0PhOwdZddlmZmZddlZddlmZmZm Z m Z ddl m Z m Z mZddlmZddlmZmZmZmZmZdd lmZdd lmZmZdd lmZdd lmZm Z m!Z!dd l"m#Z#ddl$m%Z%m&Z&m'Z'd)dZ(d*dZ) d+dZ*dddddddddd dZ+e!degeedddgeedddgeedddge hd geedddgeedddge hd!geedddgeedddgd"gdegd# d$%dddddddddd d&Z,Gd'd(eeeeZ-dS),zLocally Linear Embedding)IntegralRealN)eighqrsolvesvd) csr_matrixeye lil_matrix)eigsh) BaseEstimatorClassNamePrefixFeaturesOutMixinTransformerMixin _fit_context_UnstableArchMixin)NearestNeighbors) check_arraycheck_random_state)_init_arpack_v0)Interval StrOptionsvalidate_params) stable_cumsum) FLOAT_DTYPEScheck_is_fitted validate_dataMbP?ct|t}t|t}t|t}|j\}}|jd|ksJt j||f|j}t j||j}t|D]\}} || } | ||z } t j | | j } t j | } | dkr|| z}n|}| j dd|dzxx|z cc<t| |d}|t j|z ||ddf<|S)aCompute barycenter weights of X from Y along the first axis We estimate the weights to assign to each point in Y[indices] to recover the point X[i]. The barycenter weights sum to 1. Parameters ---------- X : array-like, shape (n_samples, n_dim) Y : array-like, shape (n_samples, n_dim) indices : array-like, shape (n_samples, n_dim) Indices of the points in Y used to compute the barycenter reg : float, default=1e-3 Amount of regularization to add for the problem to be well-posed in the case of n_neighbors > n_dim Returns ------- B : array-like, shape (n_samples, n_neighbors) Notes ----- See developers note for more information. dtyperNpos)assume_a)rrintshapenpemptyr!ones enumeratedotTtraceflatrsum)XYindicesreg n_samples n_neighborsBviindACGr-Rws `/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/sklearn/manifold/_locally_linear.pybarycenter_weightsr@s[6 A\***AA\***A'---G$]I{ 71: " " " " )[)999A  17+++AG$$   3 cF !H F1acNN  199e AAA !!+/!"""a'""" !Q ' ' 'bfQii-!QQQ$ Hct|dz||}|j}|j}||dddddf}t ||||}t jd||zdz|}t| | |f||fS) a-Computes the barycenter weighted graph of k-Neighbors for points in X Parameters ---------- X : {array-like, NearestNeighbors} Sample data, shape = (n_samples, n_features), in the form of a numpy array or a NearestNeighbors object. n_neighbors : int Number of neighbors for each sample. reg : float, default=1e-3 Amount of regularization when solving the least-squares problem. Only relevant if mode='barycenter'. If None, use the default. n_jobs : int or None, default=None The number of parallel jobs to run for neighbors search. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. Returns ------- A : sparse matrix in CSR format, shape = [n_samples, n_samples] A[i, j] is assigned the weight of edge that connects i to j. See Also -------- sklearn.neighbors.kneighbors_graph sklearn.neighbors.radius_neighbors_graph r"r5n_jobsF)return_distanceNr3rr&) rfit_fit_Xn_samples_fit_ kneighborsr@r'aranger ravel) r0r5r3rDknnr4r9dataindptrs r?barycenter_kneighbors_graphrQRsB {Qv F F F J J1 M MC A"I ..E. 2 2111abb5 9C aCS 1 1 1D Yq)k1A5{ C CF tzz||SYY[[&9)YAW X X XXrAr"arpackư>dc|dkr|jddkr ||zdkrd}nd}|dkrt|jd|} t|||zd|||\}} n%#t$r} t d | z| d } ~ wwxYw| d d |d ft j||d fS|dkrt|d r|}t||||zd z fd \}} t j t j |} | d d | ft j|fSt d|z)a0 Find the null space of a matrix M. Parameters ---------- M : {array, matrix, sparse matrix, LinearOperator} Input covariance matrix: should be symmetric positive semi-definite k : int Number of eigenvalues/vectors to return k_skip : int, default=1 Number of low eigenvalues to skip. eigen_solver : {'auto', 'arpack', 'dense'}, default='arpack' auto : algorithm will attempt to choose the best method for input data arpack : use arnoldi iteration in shift-invert mode. For this method, M may be a dense matrix, sparse matrix, or general linear operator. Warning: ARPACK can be unstable for some problems. It is best to try several random seeds in order to check results. dense : use standard dense matrix operations for the eigenvalue decomposition. For this method, M must be an array or matrix type. This method should be avoided for large problems. tol : float, default=1e-6 Tolerance for 'arpack' method. Not used if eigen_solver=='dense'. max_iter : int, default=100 Maximum number of iterations for 'arpack' method. Not used if eigen_solver=='dense' random_state : int, RandomState instance, default=None Determines the random number generator when ``solver`` == 'arpack'. Pass an int for reproducible results across multiple function calls. See :term:`Glossary `. autor rRdenseg)sigmatolmaxiterv0a Error in determining null-space with ARPACK. Error message: '%s'. Note that eigen_solver='arpack' can fail when the weight matrix is singular or otherwise ill-behaved. In that case, eigen_solver='dense' is recommended. See online documentation for more information.Ntoarrayr"T)subset_by_index overwrite_azUnrecognized eigen_solver '%s') r&rr RuntimeError ValueErrorr'r/hasattrr^rargsortabs) Mkk_skip eigen_solverr[max_iter random_stater] eigen_values eigen_vectorseindexs r? null_spacerp|sTv 71:  F R#LL"Lx QWQZ 6 6 */1v:Sc8+++ 'L--   69: :    QQQZ("&fgg1F*G*GGG  1i   A&* F Q7T' ' ' # m 26,//00QQQX&|(<(<<<9LHIIIsA$$ B.BBrVstandard-C6?-q=) r3rir[rjmethod hessian_tol modified_tolrkrDc t|dz| } | || j}|j\} }||krt d|| krt d| |fz|dk}|rt n t j}|dkrt| ||| }|r%t|jd|j i|z }|j |z} nd|j |z|j z |z }|j dd|jd dzxxdz cc< n|d krI||dzzd z}|||zkrt d | ||dzd }|ddddf}t j|d|z|zft j}d|ddd f<|| | ft j}||k}t#| D]}|||}||d z}|rt'|d d }n}/tA|%d}0|0ddddf|0ddddfz dz }1t#| D]%}t j!|1|dddf|.|/|<&|/||$z z }/|| | ft j}t#| D]}|/|}2|#|dd||2z df}3t j"#|3d t j$|2z }4t j%|2|4t j|3j t j|z }5t j"#|5}6|6| kr|5d z}5n|5|6z}5|3d t j&t j|3|5|5zz d|4z |,|dddfzz}7t j||||\}!}"||!|"fxxt j|7|7j z cc<|7d}8||||fxx|8zcc<||||gfxx|8zcc<|||fxx|2z cc<n|dkr| ||dzd }|ddddf}|| | ft j}||k}t#| D]N}|||}9|9|9d z}9|rt'|9dd }:noutput dimension must be less than or equal to input dimensionzHExpected n_neighbors <= n_samples, but n_samples = %d, n_neighbors = %drYrq)r5r3rDformatrhessianr z^for method='hessian', n_neighbors must be greater than [n_components * (n_components + 3) / 2]Fr5rEr ) full_matricesmodifiedz1modified LLE requires n_neighbors >= n_componentsTrltsag?rG)rhrir[rjrk))rrHrIr&rbr r'zerosrQr rxr,r^r.rKr(float64rangemeanrr+rrr/whereremeshgridmin transposer)medianr%r searchsortedlinalgnormsqrtfulloutertocsrrp)Snbrs_xnbrs_yVnevevalsX_nbrs_C_nbrsevivitmpw_regrhoetas_range evals_cumsum eta_ranges_iVialpha_ihnorm_hWiWi_sum1Xir7GiGiTs< r?_locally_linear_embeddingrs   a G G GDHHQKKK AgGAtd L   a V+    w&H,4Bjj"(  ' ks6     +QW.QX..2AaAAq13"++--A F$$agaj1n$ % % % * % % % % 9   \A- .! 3 ,+ + +:  OO ;?E$  aaae$ X{A $4r$9:"* M M M111a4 # #QF"* = = =$q 0 0A9Q<B "''!** B )!,,,Q/VB%%HHQK44R4(*+AAA} },<*=Bqqq!a,&&& 'L A<(( & &23AAAq1q5yL/Aaaa<FWDX2X111a!l*Q.../\A%%b66DAq!!!\A%'''(AaA01Abhs1vv +,, - FA[1y|DDNFF ffn   13 /    7 0: :    % %PQQ QOO ;?E$  aaae$ Hak2 3 3$ $$!S""$  #1XX D D9Q<1Q4/$'d$C$C$C!!eAh aKEE1XX # #9Q<1Q4/11v,,Rttt9a!!!TTrT'{! UYYq\\!fQ[[Aq))27;+?+?@@ AAAttG AAAtG ,,  AAAsttG AAAtG $ ![)**q , ,AvadCF++E!HH 1aaag&&AAA|}}$%))!,,uQQQ  5E/F/J/J1/M/MMinn (1C((($UA..  BCC(<3B3+??!C q B BA1ddd7);SAAGAJJ;$$ $ #QF"* = = =q$ $ A!*C1aaas*,,,-BinnRVVAYY//"'#,,>G W%%rtRW[5I5I(J(JJAY^^A&&F $$QV a"(26"a==!4444G uQPQPQPQSWZGX7XXB [1y|DDNFF ffn   BD!1!1 1   ffQiiG a1o   ' )    ilQC G + adGGGsNGGGGI$ L 6  OO ;?E$  aaae$ # #QF"* = = =$q H HA9Q<B "''!** B )$///2VB%%HHQK44R4(; q(89::B!!!]l]*+Bqqq!""uIRW[111Bqqq!tHF2rt$$E[1y|DDNFF ffn    &    ilIaL( ) ) )RW;-G-G-G G ) ) ) ) GGII  ! !   rAz array-likeleftclosed>rVrYrR>r~ryr}rqrk r0r5rr3rir[rjrtrurvrkrDTprefer_skip_nested_validationc 8t|||||||||| | |  S)aPerform a Locally Linear Embedding analysis on the data. Read more in the :ref:`User Guide `. Parameters ---------- X : {array-like, NearestNeighbors} Sample data, shape = (n_samples, n_features), in the form of a numpy array or a NearestNeighbors object. n_neighbors : int Number of neighbors to consider for each point. n_components : int Number of coordinates for the manifold. reg : float, default=1e-3 Regularization constant, multiplies the trace of the local covariance matrix of the distances. eigen_solver : {'auto', 'arpack', 'dense'}, default='auto' auto : algorithm will attempt to choose the best method for input data arpack : use arnoldi iteration in shift-invert mode. For this method, M may be a dense matrix, sparse matrix, or general linear operator. Warning: ARPACK can be unstable for some problems. It is best to try several random seeds in order to check results. dense : use standard dense matrix operations for the eigenvalue decomposition. For this method, M must be an array or matrix type. This method should be avoided for large problems. tol : float, default=1e-6 Tolerance for 'arpack' method Not used if eigen_solver=='dense'. max_iter : int, default=100 Maximum number of iterations for the arpack solver. method : {'standard', 'hessian', 'modified', 'ltsa'}, default='standard' standard : use the standard locally linear embedding algorithm. see reference [1]_ hessian : use the Hessian eigenmap method. This method requires n_neighbors > n_components * (1 + (n_components + 1) / 2. see reference [2]_ modified : use the modified locally linear embedding algorithm. see reference [3]_ ltsa : use local tangent space alignment algorithm see reference [4]_ hessian_tol : float, default=1e-4 Tolerance for Hessian eigenmapping method. Only used if method == 'hessian'. modified_tol : float, default=1e-12 Tolerance for modified LLE method. Only used if method == 'modified'. random_state : int, RandomState instance, default=None Determines the random number generator when ``solver`` == 'arpack'. Pass an int for reproducible results across multiple function calls. See :term:`Glossary `. n_jobs : int or None, default=None The number of parallel jobs to run for neighbors search. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. Returns ------- Y : ndarray of shape (n_samples, n_components) Embedding vectors. squared_error : float Reconstruction error for the embedding vectors. Equivalent to ``norm(Y - W Y, 'fro')**2``, where W are the reconstruction weights. References ---------- .. [1] Roweis, S. & Saul, L. Nonlinear dimensionality reduction by locally linear embedding. Science 290:2323 (2000). .. [2] Donoho, D. & Grimes, C. Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data. Proc Natl Acad Sci U S A. 100:5591 (2003). .. [3] `Zhang, Z. & Wang, J. MLLE: Modified Locally Linear Embedding Using Multiple Weights. `_ .. [4] Zhang, Z. & Zha, H. Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. Journal of Shanghai Univ. 8:406 (2004) Examples -------- >>> from sklearn.datasets import load_digits >>> from sklearn.manifold import locally_linear_embedding >>> X, _ = load_digits(return_X_y=True) >>> X.shape (1797, 64) >>> embedding, _ = locally_linear_embedding(X[:100],n_neighbors=5, n_components=2) >>> embedding.shape (100, 2) r)rrs r?locally_linear_embeddingrs@T % ! ! !!    rAceZdZUdZeedddgeedddgeedddgehdgeedddgeedddgehdgeedddgeedddgehd gd gdegd Ze e d <d dddddddddddd dZ dZ e dddZe dddZdZdS)LocallyLinearEmbeddingaLocally Linear Embedding. Read more in the :ref:`User Guide `. Parameters ---------- n_neighbors : int, default=5 Number of neighbors to consider for each point. n_components : int, default=2 Number of coordinates for the manifold. reg : float, default=1e-3 Regularization constant, multiplies the trace of the local covariance matrix of the distances. eigen_solver : {'auto', 'arpack', 'dense'}, default='auto' The solver used to compute the eigenvectors. The available options are: - `'auto'` : algorithm will attempt to choose the best method for input data. - `'arpack'` : use arnoldi iteration in shift-invert mode. For this method, M may be a dense matrix, sparse matrix, or general linear operator. - `'dense'` : use standard dense matrix operations for the eigenvalue decomposition. For this method, M must be an array or matrix type. This method should be avoided for large problems. .. warning:: ARPACK can be unstable for some problems. It is best to try several random seeds in order to check results. tol : float, default=1e-6 Tolerance for 'arpack' method Not used if eigen_solver=='dense'. max_iter : int, default=100 Maximum number of iterations for the arpack solver. Not used if eigen_solver=='dense'. method : {'standard', 'hessian', 'modified', 'ltsa'}, default='standard' - `standard`: use the standard locally linear embedding algorithm. see reference [1]_ - `hessian`: use the Hessian eigenmap method. This method requires ``n_neighbors > n_components * (1 + (n_components + 1) / 2``. see reference [2]_ - `modified`: use the modified locally linear embedding algorithm. see reference [3]_ - `ltsa`: use local tangent space alignment algorithm. see reference [4]_ hessian_tol : float, default=1e-4 Tolerance for Hessian eigenmapping method. Only used if ``method == 'hessian'``. modified_tol : float, default=1e-12 Tolerance for modified LLE method. Only used if ``method == 'modified'``. neighbors_algorithm : {'auto', 'brute', 'kd_tree', 'ball_tree'}, default='auto' Algorithm to use for nearest neighbors search, passed to :class:`~sklearn.neighbors.NearestNeighbors` instance. random_state : int, RandomState instance, default=None Determines the random number generator when ``eigen_solver`` == 'arpack'. Pass an int for reproducible results across multiple function calls. See :term:`Glossary `. n_jobs : int or None, default=None The number of parallel jobs to run. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. Attributes ---------- embedding_ : array-like, shape [n_samples, n_components] Stores the embedding vectors reconstruction_error_ : float Reconstruction error associated with `embedding_` 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 nbrs_ : NearestNeighbors object Stores nearest neighbors instance, including BallTree or KDtree if applicable. See Also -------- SpectralEmbedding : Spectral embedding for non-linear dimensionality reduction. TSNE : Distributed Stochastic Neighbor Embedding. References ---------- .. [1] Roweis, S. & Saul, L. Nonlinear dimensionality reduction by locally linear embedding. Science 290:2323 (2000). .. [2] Donoho, D. & Grimes, C. Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data. Proc Natl Acad Sci U S A. 100:5591 (2003). .. [3] `Zhang, Z. & Wang, J. MLLE: Modified Locally Linear Embedding Using Multiple Weights. `_ .. [4] Zhang, Z. & Zha, H. Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. Journal of Shanghai Univ. 8:406 (2004) Examples -------- >>> from sklearn.datasets import load_digits >>> from sklearn.manifold import LocallyLinearEmbedding >>> X, _ = load_digits(return_X_y=True) >>> X.shape (1797, 64) >>> embedding = LocallyLinearEmbedding(n_components=2) >>> X_transformed = embedding.fit_transform(X[:100]) >>> X_transformed.shape (100, 2) r"Nrrr>rVrYrR>r~ryr}rq>rVbrutekd_tree ball_treerk) r5rr3rir[rjrtrurvneighbors_algorithmrkrD_parameter_constraintsr rrVrSrTrqrrrsc ||_||_||_||_||_||_||_||_| |_| |_ | |_ | |_ dSN) r5rr3rir[rjrtrurvrkrrD) selfr5rr3rir[rjrtrurvrrkrDs r?__init__zLocallyLinearEmbedding.__init__sc '((   &((#6  rAct|j|j|j|_t |j}t||t}|j |t|j|j|j |j |j |j|j|j|j||j|j \|_|_|jjd|_dS)N)r5 algorithmrDr ) r0r5rrir[rjrtrurvrkr3rDr")rr5rrDnbrs_rrkrfloatrHrrrir[rjrtrurvr3 embedding_reconstruction_error_r&_n_features_out)rr0rks r?_fit_transformz%LocallyLinearEmbedding._fit_transforms%(.;    *$*;<< $ / / / q6Oj(**];(*%; 7 7 7 33 $4Q7rATrc0|||S)ayCompute the embedding vectors for data X. Parameters ---------- X : array-like of shape (n_samples, n_features) Training set. y : Ignored Not used, present here for API consistency by convention. Returns ------- self : object Fitted `LocallyLinearEmbedding` class instance. )rrr0ys r?rHzLocallyLinearEmbedding.fit*s" A rAc:|||jS)aCompute the embedding vectors for data X and transform X. Parameters ---------- X : array-like of shape (n_samples, n_features) Training set. y : Ignored Not used, present here for API consistency by convention. Returns ------- X_new : array-like, shape (n_samples, n_components) Returns the instance itself. )rrrs r? fit_transformz$LocallyLinearEmbedding.fit_transform>s " ArAct|t||d}|j||jd}t ||jj||j}tj |j d|j f}t|j dD]6}tj |j||j||||<7|S)a Transform new points into embedding space. Parameters ---------- X : array-like of shape (n_samples, n_features) Training set. Returns ------- X_new : ndarray of shape (n_samples, n_components) Returns the instance itself. Notes ----- Because of scaling performed by this method, it is discouraged to use it together with methods that are not scale-invariant (like SVMs). F)resetrzrFr)rrrrKr5r@rIr3r'r(r&rrr+rr,)rr0r9weightsX_newr8s r? transformz LocallyLinearEmbedding.transformRs&  $ / / /j## 4+U$  %Q (93DHMMM!'!*d&7899qwqz"" E EAvdoc!f57DDE!HH rAr)__name__ __module__ __qualname____doc__rrrrrdict__annotations__rrrrHrrrAr?rrZs BBJ!1d6BBBC!(AtFCCCDq$v6667#$?$?$?@@Aq$v6667Xh4???@:IIIJJK q$v>>>?!$4???@ * +T+T+T U UV'(" $ $D   $  ":8884\55565&\55565&rAr)r)rN)r"rRrSrTN).rnumbersrrnumpyr' scipy.linalgrrrr scipy.sparser r r scipy.sparse.linalgr baserrrrrrrutilsrr utils._arpackrutils._param_validationrrr utils.extmathrutils.validationrrrr@rQrprrrrrAr?rs #"""""""------------4444444444%%%%%%)(((((33333333++++++KKKKKKKKKK))))))KKKKKKKKKK3 3 3 3 l'Y'Y'Y'YVQUIJIJIJIJb    uuuuup, - 1d6BBBC!(AtFCCCDq$v6667#$?$?$?@@Aq$v6667Xh4???@:IIIJJK q$v>>>?!$4???@'("  #',    FFFF#"FRUUUUU# UUUUUrA