Skip to main content

A high performance mapping class to construct ElM2D plots from large datasets of inorganic compositions.

Project description


A high performance mapping class to construct ElMD distance matrices from large datasets of ionic compositions, suitable for single node usage on HPC systems. This includes helper methods to directly embed these datasets as maps of chemical space, as well as sorting lists of compositions, and exporting kernel matrices.

This Fork

:warning: For the original ElM2D repository, see :warning:

This is a refactored version which incorporates fast distance matrix computations for the modified Pettifor scale representation, and is in the process of being integrated into ElMD and ElM2D. The documentation as follows has changes relative to the original documentation. Additionally, this is packaged on PyPI and Anaconda, but under a different name: chem_wasserstein. A $10000 \times 10000$ pairwise distance matrix can be calculated on the order of 10 seconds (CPU). The distance calculations are also GPU compatible. If running on Colab, be sure to use GPU as the CPU version has some Colab-specific issues with Numba.


Recommended installation through conda with python 3.8.

conda install -c sgbaird chem_wasserstein


pip install chem_wasserstein

For the background theory, please read the paper "The Earth Mover’s Distance as a Metric for the Space of Inorganic Compositions"


125,000 compositions from the inorganic crystal structure database embedded with PCA, plotted with datashader: ICSD Map

For more interactive examples please see


Computing Distance Matrices

The computed distance matrix is accessible through the dm attribute and can be saved and loaded as a csv file.

from chem_wasserstein.ElM2D_ import ElM2D

mapper = ElM2D()["formula"])



This distance matrix can be used as a lookup table for distances between compositions given their numeric indices (distance =[i][j]) or used as a kernel matrix for embedding, regression, and classification tasks directly.


To sort a list of compositions into an ordering of chemical similarity["formula"])

sorted_indices = mapper.sort()
sorted_comps = mapper.sorted_formulas


Embeddings can be constructed through either the UMAP or PCA methods of dimensionality reduction. The most recently embedded points are accessible via the embedding property. Higher dimensional embeddings can be created with the n_components parameter.

mapper = ElM2D()["formula"])
embedding = mapper.transform()

# For new data
embedding = mapper.fit_transform(df["formula"])
embedding = mapper.fit_transform(df["formula"], how="PCA", n_components=7)

Embeddings may also be directed towards a particular chemical property in a pandas DataFrame, to bring known patterns into focus.

embedding = mapper.fit_transform(df["formula"], df["property_of_interest"])

By default, the modified Pettifor scale is used as the method of atomic similarity, this is changed through the metric attribute.

mapper = ElM2D(metric="atomic")
embedding = mapper.fit_transform(df["formula"])

These embeddings may be visualized within a jupyter notebook, or exported to HTML to view full page in the web browser.


# Returns a figure for viewing in notebooks

# Returns a figure and saves as ElM2D_Plot_UMAP.html

# Returns and saves figure, with colouring based on property from a pandas Series
mapper.plot(fp="ElM2D_Plot_UMAP.html", color=df["chemical_property"]) 

# Plotting also works in 3D
mapper.fit_transform(df["formula"], n_components=3)


Smaller datasets can be saved directly with the save( methods directly. This is limited to files of size 3GB (the python binary file size limit).

Larger datasets will require importing/exporting the distance matrix and embeddings (export_embedding(filepath.csv)/import_embedding(filepath.csv) separately as csv files if you require this processed data in future work.["formula"])"")
mapper = ElM2D()

mapper = ElM2D()
mapper.formula_list = df["formula"]

Cross Validation

Perform a K-Folds splitting of the dataset into subsets, to build up training and testing datasets.

cvs = mapper.cross_validate()
for i, (X_train, X_test) in enumerate(cvs):
    sub_mapper = ElM2D()"train_elm2d_{i}.pk")"test_elm2d_{i}.pk")
from sklearn.metrics import mean_average_error as mae

cvs = mapper.cross_validate(y=df["target"])

for X_train, X_test, y_train, y_test in cvs:, y_train)
    y_pred = clf.predict(X_test)
    errors.append(mae(y_pred, y_test))


Available Metrics

You may use either discrete scales or machine learnt representations for each element. Choose these via the metric parameter.


  • mendeleev
  • petti
  • atomic
  • mod_petti

Chemically Derived:

  • oliynyk
  • oliynyk_sc
  • jarvis
  • jarvis_sc
  • magpie
  • magpie_sc

Machine Learnt:

  • cgcnn
  • elemnet
  • mat2vec
  • matscholar
  • megnet16

Random Numbers:

  • random_200

Custom Distance Matrix

  • precomputed

Bulk featurizing can be performed with featurize.

mapper = ElM2D(metric="oliynyk_sc")
X = mapper.featurize(df["formula"])


If you would like to cite this code in your work, please use the following reference

author = {Hargreaves, Cameron J. and Dyer, Matthew S. and Gaultois, Michael W. and Kurlin, Vitaliy A. and Rosseinsky, Matthew J.},
title = {The Earth Mover’s Distance as a Metric for the Space of Inorganic Compositions},
journal = {Chemistry of Materials},
volume = {32},
number = {24},
pages = {10610-10620},
year = {2020},
doi = {10.1021/acs.chemmater.0c03381},
URL = {
eprint = {

Project details

Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distribution

chem_wasserstein-1.0.12.tar.gz (1.0 MB view hashes)

Uploaded source

Built Distribution

chem_wasserstein-1.0.12-py3-none-any.whl (1.0 MB view hashes)

Uploaded py3

Supported by

AWS AWS Cloud computing and Security Sponsor Datadog Datadog Monitoring Fastly Fastly CDN Google Google Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Sentry Sentry Error logging StatusPage StatusPage Status page