2;jidZddlmZddlZddlmZddlmZm Z ddl m Z ddl m Z ddlmZdd lmZdd lmZGd d eZdS) z6 Classical multi-dimensional scaling (classical MDS). )IntegralN)linalg) BaseEstimator _fit_context)pairwise_distances)check_symmetric)Interval)svd_flip) validate_dataceZdZUdZeedddgeegedgdZ ee d< dd dd d Z fd Z dd Z edddZxZS) ClassicalMDSa7 Classical multidimensional scaling (MDS). This is also known as principal coordinates analysis (PCoA) or Torgerson's scaling. It is a version of MDS that has exact solution in terms of eigendecomposition. If the input dissimilarity matrix consists of the pairwise Euclidean distances between some vectors, then classical MDS is equivalent to PCA applied to this set of vectors. Read more in the :ref:`User Guide `. Parameters ---------- n_components : int, default=2 Number of embedding dimensions. metric : str or callable, default='euclidean' Metric to use for dissimilarity computation. Default is "euclidean". If metric is a string, it must be one of the options allowed by `scipy.spatial.distance.pdist` for its metric parameter, or a metric listed in :func:`sklearn.metrics.pairwise.distance_metrics` If metric is "precomputed", X is assumed to be a distance matrix and must be square during fit. If metric is a callable function, it takes two arrays representing 1D vectors as inputs and must return one value indicating the distance between those vectors. This works for Scipy's metrics, but is less efficient than passing the metric name as a string. metric_params : dict, default=None Additional keyword arguments for the dissimilarity computation. Attributes ---------- embedding_ : ndarray of shape (n_samples, n_components) Stores the position of the dataset in the embedding space. dissimilarity_matrix_ : ndarray of shape (n_samples, n_samples) Pairwise dissimilarities between the points. eigenvalues_ : ndarray of shape (n_components,) Eigenvalues of the double-centered dissimilarity matrix, corresponding to each of the selected components. They are equal to the squared 2-norms of the `n_components` variables in the embedding space. n_features_in_ : int Number of features seen during :term:`fit`. feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. See Also -------- sklearn.decomposition.PCA : Principal component analysis. MDS : Metric and non-metric MDS. References ---------- .. [1] "Modern Multidimensional Scaling - Theory and Applications" Borg, I.; Groenen P. Springer Series in Statistics (1997) Examples -------- >>> from sklearn.datasets import load_digits >>> from sklearn.manifold import ClassicalMDS >>> X, _ = load_digits(return_X_y=True) >>> X.shape (1797, 64) >>> cmds = ClassicalMDS(n_components=2) >>> X_emb = cmds.fit_transform(X[:100]) >>> X_emb.shape (100, 2) Nleft)closed n_componentsmetric metric_params_parameter_constraints euclidean)rrc0||_||_||_dSNr)selfrrrs Y/root/voice-cloning/.venv/lib/python3.11/site-packages/sklearn/manifold/_classical_mds.py__init__zClassicalMDS.__init__hs!) *crt}|jdk|j_|S)N precomputed)super__sklearn_tags__r input_tagspairwise)rtags __class__s rr!zClassicalMDS.__sklearn_tags__ss.ww''))#';-#?  rc0|||S)a Compute the embedding positions. Parameters ---------- X : array-like of shape (n_samples, n_features) or (n_samples, n_samples) Input data. If ``metric=='precomputed'``, the input should be the dissimilarity matrix. y : Ignored Not used, present for API consistency by convention. Returns ------- self : object Fitted estimator. ) fit_transform)rXys rfitzClassicalMDS.fitxs& 1 rT)prefer_skip_nested_validationct||}|jdkr#||_t|jd|_n't |fd|ji|j|jni|_|jdz}|tj}|tj |dz}|tj |d d z}|d z}tj |\}}|ddd d|j }|ddddd fddd|j f}t|d\}}tj||z|_||_|jS) a Compute and return the embedding positions. Parameters ---------- X : array-like of shape (n_samples, n_features) or (n_samples, n_samples) Input data. If ``metric=='precomputed'``, the input should be the dissimilarity matrix. y : Ignored Not used, present for API consistency by convention. Returns ------- X_new : ndarray of shape (n_samples, n_components) The embedding coordinates. rT)raise_exceptionrNrr)axisr)r.keepdimsg)r rdissimilarity_matrix_rrrastypenpfloat64meanreighrr sqrt embedding_ eigenvalues_)rr(r)BwU_s rr'zClassicalMDS.fit_transforms* $ " " ;- ' ')*D &)8*D***D & &*<**{**.);)G4%%R**D &  & ) HHRZ  RWQQ    RWQQ . . .. T {1~~1 dddG'd'' ( aaa2gJqqq-D--- .4  1'!**q.r)rr)__name__ __module__ __qualname____doc__r rstrcallabledictr__annotations__rr!r*rr' __classcell__)r%s@rr r sJJZ"(AtFCCCD/$$D + + + + + + ,\5557776577777rr )rAnumbersrnumpyr3scipyr sklearn.baserrsklearn.metricsr sklearn.utilsrsklearn.utils._param_validationr sklearn.utils.extmathr sklearn.utils.validationr r rrrQs44444444......))))))444444******222222qqqqq=qqqqqr