Implementation:Scikit learn Scikit learn MDS

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

Overview

Concrete tool for multidimensional scaling (MDS) dimensionality reduction provided by scikit-learn.

Description

This module implements Multidimensional Scaling (MDS), which finds a low-dimensional representation of data in which distances between points approximate the given dissimilarity matrix. It supports both metric MDS (preserves actual distances) and non-metric MDS (preserves only the rank order of distances). The module uses the SMACOF (Scaling by MAjorizing a COmplicated Function) algorithm for iterative optimization and supports parallel execution of multiple random initializations.

Usage

Use MDS when you have a distance or dissimilarity matrix and want to visualize or embed the data in a low-dimensional space. Non-metric MDS is useful when only the ordinal relationships between distances matter.

Code Reference

Source Location

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

Signature

class MDS(BaseEstimator):
    """Multidimensional scaling."""

    def __init__(
        self,
        n_components=2,
        *,
        metric=True,
        n_init=4,
        max_iter=300,
        verbose=0,
        eps=1e-6,
        n_jobs=None,
        random_state=None,
        dissimilarity="euclidean",
        normalized_stress="auto",
    ):
        ...

def _smacof_single(
    dissimilarities,
    metric=True,
    n_components=2,
    init=None,
    max_iter=300,
    verbose=0,
    eps=1e-6,
    random_state=None,
    normalized_stress=False,
):
    ...

Import

from sklearn.manifold import MDS

I/O Contract

Inputs

Name	Type	Required	Description
X	array-like of shape (n_samples, n_features) or (n_samples, n_samples)	Yes	Data matrix or precomputed dissimilarity matrix
n_components	int	No	Target dimensionality (default: 2)
metric	bool	No	Use metric MDS if True, non-metric if False (default: True)
n_init	int	No	Number of random initializations (default: 4)
max_iter	int	No	Maximum SMACOF iterations (default: 300)
dissimilarity	str	No	Input type: 'euclidean' or 'precomputed' (default: 'euclidean')
normalized_stress	str or bool	No	Normalize stress measure (default: 'auto')

Outputs

Name	Type	Description
embedding_	ndarray of shape (n_samples, n_components)	Low-dimensional embedding coordinates
stress_	float	Final stress value (goodness of fit)
dissimilarity_matrix_	ndarray of shape (n_samples, n_samples)	Pairwise dissimilarity matrix used
n_iter_	int	Number of iterations for best result

Usage Examples

Basic Usage

from sklearn.manifold import MDS
from sklearn.metrics import euclidean_distances
import numpy as np

# Generate sample data
rng = np.random.RandomState(42)
X = rng.randn(100, 10)

# Apply metric MDS
mds = MDS(n_components=2, random_state=42)
X_embedded = mds.fit_transform(X)
print("Embedded shape:", X_embedded.shape)
print("Stress:", mds.stress_)

Related Pages

• Principle:Scikit_learn_Scikit_learn_Manifold_Learning