{Kg-w2dZddlmZmZddlZddlmZmZm Z m Z ddl m Z m Z ddlmZddlmZmZmZmZmZdd lmZdd lmZmZdd lmZdd lmZmZm Z dd l!m"Z"ddl#m$Z$m%Z%d(dZ&d)dZ' d*dZ(dddddddddd dZ)e degeedddgeedddgeedddgehdgeedddgeedddgehd geedddgeedddgd!gdegd" d#$dddddddddd d%Z*Gd&d'eeeeZ+y)+zLocally Linear Embedding)IntegralRealN)eighqrsolvesvd) csr_matrixeye)eigsh) BaseEstimatorClassNamePrefixFeaturesOutMixinTransformerMixin _fit_context_UnstableArchMixin)NearestNeighbors) check_arraycheck_random_state)_init_arpack_v0)Interval StrOptionsvalidate_params) stable_cumsum) FLOAT_DTYPEScheck_is_fittedMbP?ct|t}t|t}t|t}|j\}}|jd|k(sJt j ||f|j }t j||j }t|D]\}} || } | ||z } t j| | j} t j| } | dkDr|| z}n|}| jdd|dzxx|z cc<t| |d}|t j|z ||ddf<|S)aCompute barycenter weights of X from Y along the first axis We estimate the weights to assign to each point in Y[indices] to recover the point X[i]. The barycenter weights sum to 1. Parameters ---------- X : array-like, shape (n_samples, n_dim) Y : array-like, shape (n_samples, n_dim) indices : array-like, shape (n_samples, n_dim) Indices of the points in Y used to compute the barycenter reg : float, default=1e-3 Amount of regularization to add for the problem to be well-posed in the case of n_neighbors > n_dim Returns ------- B : array-like, shape (n_samples, n_neighbors) Notes ----- See developers note for more information. dtyperNpos)assume_a)rrintshapenpemptyrones enumeratedotTtraceflatrsum)XYindicesreg n_samples n_neighborsBviindACGr+Rws d/home/alanp/www/video.onchill/myenv/lib/python3.12/site-packages/sklearn/manifold/_locally_linear.pybarycenter_weightsr>s%6 A\*AA\*A'-G$]]I{ 771: "" " )[)9A  177+AG$3 cF !H FF1accN  19e AA !+/!"a'" !Q 'bffQi-!Q$% Hc\t|dz|j|}|j}|j}|j |dddddf}t ||||}t jd||zdz|}t|j|j|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 r3n_jobsF)return_distanceNr1r)r$) rfit_fit_Xn_samples_fit_ kneighborsr>r%aranger ravel) r.r3r1rBknnr2r7dataindptrs r=barycenter_kneighbors_graphrNSsB {Qv F J J1 MC A""I ..E. 21ab5 9C aCS 1D YYq)k1A5{ CF tzz|SYY[&9)YAW XXr?r ư>dcX|dk(r|jddkDr ||zdkrd}nd}|dk(rTt|jd|} t|||zd|||\}} | d d |d ft j ||d fS|dk(r{t|d r|j}t||||zd z fd \}} t jt j|} | d d | ft j |fSt d|z#t$r} t d | z| d } ~ wwxYw)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 arpackdenseg)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_solverrXmax_iter random_staterZ eigen_values eigen_vectorseindexs r= null_spacerm}sTTv 771: F R#L"Lx QWWQZ 6 */1v:Sc8+ 'L-QZ("&&fg1F*GGG  1i  A&* F Q7T' # m 266,/0QX&|(<<<9LHII' 69: :    sD D)D$$D)rRstandard-C6?-q=) r1rfrXrgmethod hessian_tol modified_tolrhrBc t|dz| } | j|| j}|j\} }||kDr t d|| k\rt d| |fz|dk7}|dk(rt | ||| }|rAt |jd|ji|z }|j|zj}n|j|z|jz |z j}|jdd|jd dzxxdz cc<nM|d k(r*||dzzd z}|||zkr t d | j||dzd }|ddddf}tj|d|z|zftj}d|ddd f<tj | | ftj}||kD}t#| D]i}|||}||j%d z}|rt'|d d }n8tj(||j}t+|ddddddf}|ddd|f|dddd|zf<d|z}t#|D]3}|dd||dzf|dd||fz|dd|||z|z f<|||z z }5t-|\}}|dd|dzdf}|j/d }d|tj0t3||k<||z}tj4||||\} }!|| |!fxxtj(||jz cc<l|r*t7|}n|dk(r||kr t d| j||dzd }|ddddf}tj | ||f}"t9||}#tj | |#g}$||kD}|r;t#| D]'}|||||z }%t'|%d\|"|<|$|<}&)|$d z}$nft#| D]X}|||||z }%tj(|%|%j}'t+|'\}(})|(ddd|$|<|)dddddf|"|<Zd|$j/dz}tj(|"j;d d dtj<|}*|*ddd|#fxx|$|dddfzzcc<|*dd|#dfxx|dddfzcc<tj | |f}+t#| D]!}tj(|"||*||+|<#|+|+j/ddddfz}+|$dd|dfj/d|$ddd|fj/dz },tj>|,}-tj | t@}.tC|$d}/|/ddddf|/ddddfz dz }0t#| D]#}tjD|0|dddf|-|.|<%|.||#z z }.tj | | ftj}t#| D]}|.|}1|"|dd||1z df}2tjFjI|2j/d tjJ|1z }3tjL|1|3tj(|2jtj<|z }4tjFjI|4}5|5| kr|4d z}4n|4|5z}4|2d tjNtj(|2|4|4zz d|3z |+|dddfzz}6tj4||||\} }!|| |!fxxtj(|6|6jz cc<|6j/d}7||||fxx|7zcc<||||fxx|7zcc<|||fxx|1z cc<|rzt7|}nm|dk(rg| j||dzd }|ddddf}tj | | f}||kD}t#| D]}|||}8|8|8j%d z}8|rt'|8dd }9n8tj(|8|8j}t+|ddddddf}9tj ||dzf}|9ddd|f|ddddf<dtjJ|z |ddd f<tj(||j}:tj4||||\} }!|| |!fxx|:zcc<|||||fxxdz cc<tQ|d|||| S)Nr rAz>output dimension must be less than or equal to input dimensionzHExpected n_neighbors <= n_samples, but n_samples = %d, n_neighbors = %drVrn)r3r1rBformatrhessianr z^for method='hessian', n_neighbors must be greater than [n_components * (n_components + 3) / 2]Fr3rCr) full_matricesmodifiedz1modified LLE requires n_neighbors >= n_componentsTrltsag?)rerfrXrgrh))rrErFr$r_rNr rur*tocsrr[r,rHr%r&float64zerosrangemeanrr)rrr-whererbmeshgridr min transposer'medianr#r searchsortedlinalgnormsqrtfullouterrm);r.r3 n_componentsr1rfrXrgrqrrrsrhrBnbrsNd_inM_sparseWrcdp neighborsYiuse_svdr6GiUCijrdQr;r<Snbrs_xnbrs_yVnevevalsX_nbrs_C_nbrsevivitmpw_regrhoetas_range evals_cumsum eta_ranges_iVialpha_ihnorm_hWiWi_sum1Xir5GiGiTs; r=_locally_linear_embeddingrs   a GDHHQK AggGAtd L  a V+   w&H  ' ks6  QWW.QXX.2Aq!Aq133"++-A FF$aggaj1n$ % * % 9  \A- .! 3 ,+ +:  OO ;?E$ ae$ XX{A $4r$9:"** M1a4 HHaV2:: .$qA9Q<B "''!* B!,Q/VVB%HQK4R4(*+A} },<*=Bq!a,&&& 'L A<(23Aq1q5yL/Aa<FWDX2X1a!l*Q.../\A%%)b6DAq!\A%''(AaA01Abhhs1v +, - FA[[1y|DNFF ffn 133 / 7: 1 A :   %PQ QOO ;?E$ ae$ HHak2 3$ $!S"$ 1X9Q<1Q4/$'d$C!!eAh aKE1X9Q<1Q4/1v,Rtt9a!TrT'{! UYYq\!ffQ[[Aq)277;+?@ AttG AtG ,,  AstG AtG $ ![)*qAvvadCF+E!H 1ag&&A|}$%))!,uQ  5E/F/J/J1/MMiin ((1C($UA.  BC(<3B3+??!C qA1dd7);SAGAJ;$$ HHaV2:: .qA!*C1as*,,-BiinnRVVAY/"''#,>G W%rttRWW[5I(JJAYY^^A&F $QV a"((266"a=!444G uQPQSWZGX7XXB [[1y|DNFF ffn BDD!1 1 ffQiG a1o ' )  ilAo ' )  adGsNGIL 1 A 6 OO ;?E$ ae$ HHaV $qA9Q<B "''!* B$/2VVB%HQK4R4(; q(89:B!]l]*+Bq!"uIRWW[11Bq!tHFF2rtt$E[[1y|DNFF ffn  &  ilIaL( )Q . )'*  ! ! r?z array-likeleftclosed>rRrVrU>r{rvrzrnrh r.r3rr1rfrXrgrqrrrsrhrBTprefer_skip_nested_validationc 0t|||||||||| | |  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_embeddingrs6T % ! ! !!  r?c~eZdZUdZeedddgeedddgeedddgehdgeedddgeedddgehdgeedddgeedddgehd gd gdegd Ze e d <d dddddddddddd dZ dZ e dddZe dddZdZy)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>rRrVrU>r{rvrzrn>rRbrutekd_tree ball_treerh) r3rr1rfrXrgrqrrrsneighbors_algorithmrhrB_parameter_constraintsr rrRrOrPrnrorpc ||_||_||_||_||_||_||_||_| |_| |_ | |_ | |_ yN) r3rr1rfrXrgrqrrrsrhrrB) selfr3rr1rfrXrgrqrrrsrrhrBs r=__init__zLocallyLinearEmbedding.__init__s_ '((   &((#6  r?cTt|j|j|j|_t |j }|j|t}|jj|t|j|j|j|j|j|j|j|j |j"||j$|j \|_|_|j&j*d|_y)N)r3 algorithmrBr) r.r3rrfrXrgrqrrrsrhr1rBr )rr3rrBnbrs_rrh_validate_datafloatrErrrfrXrgrqrrrsr1 embedding_reconstruction_error_r$_n_features_out)rr.rhs r=_fit_transformz%LocallyLinearEmbedding._fit_transforms%((..;;  *$*;*;<     / q6Ojj((****]];;((**%;; 7 33 $44Q7r?Trc(|j||S)ayCompute the embedding vectors for data X. Parameters ---------- X : array-like of shape (n_samples, n_features) Training set. y : Ignored Not used, present here for API consistency by convention. Returns ------- self : object Fitted `LocallyLinearEmbedding` class instance. )rrr.ys r=rEzLocallyLinearEmbedding.fit+s" A r?c<|j||jS)aCompute the embedding vectors for data X and transform X. Parameters ---------- X : array-like of shape (n_samples, n_features) Training set. y : Ignored Not used, present here for API consistency by convention. Returns ------- X_new : array-like, shape (n_samples, n_components) Returns the instance itself. )rrrs r= fit_transformz$LocallyLinearEmbedding.fit_transform?s" Ar?ct||j|d}|jj||jd}t ||jj ||j}tj|jd|jf}t|jdD]8}tj|j||j||||<:|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)resetrwrDr)rrrrHr3r>rFr1r%r&r$rrr)rr*)rr.r7weightsX_newr6s r= transformz LocallyLinearEmbedding.transformSs&      /jj## 4++U$ %Q (9(93DHHM!''!*d&7&789qwwqz"Avvdooc!f577DE!H# r?r)__name__ __module__ __qualname____doc__rrrrrdict__annotations__rrrrErrr?r=rr[s* BJ!1d6BC!(AtFCDq$v67#$?@Aq$v67h4?@IJK q$v>?!$4?@ *+T UV'(" $D $  ":8456&56&r?r)r)rN)r rUrOrPN),rnumbersrrnumpyr% scipy.linalgrrrr scipy.sparser r scipy.sparse.linalgr baser rrrrrrutilsrr utils._arpackrutils._param_validationrrr utils.extmathrutils.validationrrr>rNrmrrrrr?r=rs~ #--(%)3+KK)<3 l'YVQUIJb    up, - 1d6BC!(AtFCDq$v67#$?@Aq$v67h4?@IJK q$v>?!$4?@'(" #',    F#"FRU# Ur?