Toggle Menu
Prev Up Next

scikit-learn 1.3.2
Other versions

Please cite us if you use the software.

# `sklearn.manifold`.smacof

sklearn.manifold.smacof(dissimilarities, *, metric=True, n_components=2, init=None, n_init=8, n_jobs=None, max_iter=300, verbose=0, eps=0.001, random_state=None, return_n_iter=False, normalized_stress='warn')

  Compute multidimensional scaling using the SMACOF algorithm.

  The SMACOF (Scaling by MAjorizing a COmplicated Function) algorithm is a multidimensional scaling algorithm which minimizes an objective function (the stress) using a majorization technique. Stress majorization, also known as the Guttman Transform, guarantees a monotone convergence of stress, and is more powerful than traditional techniques such as gradient descent.

  The SMACOF algorithm for metric MDS can be summarized by the following steps:

  1. Set an initial start configuration, randomly or not.

  2. Compute the stress

  3. Compute the Guttman Transform

  4. Iterate 2 and 3 until convergence.

  The nonmetric algorithm adds a monotonic regression step before computing the stress.

  Parameters:
    dissimilarities ndarray of shape (n_samples, n_samples)

      Pairwise dissimilarities between the points. Must be symmetric.

    metric bool, default=True

      Compute metric or nonmetric SMACOF algorithm. When `False` (i.e. non-metric MDS), dissimilarities with 0 are considered as missing values.

    n_components int, default=2

      Number of dimensions in which to immerse the dissimilarities. If an `init` array is provided, this option is overridden and the shape of `init` is used to determine the dimensionality of the embedding space.

    init ndarray of shape (n_samples, n_components), default=None

      Starting configuration of the embedding to initialize the algorithm. By default, the algorithm is initialized with a randomly chosen array.

    n_init int, default=8

      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. If `init` is provided, this option is overridden and a single run is performed.

    n_jobs int, 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 `joblib.parallel_backend` context. `-1` means using all processors. See Glossary for more details.

    max_iter int, default=300

      Maximum number of iterations of the SMACOF algorithm for a single run.

    verbose int, default=0

      Level of verbosity.

    eps float, default=1e-3

      Relative tolerance with respect to stress at which to declare convergence. The value of `eps` should be tuned separately depending on whether or not `normalized_stress` is being used.

    random_state int, RandomState instance or None, default=None

      Determines the random number generator used to initialize the centers. Pass an int for reproducible results across multiple function calls. See Glossary.

    return_n_iter bool, default=False

      Whether or not to return the number of iterations.

    normalized_stress bool or “auto” default=False

      Whether use and return normed stress value (Stress-1) instead of raw stress calculated by default. Only supported in non-metric MDS.

      New in version 1.2.

  Returns:
    X ndarray of shape (n_samples, n_components)

      Coordinates of the points in a `n_components`-space.

    stress float

      The final value of the stress (sum of squared distance of the disparities and the distances for all constrained points). If `normalized_stress=True`, and `metric=False` returns Stress-1. A value of 0 indicates “perfect” fit, 0.025 excellent, 0.05 good, 0.1 fair, and 0.2 poor [1].

    n_iter int

      The number of iterations corresponding to the best stress. Returned only if `return_n_iter` is set to `True`.

  References

  [1]

  “Nonmetric multidimensional scaling: a numerical method” Kruskal, J. Psychometrika, 29 (1964)

  [2]

  “Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis” Kruskal, J. Psychometrika, 29, (1964)

  [3]

  “Modern Multidimensional Scaling - Theory and Applications” Borg, I.; Groenen P. Springer Series in Statistics (1997)