Sammon Mapping

A Python implementation of Sammon Mapping — a nonlinear dimensionality reduction technique that preserves pairwise distances between data points as faithfully as possible when projecting from a high-dimensional space into a lower-dimensional one.

Originally introduced by John W. Sammon Jr. in 1969, it is particularly effective at revealing cluster structure and manifold geometry that linear methods like PCA can miss.

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Features

• Reduce data of any dimensionality down to n dimensions (2D, 3D, …)
• Two initialisation strategies: PCA (default, faster convergence) or random
• Accepts either raw data or a precomputed distance matrix as input
• Step-halving line search for robust convergence
• Configurable iteration budget, step-halving depth, and convergence tolerance
• Returns the stress value so you can quantitatively compare runs

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Installation

pip install sammon-mapping

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Quick Start

from sammon.sammon import sammon
from sklearn.datasets import load_iris
import matplotlib.pyplot as plt

iris = load_iris()
y, stress = sammon(iris.data, n=2)

plt.scatter(y[:, 0], y[:, 1], c=iris.target, cmap='tab10')
plt.title(f'Iris — Sammon Mapping  (stress={stress:.4f})')
plt.show()

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Visualizations

Iris Dataset — 4D → 2D

Handwritten Digits — 64D → 2D

Swiss Roll Manifold — 3D → 2D

Original 3D	Sammon 2D Projection

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API Reference

sammon(x, n=2, display=0, inputdist='raw', maxhalves=20, maxiter=500, tolfun=1e-9, init='pca')

Parameter	Type	Default	Description
x	array-like (N, D)	—	Input data matrix or precomputed distance matrix
n	int	2	Number of output dimensions
display	int	0	Verbosity: 0 silent, 1 convergence message, 2 every iteration
inputdist	str	'raw'	'raw' — compute Euclidean distances from data; 'distance' — x is already a distance matrix
maxhalves	int	20	Maximum step-halving attempts per iteration
maxiter	int	500	Maximum number of gradient descent iterations
tolfun	float	1e-9	Convergence tolerance on relative change in stress
init	str	'pca'	Initialisation: 'pca' uses leading SVD components; 'random' uses Gaussian noise

Returns

Name	Type	Description
y	ndarray (N, n)	Projected coordinates in the output space
E	float	Final Sammon stress (lower is better)

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Examples

Using a precomputed distance matrix

from scipy.spatial.distance import cdist
from sammon.sammon import sammon

D = cdist(X, X)  # or any custom distance matrix
y, stress = sammon(D, n=2, inputdist='distance')

3D projection with verbose output

y, stress = sammon(X, n=3, display=2)

Random initialisation

y, stress = sammon(X, n=2, init='random')

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Reference

Sammon, J. W. (1969). A nonlinear mapping for data structure analysis. IEEE Transactions on Computers, C-18(5), 401–409. doi: 10.1109/T-C.1969.222678