8000 FEA Implement classical MDS by dkobak · Pull Request #31322 · scikit-learn/scikit-learn · GitHub
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FEA Implement classical MDS #31322

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@dkobak dkobak commented May 6, 2025 •
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Fixes #15272. Supersedes #22330.

This PR implements classical MDS, also known as principal coordinates analysis (PCoA) or Torgerson's scaling, see https://en.wikipedia.org/wiki/Multidimensional_scaling#Classical_multidimensional_scaling. As discussed in #22330, it is implemented as a new class ClassicalMDS.

Simple demonstration:

import pylab as plt
import numpy as np

from sklearn.datasets import load_iris
from sklearn.manifold import ClassicalMDS
from sklearn.decomposition import PCA

X, y = load_iris(return_X_y=True)

Z1 = PCA(n_components=2).fit_transform(X)
Z2 = ClassicalMDS(n_components=2, dissimilarity="euclidean").fit_transform(X)
Z3 = ClassicalMDS(n_components=2, dissimilarity="cosine"   ).fit_transform(X)
Z4 = ClassicalMDS(n_components=2, dissimilarity="manhattan").fit_transform(X)

fig, axs = plt.subplots(nrows=2, ncols=2, figsize=(6, 6), layout="constrained")

axs.flat[0].scatter(Z1[:,0], Z1[:,1], c=y)
axs.flat[0].set_title("PCA")

axs.flat[1].scatter(Z2[:,0], Z2[:,1], c=y)
axs.flat[1].set_title("Classical MDS, Euclidean dist.")

axs.flat[2].scatter(-Z3[:,0], Z3[:,1], c=y)
axs.flat[2].set_title("Classical MDS, cosine dist.")

axs.flat[3].scatter(Z4[:,0], Z4[:,1], c=y)
axs.flat[3].set_title("Classical MDS, Manhattan dist.")

cmds

Classical MDS is also set as default initialization for metric/non-metric MDS in the MDS() class.

For consistency, this PR also adds support for non-Euclidean metrics to the MDS class.

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github-actions bot commented May 6, 2025 •
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✔️ Linting Passed

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Generated for commit: bafac04. Link to the linter CI: here

@dkobak dkobak mentioned this pull request May 6, 2025
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dkobak commented May 8, 2025

Pinging @antoinebaker for a review :-) I have been doing some updates to this PR but am now finished with it.

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Thanks for the PR @dkobak !

Could you maybe use this PR to implement ClassicalMDS only, and do the enhancements of MDS in a separate / follow up PR ? It will ease the reviewing / merging process I think.

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dkobak commented May 12, 2025 •
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Could you maybe use this PR to implement ClassicalMDS only, and do the enhancements of MDS in a separate / follow up PR ? It will ease the reviewing / merging process I think.

All right. I took all changes to the MDS class out of this PR now. I will wait until this PR is merged and then do a follow-up PR to change the MDS class.

@dkobak dkobak changed the title Implement classical MDS FEA Implement classical MDS May 14, 2025
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sklearn MDS vs skbio PCoA
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