of these classes of mechanism are best addressed for time series classification. We perform extensive experiments and provide practical recommendations on how variations in length should be handled in time series classification. Keywords Time Series Classification, Proximity Forest, Dynamic Time Warping 1 Introduction Time series classification (TSC) is an important task in many modern world applications such as remote sensing (Pelletier et al., 2019; Petitjean et al., 2012), astronomy (Batista et al., 2011), speech recognition (Hamooni et al., 2016), and insect classification (Chen et al., 2014). The time series to be classified are the observed outputs generated by some process. The classification task often relates to identifying the class of the process that generated the series. Each class of process might be considered as a realization of one or more ideals (in the Platonic sense) or prototypes. The resulting time series can then beChang Wei Tan · Fran cois Petitjean· Geoffrey I. Webb Faculty of Information Technology 25 Exhibition Walk Monash University, Melbourne VIC 3800, Australia Email: chang.tan@monash.edu,francois.petitjean@monash.edu,geoff.webb@monash.edu An observed time series might differ from the ideal in many ways. Much of the research on time series distance measures in the last decade can be seen as the introduction of techniques to mitigate these differences, either as a preprocessing step or directly in a distance measure. For example, variations in amplitude and offset are typically addressed in time series classification by normalization of the series (Rakthanmanon et al., 2012). Some observed values may be erroneous and might be addressed by outlier detection (Basu and Meckesheimer, 2007) and subsequent reinterpolation (Pelletier et al., 2019).

Since its introduction, unsupervised representation learning has attracted a lot of attention from the research community, as it is demonstrated to be highly effective and easy-to-apply in tasks such as dimension reduction, clustering, visualization, information retrieval, and semi-supervised learning. In this work, we propose a novel unsupervised representation learning framework called neighbor-encoder, in which domain knowledge can be easily incorporated into the learning process without modifying the general encoder-decoder architecture of the classic autoencoder.In contrast to autoencoder, which reconstructs the input data itself, neighbor-encoder reconstructs the input data's neighbors. As the proposed representation learning problem is essentially a neighbor reconstruction problem, domain knowledge can be easily incorporated in the form of an appropriate definition of similarity between objects. Based on that observation, our framework can leverage any off-the-shelf similarity search algorithms or side information to find the neighbor of an input object. Applications of other algorithms (e.g., association rule mining) in our framework are also possible, given that the appropriate definition of neighbor can vary in different contexts. We have demonstrated the effectiveness of our framework in many diverse domains, including images, text, and time series, and for various data mining tasks including classification, clustering, and visualization. Experimental results show that neighbor-encoder not only outperforms autoencoder in most of the scenarios we consider, but also achieves the state-of-the-art performance on text document clustering.

In 2002, the UCR time series classification archive was first released with sixteen datasets. It gradually expanded, until 2015 when it increased in size from 45 datasets to 85 datasets. In October 2018 more datasets were added, bringing the total to 128. The new archive contains a wide range of problems, including variable length series, but it still only contains univariate time series classification problems. One of the motivations for introducing the archive was to encourage researchers to perform a more rigorous evaluation of newly proposed time series classification (TSC) algorithms. It has worked: most recent research into TSC uses all 85 datasets to evaluate algorithmic advances. Research into multivariate time series classification, where more than one series are associated with each class label, is in a position where univariate TSC research was a decade ago. Algorithms are evaluated using very few datasets and claims of improvement are not based on statistical comparisons. We aim to address this problem by forming the first iteration of the MTSC archive, to be hosted at the website www.timeseriesclassification.com. Like the univariate archive, this formulation was a collaborative effort between researchers at the University of East Anglia (UEA) and the University of California, Riverside (UCR). The 2018 vintage consists of 30 datasets with a wide range of cases, dimensions and series lengths. For this first iteration of the archive we format all data to be of equal length, include no series with missing data and provide train/test splits.

The UCR Time Series Archive - introduced in 2002, has become an important resource in the time series data mining community, with at least one thousand published papers making use of at least one dataset from the archive. The original incarnation of the archive had sixteen datasets but since that time, it has gone through periodic expansions. The last expansion took place in the summer of 2015 when the archive grew from 45 datasets to 85 datasets. This paper introduces and will focus on the new data expansion from 85 to 128 datasets. Beyond expanding this valuable resource, this paper offers pragmatic advice to anyone who may wish to evaluate a new algorithm on the archive. Finally, this paper makes a novel and yet actionable claim: of the hundreds of papers that show an improvement over the standard baseline (1-Nearest Neighbor classification), a large fraction may be misattributing the reasons for their improvement. Moreover, they may have been able to achieve the same improvement with a much simpler modification, requiring just a single line of code.