Multivariate Time Series Imputation: An Approach Based on Dictionary Learning
The problem addressed by dictionary learning (DL) is the representation of data as a sparse linear combination of columns of a matrix called dictionary. Both the dictionary and the sparse representations are learned from the data. We show how DL can be employed in the imputation of multivariate time...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/8/1057 |
| _version_ | 1797432258205843456 |
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| author | Xiaomeng Zheng Bogdan Dumitrescu Jiamou Liu Ciprian Doru Giurcăneanu |
| author_facet | Xiaomeng Zheng Bogdan Dumitrescu Jiamou Liu Ciprian Doru Giurcăneanu |
| author_sort | Xiaomeng Zheng |
| collection | DOAJ |
| description | The problem addressed by dictionary learning (DL) is the representation of data as a sparse linear combination of columns of a matrix called dictionary. Both the dictionary and the sparse representations are learned from the data. We show how DL can be employed in the imputation of multivariate time series. We use a structured dictionary, which is comprised of one block for each time series and a common block for all the time series. The size of each block and the sparsity level of the representation are selected by using information theoretic criteria. The objective function used in learning is designed to minimize either the sum of the squared errors or the sum of the magnitudes of the errors. We propose dimensionality reduction techniques for the case of high-dimensional time series. For demonstrating how the new algorithms can be used in practical applications, we conduct a large set of experiments on five real-life data sets. The missing data (MD) are simulated according to various scenarios where both the percentage of MD and the length of the sequences of MD are considered. This allows us to identify the situations in which the novel DL-based methods are superior to the existing methods. |
| first_indexed | 2024-03-09T09:57:46Z |
| format | Article |
| id | doaj.art-cf1f5fdfd91f4e7e9a6ba7041fc961a9 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T09:57:46Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-cf1f5fdfd91f4e7e9a6ba7041fc961a92023-12-01T23:40:07ZengMDPI AGEntropy1099-43002022-07-01248105710.3390/e24081057Multivariate Time Series Imputation: An Approach Based on Dictionary LearningXiaomeng Zheng0Bogdan Dumitrescu1Jiamou Liu2Ciprian Doru Giurcăneanu3Department of Statistics, University of Auckland, Auckland 1142, New ZealandDepartment of Automatic Control and Computers, University Politehnica of Bucharest, 060042 Bucharest, RomaniaSchool of Computer Science, University of Auckland, Auckland 1142, New ZealandDepartment of Statistics, University of Auckland, Auckland 1142, New ZealandThe problem addressed by dictionary learning (DL) is the representation of data as a sparse linear combination of columns of a matrix called dictionary. Both the dictionary and the sparse representations are learned from the data. We show how DL can be employed in the imputation of multivariate time series. We use a structured dictionary, which is comprised of one block for each time series and a common block for all the time series. The size of each block and the sparsity level of the representation are selected by using information theoretic criteria. The objective function used in learning is designed to minimize either the sum of the squared errors or the sum of the magnitudes of the errors. We propose dimensionality reduction techniques for the case of high-dimensional time series. For demonstrating how the new algorithms can be used in practical applications, we conduct a large set of experiments on five real-life data sets. The missing data (MD) are simulated according to various scenarios where both the percentage of MD and the length of the sequences of MD are considered. This allows us to identify the situations in which the novel DL-based methods are superior to the existing methods.https://www.mdpi.com/1099-4300/24/8/1057multivariate time seriesmissing dataimputationdictionary learninginformation theoretic criteria |
| spellingShingle | Xiaomeng Zheng Bogdan Dumitrescu Jiamou Liu Ciprian Doru Giurcăneanu Multivariate Time Series Imputation: An Approach Based on Dictionary Learning Entropy multivariate time series missing data imputation dictionary learning information theoretic criteria |
| title | Multivariate Time Series Imputation: An Approach Based on Dictionary Learning |
| title_full | Multivariate Time Series Imputation: An Approach Based on Dictionary Learning |
| title_fullStr | Multivariate Time Series Imputation: An Approach Based on Dictionary Learning |
| title_full_unstemmed | Multivariate Time Series Imputation: An Approach Based on Dictionary Learning |
| title_short | Multivariate Time Series Imputation: An Approach Based on Dictionary Learning |
| title_sort | multivariate time series imputation an approach based on dictionary learning |
| topic | multivariate time series missing data imputation dictionary learning information theoretic criteria |
| url | https://www.mdpi.com/1099-4300/24/8/1057 |
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