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MDS

#include <Skigen/Manifold>

template <typename Scalar = double>
class Skigen::MDS(n_components=2, max_iter=300, tol=1e-3, metric=true, random_state=std::nullopt, n_init=4)

Multidimensional Scaling (MDS).

Non-linear dimensionality reduction through the SMACOF (Scaling by MAjorizing a COmplicated Function) algorithm. Given an input data matrix X the algorithm minimises the criterion, which measures how well pairwise Euclidean distances in the low-dimensional embedding approximate the original pairwise distances.

Mirrors sklearn.manifold.MDS.

Parameters:

  • n_components : int, default=2 Embedding dimensionality (default 2).

  • max_iter : int, default=300 Maximum SMACOF iterations (default 300).

  • tol : Scalar, default=1e-3 Convergence tolerance on relative stress change (default 1e-3).

  • metric : bool, default=true If true, metric MDS is used (default true, the only mode supported).

  • random_state : std::optional< uint64_t >, default=std::nullopt Optional seed for reproducible initialisation.

  • n_init : int, default=4 Number of random initialisations; the best stress is retained.

Attributes:

  • embedding : MatrixType Embedding coordinates (n_samples x n_components).

  • stress : Scalar Final stress value after fitting.

  • n_iter : int Number of SMACOF iterations performed.

  • n_init : int Number of random SMACOF initialisations tried.

Methods​

SKIGEN_PARAMS()​

Fit the MDS model using the SMACOF algorithm.

Computes pairwise Euclidean distances of X then iteratively optimises an n_components-dimensional embedding that preserves those distances as faithfully as possible.

Parameters:

  • X Data matrix of shape (n_samples, n_features).

Returns:

  • result Reference to the fitted transformer (*this).

transform()​

Return the stored embedding.

For MDS the transform simply returns the embedding computed during fit. The input X is expected to match the training data.

Parameters:

  • X Data matrix (ignored; the stored embedding is returned).

Returns:

  • result : MatrixType The embedding matrix (n_samples x n_components).