B 0d!I @sdZddlZddlmZmZddlZddlmZddl m Z ddl m Z m Z mZddlmZdd lmZdd lmZdddZd ddddd dd ddd ddZGdddeZdS)z" Multi-dimensional Scaling (MDS). N)Paralleleffective_n_jobs) BaseEstimator)euclidean_distances)check_random_state check_arraycheck_symmetric)IsotonicRegression) deprecated)delayedT,MbP?cCs$t|dd}|jd}t|}dt||} | | dk} |dkrf|||} | ||f} n,|jd}||jdkrtd||f|} d} t } xvt |D]h}t | }|r|}nh|}|| dk}| | |}| }||| dk<|||f}|t||dd|d9}||dd}d||dk<||}| }|tt|tt|f|jdd 7<d |t|| } t| djdd }|dkrtd ||f| dk r | |||kr |rtd ||fP||} qW| ||dfS) aComputes multidimensional scaling using SMACOF algorithm. 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. 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. 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. 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 :term:`Glossary `. 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). n_iter : int The number of iterations corresponding to the best stress. T)Zraise_exceptionrNz'init matrix should be of shape (%d, %d)rgh㈵>)Zaxisg?zit: %d, stress %sz'breaking at iteration %d with stress %s)r shapernpZtriZravelZrandZreshape ValueErrorr ranger fit_transformcopysqrtsumZarangelendotprint)dissimilaritiesmetric n_componentsinitmax_iterverboseeps random_stateZ n_samplesZsim_flatZ sim_flat_wXZ old_stressZiritdisZ disparitiesZdis_flatZ dis_flat_wZdisparities_flatstressratioBr)G/var/www/html/venv/lib/python3.7/site-packages/sklearn/manifold/_mds.py_smacof_singlesV9         0   r+F) rrrn_initn_jobsrr r!r" return_n_iterc  s@tt| } tdrBt|dksBtd|d}d\} } t|dkrxt |D]B} t | d\}}}| dks|| kr`|} |} |}q`Wn|| j t tj j|d}t|tddd fd d |D}t|\}}}t|}||} ||} ||}| r4| | |fS| | fSdS) aCompute 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. 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 :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`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. 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 :term:`Glossary `. return_n_iter : bool, default=False Whether or not to return the number of iterations. 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). n_iter : int The number of iterations corresponding to the best stress. Returned only if ``return_n_iter`` is set to ``True``. 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) Z __array__rzTExplicit initial positions passed: performing only one init of the MDS instead of %d)NN)rrrrr r!r"N)sizer)r.r c 3s*|]"}tt|dVqdS))rrrrr r!r"N)r r+).0seed)rr!rrrrr r)r* s zsmacof..)rrhasattrrZasarrayrwarningswarnrrr+randintZiinfoZint32maxrzipZargmin)rrrrr-r.rr r!r"r/Zbest_posZ best_stressr$posr&n_iter_Z best_iterZseedsresultsZ positionsZn_itersbestr))rr!rrrrr r*smacofsJn      r>c @s^eZdZdZddddddddd d d d Zd dZededdZdddZ dddZ dS)MDSaQMultidimensional scaling. Read more in the :ref:`User Guide `. Parameters ---------- n_components : int, default=2 Number of dimensions in which to immerse the dissimilarities. metric : bool, default=True If ``True``, perform metric MDS; otherwise, perform nonmetric MDS. n_init : int, 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, 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. 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 :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. 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 :term:`Glossary `. dissimilarity : {'euclidean', 'precomputed'}, 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_ : ndarray of 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). dissimilarity_matrix_ : ndarray of shape (n_samples, n_samples) Pairwise dissimilarities between the points. Symmetric matrix that: - either uses a custom dissimilarity matrix by setting `dissimilarity` to 'precomputed'; - or constructs a dissimilarity matrix from data using Euclidean distances. n_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 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. .. versionadded:: 1.0 n_iter_ : int The number of iterations corresponding to the best stress. See Also -------- sklearn.decomposition.PCA : Principal component analysis that is a linear dimensionality reduction method. sklearn.decomposition.KernelPCA : Non-linear dimensionality reduction using kernels and PCA. TSNE : T-distributed Stochastic Neighbor Embedding. Isomap : Manifold learning based on Isometric Mapping. LocallyLinearEmbedding : Manifold learning using Locally Linear Embedding. SpectralEmbedding : Spectral embedding for non-linear dimensionality. 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) 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) rTi,rgMbP?N euclidean)rr-rr r!r.r" dissimilarityc Cs:||_| |_||_||_||_||_||_||_||_dS)N) rrBrr-rr!r r.r") selfrrr-rr r!r.r"rBr)r)r*__init__s z MDS.__init__cCsd|jdkiS)Npairwise precomputed)rB)rCr)r)r* _more_tagsszMDS._more_tagszcAttribute `_pairwise` was deprecated in version 0.24 and will be removed in 1.1 (renaming of 0.26).cCs |jdkS)NrF)rB)rCr)r)r* _pairwisesz MDS._pairwisecCs|j||d|S)a Compute the position of the points in the embedding space. Parameters ---------- X : array-like of shape (n_samples, n_features) or (n_samples, n_samples) Input data. If ``dissimilarity=='precomputed'``, the input should be the dissimilarity matrix. y : Ignored Not used, present for API consistency by convention. init : ndarray of shape (n_samples,), default=None Starting configuration of the embedding to initialize the SMACOF algorithm. By default, the algorithm is initialized with a randomly chosen array. Returns ------- self : object Fitted estimator. )r)r)rCr#yrr)r)r*fitszMDS.fitc Cs||}|jd|jdkr2|jdkr2td|jdkrD||_n(|jdkrZt||_ntdt|jt |j|j |j ||j |j |j|j|j|jdd \|_|_|_|jS) a Fit the data from `X`, and returns the embedded coordinates. Parameters ---------- X : array-like of shape (n_samples, n_features) or (n_samples, n_samples) Input data. If ``dissimilarity=='precomputed'``, the input should be the dissimilarity matrix. y : Ignored Not used, present for API consistency by convention. init : ndarray of shape (n_samples,), default=None Starting configuration of the embedding to initialize the SMACOF algorithm. By default, the algorithm is initialized with a randomly chosen array. Returns ------- X_new : ndarray of shape (n_samples, n_components) X transformed in the new space. rrrFzThe MDS API has changed. ``fit`` now constructs an dissimilarity matrix from data. To use a custom dissimilarity matrix, set ``dissimilarity='precomputed'``.rAz>Proximity must be 'precomputed' or 'euclidean'. Got %s insteadT) rrrr-r.rr r!r"r/)Z_validate_datarrBr5r6Zdissimilarity_matrix_rrstrr>rrr-r.rr r!r"Z embedding_Zstress_r;)rCr#rIrr)r)r*rs0    zMDS.fit_transform)r)NN)NN) __name__ __module__ __qualname____doc__rDrGr propertyrHrJrr)r)r)r*r?6s t  r?)TrNr rrN)rOnumpyrZjoblibrrr5baserZmetricsrutilsrrr Zisotonicr Zutils.deprecationr Z utils.fixesr r+r>r?r)r)r)r*s8      u