0Ph]dZddlZddlmZmZddlZddlmZddl m Z m Z ddl m Z ddlmZdd lmZmZmZdd lmZmZmZdd lmZmZdd lmZ d!dZedgdgeedddgddgeedddgedgeedddgdgeedddgdgdgdedhgd d d ddddddddddd dZGdd e ZdS)"z" Multi-dimensional Scaling (MDS). N)IntegralReal)effective_n_jobs) BaseEstimator _fit_context)IsotonicRegression)euclidean_distances) check_arraycheck_random_statecheck_symmetric)Interval StrOptionsvalidate_params)Paralleldelayed) validate_dataT,MbP?Fc t|d}|jd} t|}dtj| z |z} | | dk} |1|| |z} | | |f} n4|jd}| |jdkrtd| |fz|} d} t}t|D]O}t| }|r|}n|}|| dk}| | |}| }||| dk<|| | f}|tj| | dz zdz |dzz z}||z dzdz }|rAtj||dzdz z }d ||dk<||z }| }|tjt#|tjt#|fxx|d z cc<d | z tj|| z} tj| dzd }|dkrt'd ||fz| $| ||z z |kr|rt'd ||fzn||z } Q| ||dzfS)ab Computes 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. 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. 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 :term:`Glossary `. normalized_stress : bool, default=False Whether use and return normed stress value (Stress-1) instead of raw stress calculated by default. Only supported in non-metric MDS. The caller must ensure that if `normalized_stress=True` then `metric=False` .. versionadded:: 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. 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) T)raise_exceptionrNsizez'init matrix should be of shape (%d, %d)rgh㈵>)axisg?zit: %d, stress %sz'breaking at iteration %d with stress %s)r shaper nptriraveluniformreshape ValueErrorr ranger fit_transformcopysqrtsumarangelendotprint)dissimilaritiesmetric n_componentsinitmax_iterverboseeps random_statenormalized_stress n_samplessim_flat sim_flat_wX old_stressiritdis disparitiesdis_flat dis_flat_wdisparities_flatstressratioBs U/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/sklearn/manifold/_mds.py_smacof_singlerEsid&otLLLO%a(I%l33LRVI&&&/9@@BBH(a-(J |  i,&> ? ? IIy,/ 0 0z!}  1 % %9Y }t|  \}}}| || kr|} |} |}?n| t j tjj| }t!|tdz d   fd |D}t#|\}}}t j|}||} ||} ||}| r| | |fS| | fS) 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 : array-like 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 : array-like 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. 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 :term:`Glossary `. return_n_iter : bool, default=False Whether or not to return the number of iterations. normalized_stress : bool or "auto" default="auto" Whether use and return normed stress value (Stress-1) instead of raw stress calculated by default. Only supported in non-metric MDS. .. versionadded:: 1.2 .. versionchanged:: 1.4 The default value changed from `False` to `"auto"` in version 1.4. 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) Examples -------- >>> import numpy as np >>> from sklearn.manifold import smacof >>> from sklearn.metrics import euclidean_distances >>> X = np.array([[0, 1, 2], [1, 0, 3],[2, 3, 0]]) >>> dissimilarities = euclidean_distances(X) >>> mds_result, stress = smacof(dissimilarities, n_components=2, random_state=42) >>> mds_result array([[ 0.05... -1.07... ], [ 1.74..., -0.75...], [-1.79..., 1.83...]]) >>> stress np.float64(0.0012...) rKznNormalized stress is not supported for metric MDS. Either set `normalized_stress=False` or use `metric=False`. __array__rzTExplicit initial positions passed: performing only one init of the MDS instead of %dNNr-r.r/r0r1r2r3r4Nrr)rMr1c 3dK|]*}tt | V+dS)rVN)rrE) .0seedr,r2r/r0r-r.r4r1s rD zsmacof..rsu G G  $GN # #)!!"3    G G G G G G rF)r r r"hasattrrasarrayr%warningswarnrr#rErandintiinfoint32maxrzipargmin)r,r-r.r/rLrMr0r1r2r3rNr4best_pos best_stressr;posrAn_iter_ best_iterseedsresults positionsn_itersbests```` ``` ` rDsmacofrosd|"/22O%l33LF"" &J V  @   t[!!z$$$&&{{ MDFLM   F&Hk1$$-- $ $B#1)!)"3 $ $ $ C"f{&:&:$ 88::#  $"$$RXbh%7%7%;&$IIF(&#gk12E2EFFF G G G G G G G G G G G  G G G   &)']" 67y  Tl T?DM %i//$$rFc FeZdZUdZeedddgdgeedddgeedddgdgeedddgdegd ged d hgded hgd Ze e d< ddddddddd d d dZ fdZ ddZ edddZxZS)MDSafMultidimensional 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. When ``False`` (i.e. non-metric MDS), dissimilarities with 0 are considered as missing values. 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. The value of `eps` should be tuned separately depending on whether or not `normalized_stress` is being used. 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``. normalized_stress : bool or "auto" default="auto" Whether use and return normed stress value (Stress-1) instead of raw stress calculated by default. Only supported in non-metric MDS. .. versionadded:: 1.2 .. versionchanged:: 1.4 The default value changed from `False` to `"auto"` in version 1.4. 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). 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]_. 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 ---------- .. [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) 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, normalized_stress='auto') >>> X_transformed = embedding.fit_transform(X[:100]) >>> X_transformed.shape (100, 2) For a more detailed example of usage, see :ref:`sphx_glr_auto_examples_manifold_plot_mds.py`. For a comparison of manifold learning techniques, see :ref:`sphx_glr_auto_examples_manifold_plot_compare_methods.py`. rNrHrIrGr1gr3 euclidean precomputedrK) r.r-rLr0r1r2rMr3 dissimilarityr4_parameter_constraintsrTrrr) r-rLr0r1r2rMr3rtr4c ||_| |_||_||_||_||_||_||_||_| |_ dS)N) r.rtr-rLr0r2r1rMr3r4) selfr.r-rLr0r1r2rMr3rtr4s rD__init__z MDS.__init__$sT)*      (!2rFcrt}|jdk|j_|S)Nrs)super__sklearn_tags__rt input_tagspairwise)rxtags __class__s rDr|zMDS.__sklearn_tags__=s/ww''))#'#5#F  rFc4||||S)a Compute the position of the points in the embedding space. Parameters ---------- X : array-like of shape (n_samples, n_features) or (n_samples, n_samples) Input data. If ``dissimilarity=='precomputed'``, the input should be the dissimilarity matrix. y : Ignored Not used, present for API consistency by convention. init : ndarray of shape (n_samples, n_components), default=None Starting configuration of the embedding to initialize the SMACOF algorithm. By default, the algorithm is initialized with a randomly chosen array. Returns ------- self : object Fitted estimator. )r/)r$rxr8yr/s rDfitzMDS.fitBs"0 14((( rFrOct||}|jd|jdkr|jdkrtjd|jdkr||_n|jdkrt ||_t|j|j|j ||j |j |j |j |j|jd|j \|_|_|_|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, n_components), 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. rrrszThe MDS API has changed. ``fit`` now constructs an dissimilarity matrix from data. To use a custom dissimilarity matrix, set ``dissimilarity='precomputed'``.rrTrR)rrrtr]r^dissimilarity_matrix_r ror-r.rLrMr0r1r2r3r4 embedding_stress_rhrs rDr$zMDS.fit_transform]s2 $ " " 71: # #(:m(K(K M3      . .)*D & &  ; . .)Xh4???@;sD8889"'($*k=%ABBC'VH)=)=> $ $D   3 ! 333332 6\5555556555555rFrq)TrNrrrNF) rr]numbersrrnumpyrjoblibrbaserrisotonicr metricsr utilsr r r utils._param_validationrrrutils.parallelrrutils.validationrrErorqrFrDrsv""""""""######........))))))))))))DDDDDDDDDDKKKKKKKKKK........,,,,,,    QQQQh(>+!(AtFCCCDt$8Haf===>T"Xh4???@;q$v6667'(#'VH)=)=>  #'(     M%M%M%M%#"M%`GGGGG-GGGGGrF