Abstract
Motif discovery can be used as a subroutine in many time series data mining tasks such as classification, clustering and anomaly detection. A motif represents two or more highly similar subsequences of a time series. The vast majority of the motif discovery methods implicitly assume that subsequences need to be normalized before determining their similarity. While normalization is widely adopted, it may affect the discovery of motifs. We examine the effect of normalization on motif discovery using 96 real-world time series. To determine if the discovered motifs are meaningful, all time series are assigned labels that indicate the states of the system generating the time series. Our experiments show that in over half of the considered cases, normalization affects motif discovery negatively by returning motifs that are not meaningful. We therefore conclude that the assumption underlying normalization does not always hold for real-world time series and thus should not be uncritically adopted.
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Notes
- 1.
- 2.
In the practical implementation of motif discovery, an exclusion zone of length m/2 before and after the location of the subsequence of interest is commonly set [20]. This ensures that so-called trivial matches are avoided.
- 3.
The time series are downloaded from the website of the authors, where the names of some time series differ from the original naming convention.
- 4.
Due to the nature of the ECG and SLC time series, we concatenated the separate sequences into a single time series. Due to the large size of the SLC time series, we took a subset including two different states occurring at least twice.
- 5.
The selected time series, code and results are available at
Github. - 6.
It can be the case that several subsequences have minimum distance to the subsequence of interest. In this case only one subsequence is randomly chosen to be directly compared.
- 7.
Due to the demanding running time of the calculations, the maximum length of the time series is set to \(n=20,000\). We only consider time series without missing values and for which hold that the (sub)set consists of two or more states.
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van Leeuwen, F., Bosma, B., den Born, A.v., Postma, E. (2023). Normalization in Motif Discovery. In: Nicosia, G., et al. Machine Learning, Optimization, and Data Science. LOD 2022. Lecture Notes in Computer Science, vol 13811. Springer, Cham. https://doi.org/10.1007/978-3-031-25891-6_24
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