IJE TRANSACTIONS B: Applications Vol. 31, No. 2 (February 2018) 250-262   

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A. Salarpour and H. Khotanlou
( Received: October 15, 2017 – Accepted in Revised Form: November 30, 2017 )

Abstract    Multivariate time series (MTS) data are ubiquitous in science and daily life, and how to measure their similarity is a core part of MTS analyzing process. Many of the research efforts in this context have focused on proposing novel similarity measures for the underlying data. However, with the countless techniques to estimate similarity between MTS, this field suffers from a lack of comparative studies using quantitative and large scale evaluations. In order to provide a comprehensive validation, an extensive evaluation of similarity measures for MTS clustering were conducted. The 14 well-known similarity measures with their variants and testing their effectiveness on 23 MTS datasets coming from a wide variety of application domains were re-implemented. In this paper, an overview of these different techniques is given and the empirical comparison regarding their effectiveness based on agglomerative clustering task is presented. Furthermore, the statistical significance tests were used to derive meaningful conclusions. It has been found that all of similarity measures are equivalent, in terms of clustering F-measure, and there is no significant difference between similarity measures based on our datasets. The results provide a comparative background between similarity measures to find the most proper method in terms of performance and computation time in this field.


Keywords    Multivariate time series, similarity measures, clustering, evaluation


چکیده    داده­ های سری­های زمانی چند متغیره در زندگی روزمره و زمینه­ های متفاوتی از علوم به وفور یافت می­ شود و چگونگی اندازه­ گیری شباهت بین این نوع سری­های زمانی یکی از بخش­های اصلی روند آنالیز سری­های زمانی است. حجم زیادی از تحقیقات انجام شده در این زمینه بر روی ارایه معیار های شباهت جدید متمرکز شده است. با وجود ارائه روش­های بسیار برای محاسبه شباهت بین سری­های زمانی، این زمینه همچنان از فقدان یک مطالعه مقایسه ­ای با استفاده از ارزیابی کمی در مقیاس مناسب رنج می­برد. بدین منظور و برای فراهم کردن یک سنجش مقایسه ای، ارزیابی گسترده ای بر روی معیار های شباهت برای خوشه بندی سری­های زمانی انجام داده­ ایم. بدین منظور، 14 معیار شباهت معتبر (به همراه تنوعات آنها) و بررسی اثرگذاری آنها بر روی 23 دیتاست سری زمانی چند متغیره (مربوط به کاربردهای مختلف) انجام شده است. در این مقاله، مقایسه تجربی در خصوص اثر بخشی معیارهای شباهت مبتنی بر خوشه­ بندی سلسه مراتبی ارائه شده است. علاوه بر این، آزمون آماری معناداری نیز برای سنجش معناداری بین بازدهی معیارهای شباهت، بکار گرفته شد. نتایج بدست آمده یک دید مقایسه ای بین معیارهای شباهت و برای یافتن روش مناسب بر اساس بازدهی و پیچیدگی زمانی فراهم می کند. همچنین نتایج نشان داد که تمامی معیارهای شباهت از لحاظ آماری و مبتنی بر آزمون غیرپارامتری اختلاف معناداری ندارند.


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