ASTRIDE: Adaptive Symbolization for Time Series Databases

This repository contains the code to reproduce all experiments in our paper

ASTRIDE: Adaptive Symbolization for Time Series Databases

available on arXiv. All the code is written in Python (scripts and notebooks).

Toggle for the paper's abstract!

We introduce ASTRIDE (Adaptive Symbolization for Time seRIes DatabasEs), a novel symbolic representation of time series, along with its accelerated variant FASTRIDE (Fast ASTRIDE). Unlike most symbolization procedures, ASTRIDE is adaptive during both the segmentation step by performing change-point detection and the quantization step by using quantiles. Instead of proceeding signal by signal, ASTRIDE builds a dictionary of symbols that is common to all signals in a data set. We also introduce D-GED (Dynamic General Edit Distance), a novel similarity measure on symbolic representations based on the general edit distance. We demonstrate the performance of the ASTRIDE and FASTRIDE representations compared to SAX (Symbolic Aggregate approXimation), 1d-SAX, SFA (Symbolic Fourier Approximation), and ABBA (Adaptive Brownian Bridge-based Aggregation) on reconstruction and, when applicable, on classification tasks. These algorithms are evaluated on 86 univariate equal-size data sets from the UCR Time Series Classification Archive. An open source GitHub repository called astride is made available to reproduce all the experiments in Python.

Please let us know of any issue you might encounter when using this code, either by opening an issue on this repository or by sending an email to sylvain.combettes [at] ens-paris-saclay.fr. Or if you just need some clarification or help.

How is a symbolic representation implemented?

For ASTRIDE and FASTRIDE, a symbolic representation (with an associated distance) is a scikit-learn pipeline based on the following classes in the src folder:

1. SegmentFeature (in segmentation.py)
2. Segmentation (in segment_features.py)
3. Symbolization (in symbolization.py)
4. SymbolicSignalDistance (in symbolic_signal_distance.py)

An example usage is given in 07_run_reconstruction.py.

Download the ABBA/ABBA.py file from https://github.com/nla-group/ABBA, as it is used in the signal reconstruction benchmark.

Structure of the code

date_exp is a string (for example "2023_02_08") in order to version the experiments.

The code outputs the following kinds of csv files:

1. data folder: the UCR archive meta data filtered on the list of data sets under consideration
2. results/{date_exp}/acc folder: the results from the 1-NN classifcation task
3. results/{date_exp}/clean_acc folder: the results from the 1-NN classifcation task
4. results/{date_exp}/reconstruction folder: the results from signal reconstruction task

The code outputs all the figures in the paper in the results/{date_exp}/img folder.

For the Python notebooks, the configuration parameters (at the top) do the following:

• DATE_EXP sets the date of launch of the experiment (for versioning)
• if IS_EXPORT_DF=False, then no CSV files (pandas DataFrame) are exported
• if IS_SAVE_FIG=False, then no figures are exported
• if IS_COMPUTE=False, then long computations are made (no more than a few mintutes on a standard laptop)

How to use this repository to reproduce the ASTRIDE paper

Note that more details are given at the top of each notebook and that the code is commented.

1. Explore the UCR archive.
   Run the 01_explore_ucr_metadata.ipynb notebook.
   It generates:
   • the data/DataSummary_prep_equalsize.csv file which contains the 117 univariate and equal-size data sets from the UCR archive.
   • the data/DataSummary_prep_equalsize_min100samples.csv file which contains the 94 univariate and equal-size data sets with at least 100 samples from the UCR archive.
   • Table 4.
   • Data for Section 2.3.3 and Section 3.4 about the total memory usage of a symbolization method.
2. Look into the normality assumption oof the means per segment.
   Run the 02_explore_gaussian_assumption.ipynb notebook.
   
   • It performs the normality test for section 2.3.1.
   • It generates Figure 2.
3. Intrepret the symbolization methods, how they transform a signal.
   Run the 03_interpret_symbolization.ipynb notebook
   • It generates Figures 1, 3 and 4.
   • It generates Table 3.
4. For the classification benchmark of SAX, 1d-SAX, ASTRIDE, and FASTRIDE of Section 4.1.
   1. Compute the test accuracies of each method.
      Run the 04_run_classification.py script for the four symbolization methods:

      $ python3 04_run_classification.py --method_name "saxtslearn" --date_exp "2023_02_08"
      $ python3 04_run_classification.py --method_name "1dsax" --date_exp "2023_02_08"
      $ python3 04_run_classification.py --method_name "fastride" --date_exp "2023_02_08"
      $ python3 04_run_classification.py --method_name "astride" --date_exp "2023_02_08"
      

      Note that the date_exp variable is for versioning the experiments.
      It generates the results/{date_exp}/acc/df_acc_{method}_{dataset}.csv files, which are the test accuracies per method per data set and for all combination of hyper-parameters.
   2. Clean the classification results for each method.
      Run the 05_clean_classification_results.ipynb notebook. It generates the results/{date_exp}/acc_clean/df_acc_{method}_alldatasets_clean.csv files, which are the test accuracies per method for all data sets and combination of hyper-parameters, cleaned.
   3. Explore the results for each method: plot the accuracy as a function of the word length.
      Run the 06_explore_classification_results.ipynb notebook.
      It generates Figure 5.
5. For the signal reconstruction benchmark of SAX, 1d-SAX, SFA, ABBA, ASTRIDE and FASTRIDE of Section 4.2.
   1. Compute the reconstructed signals for each method and all signals of all data sets as well as the reconstruction error.
      Run the 07_run_recontruction.py script for several target memory usage ratios

      python3 07_run_reconstruction.py --denom 3 --date_exp "2023_02_08"
      python3 07_run_reconstruction.py --denom 4 --date_exp "2023_02_08"
      python3 07_run_reconstruction.py --denom 5 --date_exp "2023_02_08"
      python3 07_run_reconstruction.py --denom 6 --date_exp "2023_02_08"
      python3 07_run_reconstruction.py --denom 10 --date_exp "2023_02_08"
      python3 07_run_reconstruction.py --denom 15 --date_exp "2023_02_08"
      python3 07_run_reconstruction.py --denom 20 --date_exp "2023_02_08"
      

      Note that the denom variable is the inverse of the target memory usage ratio.
      It generates:
      • the results/reconstruction/{denom}/reconstruction_errors_{dataset}.csv files, which are the
      • the results/reconstruction/{denom}/reconstructed_signals/reconstructed_{dataset}_{method}.csv files, which are the reconstructed signals for each symbolization method.
   2. Compute the reconstruction errors.
      Run the 08_explore_recontruction_results.ipynb notebook.
      It generates Figures 6 and 7.
   3. Interpret the signal reconstruction for each symbolization method.
      Run the 09_interpret_reconstruction.ipynb notebook.
      It generates Figure 8.
6. Compare the symbolization and classification durations of SAX, 1d-SAX, ASTRIDE, and FASTRIDE.
   Run the 10_processing_time.ipynb notebook.
   It generates Table 6.

Requirements

• loadmydata==0.0.9
• matplotlib==3.4.1
• numpy==1.20.2
• pandas==1.2.4
• plotly==5.5.0
• ruptures==1.1.6.dev3+g1def4ff
• scikit-learn==1.0.1
• scipy==1.6.2
• seaborn==0.11.1
• statsmodels==0.13.1
• tslearn==0.5.2
• weighted-levenshtein==0.2.1

Citing

If you use this code or publication, please cite (arXiv: https://arxiv.org/abs/2302.04097):

@article{2023_combettes_astride,
    doi = {10.48550/ARXIV.2302.04097},
    url = {https://arxiv.org/abs/2302.04097},
    author = {Combettes, Sylvain W. and Truong, Charles and Oudre, Laurent},
    title = {ASTRIDE: Adaptive Symbolization for Time Series Databases},
    journal = {arXiv preprint arXiv:2302.04097},
    year = {2023},
}

Licence

This project is licensed under the MIT License, see the LICENSE.md file for more information.

Contributors

• Sylvain W. Combettes (Centre Borelli, ENS Paris-Saclay)
• Charles Truong (Centre Borelli, ENS Paris-Saclay)
• Laurent Oudre (Centre Borelli, ENS Paris-Saclay)

Acknowledgments

Sylvain W. Combettes is supported by the IDAML chair (ENS Paris-Saclay) and UDOPIA (ANR-20-THIA-0013-01). Charles Truong is funded by the PhLAMES chair (ENS Paris-Saclay). Part of the computations has been executed on Atos Edge computer, funded by the IDAML chair (ENS Paris-Saclay).