MDS

Multidimensional scaling places points in a low-dimensional space so that pairwise distances match the originals as closely as possible.

Algorithm

Metric (and non-metric) MDS via the SMACOF majorisation iteration, which monotonically decreases the stress functional.

Constructor

Skigen::MDS<Scalar> model(
	int n_components = 2,
	int max_iter = 300,
	Scalar tol = 1e-3,
	bool metric = true,
	std::optional<uint64_t> random_state = std::nullopt,
	int n_init = 4);

Parameters

Parameter	Default	Description
n_components	2	Embedding dimensionality.
max_iter	300	SMACOF iterations.
tol	1e-3	Stress-convergence tolerance.
metric	true	Metric MDS; non-metric MDS is deferred.
random_state	nullopt	Optional seed for reproducible starts.
n_init	4	Number of random SMACOF starts; the best stress is retained.

Methods

Method	Description
fit_transform(X)	Return the embedding.

Fitted Attributes

Accessor	Description
stress()	Final stress value.
n_iter()	Number of SMACOF iterations used by the best start.
n_init()	Number of random starts tried.

Example

Skigen::MDS<double> mds(2);
auto Y = mds.fit_transform(X);

Verified against scikit-learn

This estimator is checked by the parity suite. See the generator tests/parity/generate_manifold_reference.py and the reference fixtures in tests/parity/data/mds/, exercised by tests/parity/parity_manifold.cpp.

API Reference

For full signatures see the MDS API Reference.