Implementation:Scikit learn Scikit learn ClassicalMDS

Knowledge Sources	Scikit_learn Scikit-learn Docs
Domains	Machine Learning, Dimensionality Reduction
Last Updated	2026-02-08 15:00 GMT

Overview

Concrete tool for performing classical multidimensional scaling (MDS) via eigendecomposition, provided by scikit-learn.

Description

The ClassicalMDS class implements classical multidimensional scaling, also known as principal coordinates analysis (PCoA) or Torgerson's scaling. It is a version of MDS that has an exact solution via eigendecomposition. When the input dissimilarity matrix consists of pairwise Euclidean distances, classical MDS is equivalent to PCA. It supports configurable distance metrics and precomputed distance matrices.

Usage

Use this estimator when you need to embed data into a lower-dimensional space based on pairwise dissimilarities, especially when an exact closed-form solution is preferred over iterative optimization.

Code Reference

Source Location

• Repository: scikit-learn
• File: sklearn/manifold/_classical_mds.py

Signature

class ClassicalMDS(BaseEstimator):
    def __init__(
        self,
        n_components=2,
        *,
        metric="euclidean",
        metric_params=None,
    ):

Import

from sklearn.manifold import ClassicalMDS

I/O Contract

Inputs

Name	Type	Required	Description
n_components	int	No	Number of embedding dimensions (default 2)
metric	str or callable	No	Dissimilarity metric (default 'euclidean'); use 'precomputed' for distance matrices
metric_params	dict or None	No	Additional keyword arguments for the dissimilarity computation (default None)

Outputs

Name	Type	Description
embedding_	ndarray of shape (n_samples, n_components)	Position of dataset in the embedding space
dissimilarity_matrix_	ndarray of shape (n_samples, n_samples)	Pairwise dissimilarity matrix

Usage Examples

Basic Usage

from sklearn.manifold import ClassicalMDS
import numpy as np

X = np.random.randn(50, 10)
mds = ClassicalMDS(n_components=2)
X_embedded = mds.fit_transform(X)
print(X_embedded.shape)  # (50, 2)

Related Pages

• Principle:Scikit_learn_Scikit_learn_Dimensionality_Reduction