$d_{symb}$: An Interpretable Distance Measure for Multivariate Non-Stationary Physiological Signals

NOTE: 🆕 🆕 We developed and published the $d_{symb}$ playground [website / code / Streamlit app / 4 min YouTube video], a online tool (Streamlit application) to apply $d_{symb}$ to your uploaded data.

This repository contains the code to reproduce all experiments in our $d_{symb}$ publication [paper / PDF]:

S. W. Combettes, C. Truong, and L. Oudre. An Interpretable Distance Measure for Multivariate Non-Stationary Physiological Signals. In Proceedings of the International Conference on Data Mining Workshops (ICDMW), Shanghai, China, 2023.

@inproceedings{2023_combettes_dsymb_icdm,
  author={Combettes, Sylvain W. and Truong, Charles and Oudre, Laurent},
  booktitle={2023 IEEE International Conference on Data Mining Workshops (ICDMW)}, 
  title={An Interpretable Distance Measure for Multivariate Non-Stationary Physiological Signals}, 
  year={2023},
  pages={533-539},
  doi={10.1109/ICDMW60847.2023.00076},
  location={Shanghai, China},
}

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

Toggle for the paper's abstract!

We introduce d_{symb}, a novel distance measure for comparing multivariate non-stationary physiological signals. Unlike most distance measures on multivariate signals such as variants of Dynamic Time Warping (DTW), d_{symb} can take into account their non-stationarity thanks to a symbolization step. This step is based on a change-point detection procedure, that splits a non-stationary signal into several stationary segments, followed by quantization using K-means clustering. The proposed distance measure leverages the general edit distance that is applied to the symbolic sequences. The performance of d_{symb} compared to two commonly used DTW variants is illustrated by applying it to physiological signals recorded during walking protocols. In particular, d_{symb} is shown to be interpretable: its symbolization detects the segments that correspond to salient behaviors. An open source GitHub repository 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 $d_{symb}$, 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)

Structure of the code

date_exp is a string (for example "2023_12_01") in order to version the experiments.

The code inputs / outputs the following files:

1. in the data folder: the gait data set (the only necessary input)
2. in the results/{date_exp} folder: results such distance matrices (it also currently contains precomputed outputs)
3. in the results/{date_exp}/img folder: figures, plots

How to use this repository to reproduce the $d_{symb}$ paper

Run the interpret_distance_dsymb_gait.ipynb notebook. More information is provided at the beginning of this notebook.

Requirements

• loadmydata==0.0.9
• matplotlib==3.7.2
• numpy==1.23.5
• pandas==2.0.3
• plotly==5.10.0
• ruptures==1.1.7
• scikit-learn==1.2.2
• scipy==1.9.3
• seaborn==0.12.2
• statsmodels==0.14.0
• tslearn==0.6.1
• weighted-levenshtein==0.2.1

Licence

This project is licensed under the BSD 2-Clause 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).