Proximity Forest: an effective and scalable distance-based classifier for time series

Abstract

Research into the classification of time series has made enormous progress in the last decade. The UCR time series archive has played a significant role in challenging and guiding the development of new learners for time series classification. The largest dataset in the UCR archive holds 10,000  time series only; which may explain why the primary research focus has been on creating algorithms that have high accuracy on relatively small datasets. This paper introduces Proximity Forest, an algorithm that learns accurate models from datasets with millions of time series, and classifies a time series in milliseconds. The models are ensembles of highly randomized Proximity Trees. Whereas conventional decision trees branch on attribute values (and usually perform poorly on time series), Proximity Trees branch on the proximity of time series to one exemplar time series or another; allowing us to leverage the decades of work into developing relevant measures for time series. Proximity Forest gains both efficiency and accuracy by stochastic selection of both exemplars and similarity measures. Our work is motivated by recent time series applications that provide orders of magnitude more time series than the UCR benchmarks. Our experiments demonstrate that Proximity Forest is highly competitive on the UCR archive: it ranks among the most accurate classifiers while being significantly faster. We demonstrate on a 1M time series Earth observation dataset that Proximity Forest retains this accuracy on datasets that are many orders of magnitude greater than those in the UCR repository, while learning its models at least 100,000 times faster than current state-of-the-art models Elastic Ensemble and COTE.

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Notes

  1. 1.

    Note that these parametrisations can be performed in constant time also if the data are z-normalized, which is the case for all UCR datasets.

  2. 2.

    The split ensures that no 2 times series come from the same plot of land.

  3. 3.

    It should be highlighted that the results presented here are for the original BOSS algorithm, and not the BOSS-VS discussed above in the SITS experiments. BOSS-VS is a scalable variation of BOSS, where concessions are made to accuracy in favor of training time. The original BOSS is therefore more competitive in this section.

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Acknowledgements

This research was supported by the Australian Research Council under Grant DE170100037. This material is based upon work supported by the Air Force Office of Scientific Research, Asian Office of Aerospace Research and Development (AOARD) under award number FA2386-17-1-4036. We are grateful to the editor and anonymous reviewers whose suggestions and comments have greatly strengthened the paper. The authors would also like to thank Prof Eamonn Keogh and all of the people who have contributed to the UCR time series classification archive.

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Appendices

Appendix A: Detailed UCR results

See Table 1.

Table 1 Detailed UCR results for five state-of-the-art algorithms and Proximity Forest

Appendix B: On a variation of the proximity forest

We decided to explore another variant of the Proximity Forest algorithm by randomly selecting a distance measure for each tree, rather than for each node. In this new variant, only the exemplars and the parameters of the distance-metric are randomly chosen at each node. The UCR experiments were repeated for 100 trees and 1 candidate for this new ‘on tree’ variant. Each Proximity Forest result is averaged over 50 runs.

Figure 12 compares classification accuracy for the original version ‘on node’, presented in Sect. 3.2, and the proposed variant ‘on tree’. Each point represents a single dataset of the UCR dataset. The number of trees has been fixed to 100.

Fig. 12
figure12

Accuracy of Proximity Forest when randomly selecting the distance measure ‘on node’ and ‘on tree’

The results show a slight advantage for the ‘on node’ approach with 44 wins, 39 losses and 2 ties. Where the ‘on tree’ variant uses a single distance measure per tree, the ‘on node’ variant allows multiple combinations of measures in a single tree, thus making it more robust to inefficient metrics.

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Lucas, B., Shifaz, A., Pelletier, C. et al. Proximity Forest: an effective and scalable distance-based classifier for time series. Data Min Knowl Disc 33, 607–635 (2019). https://doi.org/10.1007/s10618-019-00617-3

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Keywords

  • Time series classification
  • Scalable classification
  • Time-warp similarity measures
  • Ensemble