8.16.3. sklearn.manifold.MDS

class sklearn.manifold.MDS(n_components=2, metric=True, n_init=4, max_iter=300, verbose=0, eps=0.001, n_jobs=1, random_state=None)

Multidimensional scaling

Parameters :

metric : boolean, optional, default: True

compute metric or nonmetric SMACOF (Scaling by Majorizing a Complicated Function) algorithm

n_components : int, optional, default: 2

number of dimension in which to immerse the similarities overridden if initial array is provided.

n_init : int, optional, default: 4

Number of time the smacof algorithm will be run with different initialisation. The final results will be the best output of the n_init consecutive runs in terms of 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-6

relative tolerance w.r.t stress to declare converge

n_jobs : int, optional, default: 1

The number of jobs to use for the computation. This works by breaking down the pairwise matrix into n_jobs even slices and computing them in parallel.

If -1 all CPUs are used. If 1 is given, no parallel computing code is used at all, which is useful for debuging. For n_jobs below -1, (n_cpus + 1 - n_jobs) are used. Thus for n_jobs = -2, all CPUs but one are used.

random_state : integer or numpy.RandomState, optional

The generator used to initialize the centers. If an integer is given, it fixes the seed. Defaults to the global numpy random number generator.

Notes

“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)

Attributes

embedding_ array-like, shape [n_components, n_samples] 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)

Methods

fit(X[, init, y]) Computes the position of the points in the embedding space
fit_transform(X[, init, y]) Fit the data from X, and returns the embedded coordinates
get_params([deep]) Get parameters for the estimator
set_params(**params) Set the parameters of the estimator.
__init__(n_components=2, metric=True, n_init=4, max_iter=300, verbose=0, eps=0.001, n_jobs=1, random_state=None)
fit(X, init=None, y=None)

Computes the position of the points in the embedding space

Parameters :

X: array, shape=[n_samples, n_samples], symetric :

Proximity matrice

init: {None or ndarray, shape (n_samples,)} :

if None, randomly chooses the initial configuration if ndarray, initialize the SMACOF algorithm with this array

fit_transform(X, init=None, y=None)

Fit the data from X, and returns the embedded coordinates

Parameters :

X: array, shape=[n_samples, n_samples], symetric :

Proximity matrice

init: {None or ndarray, shape (n_samples,)} :

if None, randomly chooses the initial configuration if ndarray, initialize the SMACOF algorithm with this array

get_params(deep=True)

Get parameters for the estimator

Parameters :

deep: boolean, optional :

If True, will return the parameters for this estimator and contained subobjects that are estimators.

set_params(**params)

Set the parameters of the estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The former have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns :self :
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