tsdr: Time-Series Dimension Reduction

tsdr is a Python package of time-series dimension reduction (TSDR) methods: algorithms that reduce multivariate data to a few components by exploiting temporal structure. In contrast to general dimension reduction (GDR) methods, whose outputs are invariant to temporal permutation, TSDR methods are sensitive to temporal structure. The package implements 30 methods from the seven categories of TSDR methods defined in Owens & Fulcher (2025), written in a simple, readable style to help time-series analysts understand the algorithms discussed in that review.

Installation

pip install tsdr

The package is on PyPI and requires Python 3.8 or later. It depends on numpy, scipy, scikit-learn, pywavelets and kneed. The example below also uses matplotlib.

Quick start

Every method is a class with a scikit-learn-style fit, transform and fit_transform. Here we extract a slow sinusoid from a linear mixture of noise channels using slow feature analysis (SFA):

from tsdr.slowness import SFA

import numpy as np
import scipy
import matplotlib.pyplot as plt

# create a dataset for analysis
# a sinusoid
z = np.sin(np.linspace(0, 4*np.pi, 1000))
# multichannel noise
D = 5
noise = np.random.normal(scale=1.0, size=((len(z), D-1)))
# linear mixing
A = scipy.stats.ortho_group.rvs(D, random_state=1)
X = np.concatenate([z.reshape(-1,1), noise], axis=1) @ A

# extract a slow component using SFA
slow_component = SFA(n_components=1).fit_transform(X)

# visualize the component
fig, axs = plt.subplots(6, 1, figsize=(8, 8))
axs[0].plot(slow_component, lw=1.0)
axs[0].set_ylabel('SFA1')
for i in range(D):
    axs[i].spines[['right', 'top', 'bottom']].set_visible(False)
    axs[i].set_xticks([])
    axs[i+1].plot(X[:, i], c='black', linewidth=0.5)
    axs[i+1].set_ylabel(f'X{i+1}')
axs[D].spines[['right', 'top']].set_visible(False)
axs[D].set_xlabel('Time')
plt.tight_layout()

Available methods

The methods are grouped by the aspect of temporal structure that they exploit. Each is imported from the module named in the first column, e.g., from tsdr.slowness import SFA.

The figure at the top summarizes these categories.

A few methods differ from the common pattern:

• Methods with a random initialization or random order of updates (BioSFA, ISFA, SICA, ForeCA, DCA, BSSnonstat, and LDS and DFA with init='random') accept a random_state argument for reproducible results; TCCA_Stiefel uses a seed argument. LDS and DFA are initialised deterministically by default (init='autocorrelation').
• The diffusion methods are nonlinear, so they have fit_transform but no separate transform. DMcov and DIG embed sliding windows of the time series (of length window, every step samples), so they return one row per window; NLSA embeds the time series with q lags, so it returns n_samples - q rows (for time points q onwards).

Citation

If you use this software, please read and cite the open-access article:

Owens, K. S. & Fulcher, B. D. (2025). Time-series dimension reduction: a comprehensive review and conceptual unification of algorithms. TechRxiv. doi:10.36227/techrxiv.176409662.29359239/v1

@article{owens2025tsdr,
  title   = {Time-series dimension reduction: a comprehensive review and conceptual unification of algorithms},
  author  = {Owens, Kieran S. and Fulcher, Ben D.},
  journal = {TechRxiv},
  year    = {2025},
  doi     = {10.36227/techrxiv.176409662.29359239/v1}
}

License

tsdr is released under the MIT License.