Multi-Variate Time Series Similarity Measures and Their Robustness Against Temporal Asynchrony

abstract: The amount of time series data generated is increasing due to the integration of sensor technologies with everyday applications, such as gesture recognition, energy optimization, health care, video surveillance. The use of multiple sensors simultaneously for capturing different aspects of the real world attributes has also led to an increase in dimensionality from uni-variate to multi-variate time series. This has facilitated richer data representation but also has necessitated algorithms determining similarity between two multi-variate time series for search and analysis. Various algorithms have been extended from uni-variate to multi-variate case, such as multi-variate versions of Euclidean distance, edit distance, dynamic time warping. However, it has not been studied how these algorithms account for asynchronous in time series. Human gestures, for example, exhibit asynchrony in their patterns as different subjects perform the same gesture with varying movements in their patterns at different speeds. In this thesis, we propose several algorithms (some of which also leverage metadata describing the relationships among the variates). In particular, we present several techniques that leverage the contextual relationships among the variates when measuring multi-variate time series similarities. Based on the way correlation is leveraged, various weighing mechanisms have been proposed that determine the importance of a dimension for discriminating between the time series as giving the same weight to each dimension can led to misclassification. We next study the robustness of the considered techniques against different temporal asynchronies, including shifts and stretching. Exhaustive experiments were carried on datasets with multiple types and amounts of temporal asynchronies. It has been observed that accuracy of algorithms that rely on data to discover variate relationships can be low under the presence of temporal asynchrony, whereas in case of algorithms that rely on external metadata, robustness against asynchronous distortions tends to be stronger. Specifically, algorithms using external metadata have better classification accuracy and cluster separation than existing state-of-the-art work, such as EROS, PCA, and naive dynamic time warping.Dissertation/ThesisMasters Thesis Computer Science 201

Identifying Algebraic Properties to Support Optimization of Unary Similarity Queries ⋆

Abstract. Conventional operators for data retrieval are either based on exact matching or on total order relationship among elements. Neither of them is appropriate to manage complex data, such as multimedia data, time series and genetic sequences. In fact, the most meaningful way to compare complex data is by similarity. However, the Relational Algebra, employed in the Relational Database Management Systems (RDBMS), cannot express similarity criteria. In order to address this issue, we provide here an extension of the Relational Algebra, aimed at representing similarity queries in algebraic expressions. This paper identifies fundamental properties to allow the integration of the unary similarity operators into the Relational Algebra to handle similarity-based operators, either alone or combined with the existing (exact matching and/or relational) operators. We also show how to take advantage of such properties to optimize similarity queries, including these properties into a similarity query optimizer developed for a Similarity Retrieval Engine, which uses an existing RDBMS to answer similarity queries. Key words: similarity algebra, algebraic properties, query optimization, unary similarity queries