Multidimensional scaling
Read more in the :ref:`User Guide <multidimensional_scaling>`.
Parameters ---------- n_components : int, optional, default: 2 Number of dimensions in which to immerse the dissimilarities.
metric : boolean, optional, default: True If ``True``, perform metric MDS; otherwise, perform nonmetric MDS.
n_init : int, optional, default: 4 Number of times the SMACOF algorithm will be run with different initializations. The final results will be the best output of the runs, determined by the run with the smallest final stress.
max_iter : int, optional, default: 300 Maximum number of iterations of the SMACOF algorithm for a single run.
verbose : int, optional, default: 0 Level of verbosity.
eps : float, optional, default: 1e-3 Relative tolerance with respect to stress at which to declare convergence.
n_jobs : int or None, optional (default=None) The number of jobs to use for the computation. If multiple initializations are used (``n_init``), each run of the algorithm is computed in parallel.
``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary <n_jobs>` for more details.
random_state : int, RandomState instance, default=None Determines the random number generator used to initialize the centers. Pass an int for reproducible results across multiple function calls. See :term: `Glossary <random_state>`.
dissimilarity : 'euclidean' | 'precomputed', optional, default: 'euclidean' Dissimilarity measure to use:
- 'euclidean': Pairwise Euclidean distances between points in the dataset.
- 'precomputed': Pre-computed dissimilarities are passed directly to ``fit`` and ``fit_transform``.
Attributes ---------- embedding_ : array-like, shape (n_samples, n_components) Stores the position of the dataset in the embedding space.
stress_ : float The final value of the stress (sum of squared distance of the disparities and the distances for all constrained points).
Examples -------- >>> from sklearn.datasets import load_digits >>> from sklearn.manifold import MDS >>> X, _ = load_digits(return_X_y=True) >>> X.shape (1797, 64) >>> embedding = MDS(n_components=2) >>> X_transformed = embedding.fit_transform(X:100
) >>> X_transformed.shape (100, 2)
References ---------- 'Modern Multidimensional Scaling - Theory and Applications' Borg, I.; Groenen P. Springer Series in Statistics (1997)
'Nonmetric multidimensional scaling: a numerical method' Kruskal, J. Psychometrika, 29 (1964)
'Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis' Kruskal, J. Psychometrika, 29, (1964)