Consensus Patterns of a Set of Time Series via a Wavelet-Based Temporal Localization: Emphasizing the Utility over Point-Wise Averaging and Averaging under Dynamic Time Warping

Chekhaprabha Priyadarshanee Waduge,Naleen Chaminda Ganegoda,Darshana Chitraka Wickramarachchi,Ravindra Shanthakumar Lokupitiya,Fernando Simoes

doi:10.1155/2021/5535363

Chekhaprabha Priyadarshanee Waduge, Naleen Chaminda Ganegoda + Show 3 more

Open Access

https://doi.org/10.1155/2021/5535363

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Abstract

Summarizing or averaging a sequential data set (i.e., a set of time series) can be comprehensively approached as a result of sophisticated computational tools. Averaging under Dynamic Time Warping (DTW) is one such tool that captures consensus patterns. DTW acts as a similarity measure between time series, and subsequently, an averaging method must be executed upon the behaviour of DTW. However, averaging under DTW somewhat neglects temporal aspect since it is on the search of similar appearances rather than stagnating on corresponding time-points. On the contrary, the mean series carrying point-wise averages provides only a weak consensus pattern as it may over-smooth important temporal variations. As a compromise, a pool of consensus series termed Ultimate Tamed Series (UTS) is studied here that adheres to temporal decomposition supported by the discrete Haar wavelet. We claim that UTS summarizes localized patterns, which would not be reachable via the series under DTW or the mean series. Neighbourhood of localization can be altered as a user can customize different levels of decomposition. In validation, comparisons are carried out with the series under DTW and the mean series via Euclidean distance and the distance resulted by DTW itself. Two sequential data sets are selected for this purpose from a standard repository.

Highlights

Classical topic of summarizing and classifying a sequential data set has recently gained a new outlook because of data mining and machine learning procedures [1,2,3]
We present consensus series (UTS-Lh, Dynamic Time Warping Series (DTWS), and the mean series) in a systematic way for comparisons
Applicability of Ultimate Tamed Series (UTS)- Lh is overseen on top of DTWS and the mean series

Summary

Introduction

Classical topic of summarizing and classifying a sequential data set (i.e., a set of time series) has recently gained a new outlook because of data mining and machine learning procedures [1,2,3]. Investigating common pattern (or shape) attributes (e.g., monotonic, oscillatory, and periodic) of a set of time series is ever so attainable, but still challenging even with advanced computer technology. The basic reason is that data are ordered unlike in a usual data set. Time series arise in many scenarios such as economic and financial indices, weather forecasting, disease transmission, census data, market surveys, quality control, and inventory studies [4]. We always need effective and efficient techniques to extract valuable information from sequential data [6,7,8]

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