Implementation:Scikit learn Scikit learn Isomap

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

Overview

Concrete tool for non-linear dimensionality reduction through Isometric Mapping provided by scikit-learn.

Description

This module implements the Isomap algorithm for non-linear dimensionality reduction. Isomap extends classical Multidimensional Scaling (MDS) by replacing Euclidean distances with geodesic distances computed on a nearest-neighbor graph. It first constructs a k-nearest neighbor or radius-based graph, computes shortest path distances between all pairs of points, and then applies Kernel PCA with a precomputed distance kernel. The algorithm preserves the global geometric structure of the data manifold.

Usage

Use Isomap when your data lies on a non-linear manifold and you want to preserve geodesic distances in the low-dimensional embedding. It works well when the data manifold is globally connected and approximately isometric to Euclidean space.

Code Reference

Source Location

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

Signature

class Isomap(ClassNamePrefixFeaturesOutMixin, TransformerMixin, BaseEstimator):
    """Isomap Embedding."""

    def __init__(
        self,
        *,
        n_neighbors=5,
        radius=None,
        n_components=2,
        eigen_solver="auto",
        tol=0,
        max_iter=None,
        path_method="auto",
        neighbors_algorithm="auto",
        n_jobs=None,
        metric="minkowski",
        p=2,
        metric_params=None,
    ):
        ...

Import

from sklearn.manifold import Isomap

I/O Contract

Inputs

Name	Type	Required	Description
X	array-like of shape (n_samples, n_features)	Yes	Training data
n_neighbors	int or None	No	Number of neighbors for graph construction (default: 5)
radius	float or None	No	Radius for radius-based graph (alternative to n_neighbors)
n_components	int	No	Target dimensionality (default: 2)
eigen_solver	str	No	Eigenvalue solver: 'auto', 'arpack', or 'dense' (default: 'auto')
path_method	str	No	Shortest path algorithm: 'auto', 'FW', or 'D' (default: 'auto')
metric	str	No	Distance metric for neighbors (default: 'minkowski')

Outputs

Name	Type	Description
embedding_	ndarray of shape (n_samples, n_components)	Low-dimensional embedding of training data
kernel_pca_	KernelPCA	Internal KernelPCA instance used for the embedding
dist_matrix_	ndarray of shape (n_samples, n_samples)	Geodesic distance matrix
nbrs_	NearestNeighbors	Internal NearestNeighbors instance

Usage Examples

Basic Usage

from sklearn.manifold import Isomap
from sklearn.datasets import make_swiss_roll

# Generate Swiss roll data
X, color = make_swiss_roll(n_samples=1000, random_state=42)

# Apply Isomap
isomap = Isomap(n_neighbors=10, n_components=2)
X_embedded = isomap.fit_transform(X)
print("Embedded shape:", X_embedded.shape)
print("Reconstruction error:", isomap.reconstruction_error())

Related Pages

• Principle:Scikit_learn_Scikit_learn_Manifold_Learning