o ?HhOw@sdZddlmZmZddlZddlmZmZm Z m Z ddl m Z m Z mZddlmZddlmZmZmZmZmZdd lmZdd lmZmZdd lmZdd lmZm Z m!Z!dd l"m#Z#ddl$m%Z%m&Z&m'Z'd.ddZ(d/ddZ) d0ddZ*dddddddddd dd Z+e!d!egeeddd"d#geeddd"d#geeddd"d#ge hd$geeddd"d#geeddd"d#ge hd%geeddd"d#geeddd"d#gd&gdegd' d(d)dddddddddd d*d+Z,Gd,d-d-eeeeZ-dS)1zLocally 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?cCst|td}t|td}t|td}|j\}}|jd|ks Jtj||f|jd}tj||jd}t|D]G\}} || } | ||} t | | j } t | } | dkrY|| }n|}| j dd|d|7<t | |dd}|t|||ddf<q6|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+Rwr=`/home/air/sanwanet/gpt-api/venv/lib/python3.10/site-packages/sklearn/manifold/_locally_linear.pybarycenter_weightss&       r?c Cst|d|d|}|j}|j}|j|ddddddf}t||||d}td||d|}t| | |f||fdS) 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_distanceNr1rr$) rfit_fit_Xn_samples_fit_ kneighborsr?r%arangerravel) r.r3r1rAknnr2r7dataindptrr=r=r>barycenter_kneighbors_graphRs!rNr arpackư>dc Cs |dkr|jddkr||dkrd}nd}|dkrYt|jd|}zt|||d|||d\}} WntyE} ztd | | d } ~ ww| d d |d ft||d fS|dkrt|d rf|}t ||||d fd d\}} t t |} | d d | ft|fStd|)a0 Find the null space of a matrix M. Parameters ---------- M : {array, matrix, sparse matrix, LinearOperator} Input covariance matrix: should be symmetric positive semi-definite k : int Number of eigenvalues/vectors to return k_skip : int, default=1 Number of low eigenvalues to skip. eigen_solver : {'auto', 'arpack', 'dense'}, default='arpack' auto : algorithm will attempt to choose the best method for input data arpack : use arnoldi iteration in shift-invert mode. For this method, M may be a dense matrix, sparse matrix, or general linear operator. Warning: ARPACK can be unstable for some problems. It is best to try several random seeds in order to check results. dense : use standard dense matrix operations for the eigenvalue decomposition. For this method, M must be an array or matrix type. This method should be avoided for large problems. tol : float, default=1e-6 Tolerance for 'arpack' method. Not used if eigen_solver=='dense'. max_iter : int, default=100 Maximum number of iterations for 'arpack' method. Not used if eigen_solver=='dense' random_state : int, RandomState instance, default=None Determines the random number generator when ``solver`` == 'arpack'. Pass an int for reproducible results across multiple function calls. See :term:`Glossary `. autor rOdenseg)sigmatolmaxiterv0a Error in determining null-space with ARPACK. Error message: '%s'. Note that eigen_solver='arpack' can fail when the weight matrix is singular or otherwise ill-behaved. In that case, eigen_solver='dense' is recommended. See online documentation for more information.Ntoarrayr T)subset_by_index overwrite_azUnrecognized eigen_solver '%s') r$rr RuntimeError ValueErrorr%r-hasattrrZrargsortabs) Mkk_skip eigen_solverrWmax_iter random_staterY eigen_values eigen_vectorseindexr=r=r> null_space|s<*&    rlrRstandard-C6?-q=) r1rerWrfmethod hessian_tol modified_tolrgrAc < Cst|d| d} | || j}|j\} }||krtd|| kr)td| |f|dk}|r1tntj}|dkrst| ||| d}|rTt |jd|j i|}|j |}n|j ||j | }|j dd|jd dd7<n|d kr||dd }|||krtd | j||dd d}|ddddf}tj|d||ftjd}d|ddd f<|| | ftjd}||k}t| D]}|||}||d 8}|rt|d dd }nt||j }t|ddddddf}|ddd|f|dddd|f<d|}t|D]+}|dd||df|dd||f|dd||||f<|||7}qt|\}}|dd|ddf}|d } d| tt| |k<|| }t||||\}!}"||!|"ft||j 7<qŐn|dkr||krtd| j||dd d}|ddddf}t| ||f}#t||}$t| |$g}%||k}|rt| D]}|||||}&t|&dd\|#|<|%|<}'q|%d C}%n5t| D]0}|||||}&t|&|&j }(t|(\})}*|)ddd|%|<|*dddddf|#|<qd|%d}t|#d d dt|}+|+ddd|$f|%|dddf<|+dd|$df|dddf<t| |f},t| D]}t|#||+||,|<qa|,|,ddddf},|%dd|dfd|%ddd|fd}-t|-}.tj| td}/t |%d}0|0ddddf|0ddddfd}1t| D]}t!|1|dddf|.|/|<q|/||$7}/|| | ftjd}t| D]}|/|}2|#|dd||2df}3tj"#|3d t$|2}4t%|2|4t|3j t|}5tj"#|5}6|6| kr*|5d 9}5n|5|6}5|3d t&t|3|5|5d|4|,|dddf}7t||||\}!}"||!|"ft|7|7j 7<|7d}8||||f|88<||||gf|88<|||f|27<qn|dkrC| j||dd d}|ddddf}|| | ftjd}||k}t| D]}|||}9|9|9d 8}9|rt|9ddd }:nt|9|9j }t|ddddddf}:t||df}|:ddd|f|ddddf<dt$||ddd f<t||j };t||||\}!}"||!|"f|;8<|||||ftj|d7<q|rJ|'}t(||d|||| dS)Nr r@z>output dimension must be less than or equal to input dimensionzHExpected n_neighbors <= n_samples, but n_samples = %d, n_neighbors = %drUrm)r3r1rAformatrhessianr z^for method='hessian', n_neighbors must be greater than [n_components * (n_components + 3) / 2]Fr3rBr) full_matricesmodifiedz1modified LLE requires n_neighbors >= n_componentsTrltsag?rD)rdrerWrfrg))rrErFr$r^r r%zerosrNr rsr*rZr,rHr&float64rangemeanrr)rrr-whererameshgridmin transposer'medianr#r searchsortedlinalgnormsqrtfulloutertocsrrl)_locally_linear_embeddings&  &     ( D           ,( 4  , "      6  &   $(rz array-likeleftclosed>rRrUrO>ryrtrxrmrg r.r3rr1rerWrfrprqrrrgrATprefer_skip_nested_validationc Cs t|||||||||| | | d 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)rrr=r=r>locally_linear_embeddings rc@seZdZUdZeeddddgeeddddgeeddddgehdgeeddddgeeddddgehdgeeddddgeeddddgehd gd gdegd Ze e d <d dddddddddddd ddZ ddZ e ddd"ddZe ddd"ddZd d!ZdS)#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>rRrUrO>ryrtrxrm>rRbrutekd_tree ball_treerg) r3rr1rerWrfrprqrrneighbors_algorithmrgrA_parameter_constraintsr rrRrPrQrmrnroc CsL||_||_||_||_||_||_||_||_| |_| |_ | |_ | |_ dSN) r3rr1rerWrfrprqrrrgrrA) selfr3rr1rerWrfrprqrrrrgrAr=r=r>__init__s zLocallyLinearEmbedding.__init__cCst|j|j|jd|_t|j}t||td}|j |t |j|j|j |j |j |j|j|j|j||j|jd \|_|_|jjd|_dS)N)r3 algorithmrAr) r.r3rrerWrfrprqrrrgr1rAr )rr3rrAnbrs_rrgrfloatrErrrerWrfrprqrrr1 embedding_reconstruction_error_r$_n_features_out)rr.rgr=r=r>_fit_transforms.  z%LocallyLinearEmbedding._fit_transformTrcCs|||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.yr=r=r>rE*s zLocallyLinearEmbedding.fitcCs|||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. )rrrr=r=r> fit_transform>s z$LocallyLinearEmbedding.fit_transformcCst|t||dd}|jj||jdd}t||jj||jd}t |j d|j f}t |j dD]}t |j||j||||<q2|S)a Transform new points into embedding space. Parameters ---------- X : array-like of shape (n_samples, n_features) Training set. Returns ------- X_new : ndarray of shape (n_samples, n_components) Returns the instance itself. Notes ----- Because of scaling performed by this method, it is discouraged to use it together with methods that are not scale-invariant (like SVMs). F)resetrurCr)rrrrHr3r?rFr1r%r&r$rr|r)rr*)rr.r7weightsX_newr6r=r=r> transformRs"z LocallyLinearEmbedding.transformr)__name__ __module__ __qualname____doc__rrrrrdict__annotations__rrrrErrr=r=r=r>rZsF        r)r)rN)r rOrPrQN).rnumbersrrnumpyr% scipy.linalgrrrr scipy.sparserr r scipy.sparse.linalgr baser rrrrrrutilsrr utils._arpackrutils._param_validationrrr utils.extmathrutils.validationrrrr?rNrlrrrr=r=r=r>sz      6+ Q y