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)

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.

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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.

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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.

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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).

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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).

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