altx — Adaptive Law-Based Transformation#

altx is an open-source Python package for efficient time series classification (TSC). It converts raw time series into a linearly separable feature space by discovering linear laws — eigenvectors of symmetric Hankel matrices that correspond to conserved quantities in the data. Variable-length shifted time windows let the algorithm capture patterns at multiple temporal scales simultaneously.

altx achieves state-of-the-art performance on TSC benchmarks from physics and related domains while keeping computational overhead low.

Getting started

Reference

How it works#

The pipeline has two phases:

Train — For each (R, L, K) configuration, every training instance is scanned with a sliding window of length R (step K). Each window is embedded into a symmetric L×L Hankel matrix, and the eigenvector for the smallest absolute eigenvalue is stored as a law.

Transform — For a test instance, windows are projected onto every stored law. The resulting scores are partitioned by training class and summarised into scalar features by a chosen extraction method. The final feature vector has length len(RLK) × noc × n_methods × m.

Quick start#

import torch
from altx import ALT as Altx

# Training data: 6 univariate instances of length 50, two classes
_ = torch.manual_seed(0)
train_data    = torch.randn(6, 50)
train_classes = torch.tensor([0, 0, 0, 1, 1, 1])

model = Altx(train_data, train_classes, L=3, K=1)
model.train()

# Transform a test set
test_data = torch.randn(4, 50)
features  = model.transform_set(test_data, [["mean", 0.05]])
print(features.shape)   # torch.Size([4, 2])

See the Usage page for a full walkthrough with all options and extraction methods.

Citation#

If you use altx in your research, please cite:

[1] M. T. Kurbucz, B. Hajós, B. P. Halmos, V. Á. Molnár, A. Jakovác,

Adaptive law-based feature representation for time series classification,
Scientific Reports 15 (1), 41775, 2025.
https://doi.org/10.1038/s41598-025-25667-0

[2] B. P. Halmos, B. Hajós, V. Á. Molnár, M. T. Kurbucz, A. Jakovác,

altx: a Python package for adaptive law-based transformation in time series classification,
Machine Learning: Science and Technology 7 (1), 015034, 2026.
https://doi.org/10.1088/2632-2153/ae3e4f

@article{kurbucz2025adaptive,
  title   = {Adaptive law-based feature representation for time series classification},
  author  = {Kurbucz, Marcell T and Haj{\'o}s, Bal{\'a}zs and Halmos, Bal{\'a}zs P
             and Moln{\'a}r, Vince {\'A} and Jakov{\'a}c, Antal},
  journal = {Scientific Reports},
  volume  = {15},
  number  = {1},
  pages   = {41775},
  year    = {2025},
  doi     = {10.1038/s41598-025-25667-0},
}

@article{halmos2026altx,
  title   = {altx: a python package for adaptive law-based transformation
             in time series classification},
  author  = {Halmos, Bal{\'a}zs P and Haj{\'o}s, Bal{\'a}zs and Moln{\'a}r, Vince {\'A}
             and Kurbucz, Marcell T and Jakov{\'a}c, Antal},
  journal = {Machine Learning: Science and Technology},
  volume  = {7},
  number  = {1},
  pages   = {015034},
  year    = {2026},
  doi     = {10.1088/2632-2153/ae3e4f},
}

License#

altx is released under the GPLv3 license.