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
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...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5535363 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832561355700305920 |
|---|---|
| author | Chekhaprabha Priyadarshanee Waduge Naleen Chaminda Ganegoda Darshana Chitraka Wickramarachchi Ravindra Shanthakumar Lokupitiya |
| author_facet | Chekhaprabha Priyadarshanee Waduge Naleen Chaminda Ganegoda Darshana Chitraka Wickramarachchi Ravindra Shanthakumar Lokupitiya |
| author_sort | Chekhaprabha Priyadarshanee Waduge |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5691d0f9be784234a4b955bea03cb65e |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-5691d0f9be784234a4b955bea03cb65e2025-02-03T01:25:12ZengWileyJournal of Applied Mathematics1110-757X1687-00422021-01-01202110.1155/2021/55353635535363Consensus 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 WarpingChekhaprabha Priyadarshanee Waduge0Naleen Chaminda Ganegoda1Darshana Chitraka Wickramarachchi2Ravindra Shanthakumar Lokupitiya3Faculty of Graduate Studies, University of Sri Jayewardenepura, Nugegoda, Sri LankaDepartment of Mathematics, University of Sri Jayewardenepura, Nugegoda, Sri LankaDepartment of Statistics, University of Sri Jayewardenepura, Nugegoda, Sri LankaDepartment of Statistics, University of Sri Jayewardenepura, Nugegoda, Sri LankaSummarizing 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.http://dx.doi.org/10.1155/2021/5535363 |
| spellingShingle | Chekhaprabha Priyadarshanee Waduge Naleen Chaminda Ganegoda Darshana Chitraka Wickramarachchi Ravindra Shanthakumar Lokupitiya 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 Journal of Applied Mathematics |
| title | 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 |
| title_full | 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 |
| title_fullStr | 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 |
| title_full_unstemmed | 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 |
| title_short | 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 |
| title_sort | 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 |
| url | http://dx.doi.org/10.1155/2021/5535363 |
| work_keys_str_mv | AT chekhaprabhapriyadarshaneewaduge consensuspatternsofasetoftimeseriesviaawaveletbasedtemporallocalizationemphasizingtheutilityoverpointwiseaveragingandaveragingunderdynamictimewarping AT naleenchamindaganegoda consensuspatternsofasetoftimeseriesviaawaveletbasedtemporallocalizationemphasizingtheutilityoverpointwiseaveragingandaveragingunderdynamictimewarping AT darshanachitrakawickramarachchi consensuspatternsofasetoftimeseriesviaawaveletbasedtemporallocalizationemphasizingtheutilityoverpointwiseaveragingandaveragingunderdynamictimewarping AT ravindrashanthakumarlokupitiya consensuspatternsofasetoftimeseriesviaawaveletbasedtemporallocalizationemphasizingtheutilityoverpointwiseaveragingandaveragingunderdynamictimewarping |