Distance measures are fundamental to time series analysis and have been extensively studied for decades. Until now, research efforts mainly focused on univariate time series, leaving multivariate cases largely under-explored. Furthermore, the existing experimental studies on multivariate distances have critical limitations: (a) focusing only on lock-step and elastic measures while ignoring categories such as sliding and kernel measures; (b) considering only one normalization technique; and (c) placing limited focus on statistical analysis of findings. Motivated by these shortcomings, we present the most complete evaluation of multivariate distance measures to date. Our study examines 30 standalone measures across 8 categories, 2 channel-dependency models, and considers 13 normalizations. We perform a comprehensive evaluation across 30 datasets and 3 downstream tasks, accompanied by rigorous statistical analysis. To ensure fairness, we conduct a thorough investigation of parameters for methods in both a supervised and an unsupervised manner. Our work verifies and extends earlier findings, showing that insights from univariate distance measures also apply to the multivariate case: (a) alternative normalization methods outperform Z-score, and for the first time, we demonstrate statistical differences in certain categories for the multivariate case; (b) multiple lock-step measures are better suited than Euclidean distance, when it comes to multivariate time series; and (c) newer elastic measures outperform the widely adopted Dynamic Time Warping distance, especially with proper parameter tuning in the supervised setting. Moreover, our results reveal that (a) sliding measures offer the best trade-off between accuracy and runtime; (b) current normalization techniques fail to significantly enhance accuracy on multivariate time series and, surprisingly, do not outperform the no normalization case, indicating a lack of appropriate solutions for normalizing multivariate time series; and (c) independent consideration of time series channels is beneficial only for elastic measures. In summary, we offer guidelines to aid in designing and selecting preprocessing strategies and multivariate distance measures for our community.

The similarity search task involves identifying pairs of similar vectors, e.g., time series. For example, given a query$q$, the user might wish to find all vectors in a dataset with a cosine similarity with$q$higher than a threshold$t$, or to find the top-k most similar vectors with$q$, using Euclidean distance. The task has been widely considered in different domains, ranging from data science for detecting correlations that help the analyst extract insights from the data, to e-commerce for recommending additional purchases to the users based on their shopping behavior. Accordingly, many similarity search algorithms and indices were proposed in the literature, focusing on efficiency, scalability for big datasets, and different distance measures. However, the majority of past work only considers pairwise similarity/distance measures. In this talk we will revisit similarity search under the lens of multivariate similarity measures.

Abstract Correlation analysis is an invaluable tool in many domains, for better understanding the data and extracting salient insights. Most works to date focus on detecting high pairwise correlations. A generalization of this problem with known applications but no known efficient solutions involves the discovery of strong multivariate correlations, i.e., finding vectors (typically in the order of 3–5 vectors) that exhibit a strong dependence when considered altogether. In this work, we propose algorithms for detecting multivariate correlations in static and streaming data. Our algorithms, which rely on novel theoretical results, support four different correlation measures, and allow for additional constraints. Our extensive experimental evaluation examines the properties of our solution and demonstrates that our algorithms outperform the state-of-the-art, typically by an order of magnitude.

Correlation analysis is an invaluable tool in many domains, for better understanding data and extracting salient insights. Most works to date focus on detecting high pairwise correlations. A generalization of this problem with known applications but no known efficient solutions involves the discovery of strong multivariate correlations, i.e., finding vectors (typically in the order of 3 to 5 vectors) that exhibit a strong dependence when considered altogether. In this work we propose algorithms for detecting multivariate correlations in static and streaming data. Our algorithms, which rely on novel theoretical results, support two different correlation measures, and allow for additional constraints. Our extensive experimental evaluation examines the properties of our solution and demonstrates that our algorithms outperform the state-of-the-art, typically by an order of magnitude.