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Multi-dimensional Scaling (MDS) iÿÿÿÿNi(t BaseEstimator(teuclidean_distances(tcheck_random_statet check_arraytcheck_symmetric(tParallel(tdelayed(teffective_n_jobs(tIsotonicRegressioni,igü©ñÒMbP?cCs×t|dtƒ}|jd}t|ƒ}dtj|ƒ|jƒ} | | dk} |d kr|j||ƒ} | j ||fƒ} n?|jd}||jdkrÈt d||fƒ‚n|} d } t ƒ} xæt |ƒD]Ø}t | ƒ}|r |}nŒ|jƒ}|| dk}| j| |ƒ}|jƒ}||| dk<|j ||fƒ}|tj||dd|djƒƒ9}|jƒ|jƒdjƒd}d||dk<||}| }|tjt|ƒƒtjt|ƒƒfc|jddƒ7taxisgð?sit: %d, stress %ss'breaking at iteration %d with stress %sN(RtTruetshapeRtnpttritraveltNonetrandtreshapet ValueErrorRtrangeRt fit_transformtcopytsqrttsumtarangetlentdot(tdissimilaritiestmetrict n_componentstinittmax_itertverbosetepst random_statet n_samplestsim_flatt sim_flat_wtXt old_stresstirtittdist disparitiestdis_flatt dis_flat_wtdisparities_flattstresstratiotB((s3lib/python2.7/site-packages/sklearn/manifold/mds.pyt_smacof_singlesX2         $ @%   ic sàtˆƒ‰t| ƒ} tˆdƒretjˆƒjƒ‰|dksetjd|ƒd}qend\} } t |ƒdkrx9t |ƒD]x} t ˆdˆdˆdˆdˆdˆd ˆd | ƒ\}}}| dksí|| kr|} |jƒ} |}qqWn°| j tj tjƒjd |ƒ}td |dtˆdd ƒƒ‡‡‡‡‡‡‡fd†|Dƒƒ}t|Œ\}}}tj|ƒ}||} ||} ||}| rÒ| | |fS| | fSdS(sŠComputes 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 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, shape (n_samples, n_samples) Pairwise dissimilarities between the points. Must be symmetric. metric : boolean, optional, default: True Compute metric or nonmetric SMACOF algorithm. n_components : int, optional, 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, shape (n_samples, n_components), optional, 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, optional, 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 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 ` for more details. 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. random_state : int, RandomState instance or None, optional, default: None The generator used to initialize the centers. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. return_n_iter : bool, optional, default: False Whether or not to return the number of iterations. Returns ------- X : ndarray, 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) t __array__isTExplicit initial positions passed: performing only one init of the MDS instead of %dRRRR R!R"R#tsizetn_jobsic3sK|]A}ttƒˆdˆdˆdˆdˆdˆdˆd|ƒVqdS(RRRR R!R"R#N(RR3(t.0tseed(RR"RR RRR!(s3lib/python2.7/site-packages/sklearn/manifold/mds.pys sN(NN(RRthasattrR tasarrayRtwarningstwarnRRRR3trandinttiinfotint32tmaxRtziptargmin(RRRRtn_initR6R R!R"R#t return_n_itertbest_post best_stressR*tposR0tn_iter_t best_itertseedstresultst positionstn_iterstbest((RR"RR RRR!s3lib/python2.7/site-packages/sklearn/manifold/mds.pytsmacof‡sBc         $     tMDSc Bs_eZdZdeddddd d dd„ Zed„ƒZd d d „Zd d d „Z RS( s+ Multidimensional scaling Read more in the :ref:`User Guide `. 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 ` for more details. random_state : int, RandomState instance or None, optional, default: None The generator used to initialize the centers. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. 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) iii,igü©ñÒMbP?t euclideanc CsU||_| |_||_||_||_||_||_||_||_dS(N( Rt dissimilarityRRCR R"R!R6R#( tselfRRRCR R!R"R6R#RR((s3lib/python2.7/site-packages/sklearn/manifold/mds.pyt__init__ms        cCs |jdkS(Nt precomputed(tkernel(RS((s3lib/python2.7/site-packages/sklearn/manifold/mds.pyt _pairwisezscCs|j|d|ƒ|S(sF Computes the position of the points in the embedding space Parameters ---------- X : array, shape (n_samples, n_features) or (n_samples, n_samples) Input data. If ``dissimilarity=='precomputed'``, the input should be the dissimilarity matrix. y : Ignored init : ndarray, shape (n_samples,), optional, default: None Starting configuration of the embedding to initialize the SMACOF algorithm. By default, the algorithm is initialized with a randomly chosen array. R(R(RSR'tyR((s3lib/python2.7/site-packages/sklearn/manifold/mds.pytfit~scCst|ƒ}|jd|jdkrE|jdkrEtjdƒn|jdkr`||_n:|jdkrt|ƒ|_ntdt|jƒƒ‚t |jd|j d|j d |d |j d |j d |jd |jd|jd|jdtƒ \|_|_|_|jS(sE Fit the data from X, and returns the embedded coordinates Parameters ---------- X : array, shape (n_samples, n_features) or (n_samples, n_samples) Input data. If ``dissimilarity=='precomputed'``, the input should be the dissimilarity matrix. y : Ignored init : ndarray, shape (n_samples,), optional, default: None Starting configuration of the embedding to initialize the SMACOF algorithm. By default, the algorithm is initialized with a randomly chosen array. iiRUsThe MDS API has changed. ``fit`` now constructs an dissimilarity matrix from data. To use a custom dissimilarity matrix, set ``dissimilarity='precomputed'``.RQs>Proximity must be 'precomputed' or 'euclidean'. 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