MOMENTI

Scalable discovery of multidimensional motifs in time series

The algorithm employs Locality Sensitive Hashing (LSH) to prune the number of distance computations required to discover subdimensional motifs in multidimensional time series.

Implementation details

The code is implemented in Python 3.12, and it heavily relies on the numba, multiprocessing and numpy libraries to ensure scalability.

pyproject.toml is provided to allow the creation of a working environment.

The algorithm has anytime properties, computation can be stopped at any given point (i.e., CTRL + C) and the algorithm will return the best results it achieved.

Discretized Random Projections LSH has been implemented with the use of tensoring to minimize the hash evaluations.

For general use the MOMENTI function does all the heavy lifting (i.e., deals with NaN values, transforms the time series in the correct format for the algorithm, etc.).

We additionally include our implementation of the axis-aligned projection algorithm introduced in the work of Minnen et al., 2007.

Reproducibility

The scripts in the folder tests replicate all the tests performed in the paper and some additional tests that we could not fit in the paper due to space limitations, the scripts produce .csv files in the results folder.

The *_plotter.py scripts in the folder results collect the raw results and plot them.

Installation as a Python package

pip install git+https://github.com/aidaLabDEI/MOMENTI-motifs

from MOMENTI import MOMENTI
# Example usage
# Find k multidimensional motifs for each dimensionality from 2 to D:
# let Ts be a D-dimensional time series as a numpy array,
# window the length of the motifs to discover,
# and k the number of motifs to discover
motifs, _ = MOMENTI(Ts, window, k, (2,D))
# Find k multidimensional motifs that span d dimensions, d∈[2,D]:
motifs, _ = MOMENTI(Ts, window, k, (d,d))

Citing

@article{Ceccarello2025MOMENTI,
  author = {Ceccarello, Matteo and Monaco, Francesco Pio and Silvestri, Francesco},
  title = {{MOMENTI: Scalable Motif Mining in Multidimensional Time Series}},
  journal = {PVLDB},
  volume = {18},
  number = {10},
  pages = {3463--3476},
  year = {2025},
  doi = {10.14778/3748191.3748208},
  url = {https://github.com/aidaLabDEI/MOMENTI-motifs}
}