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On the classification of time series and cross wavelet phase variance
The continuous wavelet transform (CWT) is arguably one of the best tools to explore underlying characteristic features of time series data. Its application in large time series classification experiments, however, has been severely limited due to the large amount of redundant associated information....
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| Format: | Thesis |
| Language: | English |
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Department of Electrical Engineering
2017
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| _version_ | 1867613624138203136 |
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| access_status_str | Open Access |
| author | Pienaar, Marc |
| author2 | Nicolls, Fred C |
| author_browse | Nicolls, Fred C Pienaar, Marc |
| author_facet | Nicolls, Fred C Pienaar, Marc |
| author_sort | Pienaar, Marc |
| collection | Thesis |
| description | The continuous wavelet transform (CWT) is arguably one of the best tools to explore underlying characteristic features of time series data. Its application in large time series classification experiments, however, has been severely limited due to the large amount of redundant associated information. By extending the capabilities of the CWT to perform cross wavelet analysis (CWA), common frequency behaviour between two time series is highlighted, and the potential to extract amplitude modulated (AM) and frequency modulation (FM) characteristics in an automated way is possible. Characterisation of AM is relatively straightforward and can be resolved by any number of Euclidean based techniques in both the time and frequency domains. FM on the other hand, is somewhat more difficult as it transcends multiple wavelet scales. In this study, linear combinations of scales are used to extract both AM similarity (derived from global wavelet power spectra) and FM coherency, using a new method developed called cross wavelet phase variance (CWPV). The methodology is applied to large scale classification problems (using benchmark time series), in which the method clearly outperforms other common distance-based measures. Lastly, the approach provides a powerful framework in which AM and FM characteristics common between time series can be explicitly mapped to their corresponding scales, and with some initial optimisation, can be applied to any classification problem. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/22869 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:39:06.311Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2017 |
| publishDateRange | 2017 |
| publishDateSort | 2017 |
| publisher | Department of Electrical Engineering |
| publisherStr | Department of Electrical Engineering |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/22869 On the classification of time series and cross wavelet phase variance Pienaar, Marc Nicolls, Fred C Electrical Engineering The continuous wavelet transform (CWT) is arguably one of the best tools to explore underlying characteristic features of time series data. Its application in large time series classification experiments, however, has been severely limited due to the large amount of redundant associated information. By extending the capabilities of the CWT to perform cross wavelet analysis (CWA), common frequency behaviour between two time series is highlighted, and the potential to extract amplitude modulated (AM) and frequency modulation (FM) characteristics in an automated way is possible. Characterisation of AM is relatively straightforward and can be resolved by any number of Euclidean based techniques in both the time and frequency domains. FM on the other hand, is somewhat more difficult as it transcends multiple wavelet scales. In this study, linear combinations of scales are used to extract both AM similarity (derived from global wavelet power spectra) and FM coherency, using a new method developed called cross wavelet phase variance (CWPV). The methodology is applied to large scale classification problems (using benchmark time series), in which the method clearly outperforms other common distance-based measures. Lastly, the approach provides a powerful framework in which AM and FM characteristics common between time series can be explicitly mapped to their corresponding scales, and with some initial optimisation, can be applied to any classification problem. 2017-01-23T07:37:46Z 2017-01-23T07:37:46Z 2016 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/22869 eng application/pdf Department of Electrical Engineering Faculty of Engineering and the Built Environment University of Cape Town |
| spellingShingle | Electrical Engineering Pienaar, Marc On the classification of time series and cross wavelet phase variance |
| thesis_degree_str | Doctoral |
| title | On the classification of time series and cross wavelet phase variance |
| title_full | On the classification of time series and cross wavelet phase variance |
| title_fullStr | On the classification of time series and cross wavelet phase variance |
| title_full_unstemmed | On the classification of time series and cross wavelet phase variance |
| title_short | On the classification of time series and cross wavelet phase variance |
| title_sort | on the classification of time series and cross wavelet phase variance |
| topic | Electrical Engineering |
| url | http://hdl.handle.net/11427/22869 |
| work_keys_str_mv | AT pienaarmarc ontheclassificationoftimeseriesandcrosswaveletphasevariance |