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xeofs is a specialized Python package designed for dimensionality reduction in climate science, aimed at extracting meaningful patterns from large datasets. It provides eigenmethods such as Principal Component Analysis (EOF analysis) and several related variants. Seamlessly integrated with xarray and Dask, xeofs enables efficient handling and scalable computation of large, multi-dimensional datasets.

• Multi-Dimensional: Designed for xarray objects, it applies dimensionality reduction to multi-dimensional data while maintaining data labels.
• Dask-Integrated: Supports large datasets via Dask xarray objects
• Extensive Methods: Offers various dimensionality reduction techniques
• Adaptable Output: Provides output corresponding to the type of input, whether single or list of xr.DataArray or xr.Dataset
• Missing Values: Handles NaN values within the data
• Bootstrapping: Comes with a user-friendly interface for model evaluation using bootstrapping
• Efficient: Ensures computational efficiency, particularly with large datasets through randomized SVD
• Modular: Allows users to implement and incorporate new dimensionality reduction methods

To install the package, use either of the following commands:

conda install -c conda-forge xeofs

or

pip install xeofs

In order to get started with xeofs, follow these simple steps:

Import the package

>>> import xarray as xr  # for example data only
>>> import xeofs as xe

Load example data

>>> t2m = xr.tutorial.open_dataset("air_temperature")
>>> t2m_west = t2m.isel(lon=slice(None, 20))
>>> t2m_east = t2m.isel(lon=slice(21, None))

EOF analysis Initiate and fit the EOF/PCA model to the data

>>> eof = xe.single.EOF(n_modes=10)
>>> eof.fit(t2m, dim="time")  # doctest: +ELLIPSIS
<xeofs.single.eof.EOF object at ...>

Now, you can access the model's EOF components and PC scores:

>>> comps = eof.components()  # EOFs (spatial patterns)
>>> scores = eof.scores()  # PCs (temporal patterns)

Varimax-rotated EOF analysis Initiate and fit an EOFRotator class to the model to obtain a varimax-rotated EOF analysis

>>> rotator = xe.single.EOFRotator(n_modes=3)
>>> rotator.fit(eof) # doctest: +ELLIPSIS
<xeofs.single.eof_rotator.EOFRotator object at ...>

>>> rot_comps = rotator.components()  # Rotated EOFs (spatial patterns)
>>> rot_scores = rotator.scores()  # Rotated PCs (temporal patterns)

Maximum Covariance Analysis (MCA)

>>> mca = xe.cross.MCA(n_modes=10)
>>> mca.fit(t2m_west, t2m_east, dim="time")  # doctest: +ELLIPSIS
<xeofs.cross.mca.MCA object at ...>

>>> comps1, comps2 = mca.components()  # Singular vectors (spatial patterns)
>>> scores1, scores2 = mca.scores()  # Expansion coefficients (temporal patterns)

Varimax-rotated MCA

>>> rotator = xe.cross.MCARotator(n_modes=10)
>>> rotator.fit(mca)  # doctest: +ELLIPSIS
<xeofs.cross.mca_rotator.MCARotator object at ...>

>>> rot_comps = rotator.components()  # Rotated singular vectors (spatial patterns)
>>> rot_scores = rotator.scores()  # Rotated expansion coefficients (temporal patterns)

To further explore the capabilities of xeofs, check out the available documentation and examples. For a full list of currently available methods, see the Reference API.

For a more comprehensive overview and usage examples, visit the documentation.

Contributions are highly welcomed and appreciated. If you're interested in improving xeofs or fixing issues, please read our Contributing Guide.

This project is licensed under the terms of the MIT license.

For questions or support, please open a Github issue.

• Randomized PCA: scikit-learn
• EOF analysis: Python package eofs by Andrew Dawson
• MCA: Python package xMCA by Yefee
• CCA: Python package CCA-Zoo by James Chapman
• ROCK-PCA: Matlab implementation by Diego Bueso
• Sparse PCA: Based on Ristretto library by Benjamin Erichson

When using xeofs, kindly remember to cite the original references of the methods employed in your work. Additionally, if xeofs is proving useful in your research, we'd appreciate if you could acknowledge its use with the following citation:

@article{rieger_xeofs_2024,
author = {Rieger, Niclas and Levang, Samuel J.},
doi = {10.21105/joss.06060},
journal = {Journal of Open Source Software},
month = jan,
number = {93},
pages = {6060},
title = {{xeofs: Comprehensive EOF analysis in Python with xarray}},
url = {https://joss.theoj.org/papers/10.21105/joss.06060},
volume = {9},
year = {2024}
}