o tBhnm @sdZddlZddlmZmZmZmZddlm Z m Z ddl m Z ddl mZmZmZmZddlmZmZdd lmZdd lmZdd lmZdd lmZdd lmZd"ddZd#ddZ d$ddZ dddddddddd ddZ!Gd d!d!eeeeZ"dS)%zLocally Linear EmbeddingN)eighsvdqrsolve)eye csr_matrix)eigsh) BaseEstimatorTransformerMixin_UnstableArchMixin _ClassNamePrefixFeaturesOutMixin)check_random_state check_array)_init_arpack_v0) stable_cumsum)check_is_fitted) FLOAT_DTYPES)NearestNeighborsMbP?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. dtyperNT)sym_pos)rrintshapenpemptyrones enumeratedotTtraceflatrsum)XYindicesreg n_samples n_neighborsBviindACGr"Rwr4w/var/www/html/riverr-enterprise-integrations-main/venv/lib/python3.10/site-packages/sklearn/manifold/_locally_linear.pybarycenter_weightss&       r6c 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 rr*n_jobsF)return_distanceNr(r)r) rfit_fit_Xn_samples_fit_ kneighborsr6rarangerravel) r%r*r(r8knnr)r.dataindptrr4r4r5barycenter_kneighbors_graphPs!rDrarpackư>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 rEdenseg)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.NtoarrayrT)eigvals overwrite_azUnrecognized eigen_solver '%s') rrr RuntimeError ValueErrorrr$hasattrrPrargsortabs) Mkk_skip eigen_solverrMmax_iter random_staterO eigen_values eigen_vectorseindexr4r4r5 null_spacezs<*&    rbrHstandard-C6?-q=) r(r[rMr\method hessian_tol modified_tolr]r8c ; Cs|dvr td||dvrtd|t|d| d} | || j}|j\} }||kr1td|| kr=td| |f|d krEtd |d k}|d krt| ||| d }|rkt|jd|ji|}|j| }n|j||j| }|j dd|jd dd7<n|dkr||dd}|||krtd| j ||ddd}|ddddf}t j|d||ft jd}d|ddd f<t j| | ft jd}||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}q)t|\}}|dd|ddf}|d }d|t t||k<||}t ||||\} }!|| |!ft ||j7<q|rt|}n|dkr||krtd| j ||ddd}|ddddf}t | ||f}"t||}#t | |#g}$||k}|rt| D]}|||||}%t|%dd\|"|<|$|<}&q|$dC}$n5t| D]0}|||||}%t |%|%j}'t|'\}(})|(ddd|$|<|)dddddf|"|<qd|$d}t |"d ddt |}*|*ddd|#f|$|dddf<|*dd|#df|dddf<t | |f}+t| D]}t |"||*||+|<q|+|+ddddf}+|$dd|dfd|$ddd|fd},t |,}-t j| t d}.t!|$d}/|/ddddf|/ddddfd}0t| D]}t "|0|dddf|-|.|<q|.||#7}.t j| | ft jd}t| D]}|.|}1|"|dd||1df}2t j#$|2d t %|1}3t &|1|3t |2jt |}4t j#$|4}5|5| krJ|4d 9}4n|4|5}4|2dt 't |2|4|4d|3|+|dddf}6t ||||\} }!|| |!ft |6|6j7<|6d}7||||f|78<||||f|78<|||f|17<q |rt|}n|dkrc| j ||ddd}|ddddf}t | | f}||k}t| D]}|||}8|8|8d 8}8|rt|8ddd }9nt |8|8j}t|ddddddf}9t ||df}|9ddd|f|ddddf<dt %||ddd f<t ||j}:t ||||\} }!|| |!f|:8<|||||fd7<qt(||d|||| dS)aGPerform 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 : array-like, 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. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.382 .. [4] Zhang, Z. & Zha, H. Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. Journal of Shanghai Univ. 8:406 (2004) )rHrErKzunrecognized eigen_solver '%s')rchessianmodifiedltsazunrecognized method '%s'rr7z>output dimension must be less than or equal to input dimensionzHExpected n_neighbors <= n_samples, but n_samples = %d, n_neighbors = %drzn_neighbors must be positiverKrc)r*r(r8formatNrir z^for method='hessian', n_neighbors must be greater than [n_components * (n_components + 3) / 2]Fr*r9r) full_matricesrjz1modified LLE requires n_neighbors >= n_componentsTrrkg?)rZr[rMr\r]))rTrr;r<rrDrrlr!tocsrrPr#r>rrfloat64zerosrangemeanrr rrr$whererWmeshgridrmin transposermedianrr searchsortedlinalgnormsqrtfullouterrb);r%r* n_componentsr(r[rMr\rfrgrhr]r8nbrsNd_inM_sparseWrXdp neighborsYiuse_svdr-GiUCijrYQr2r3Snbrs_xnbrs_yVnevevalsX_nbrs_C_nbrsevivitmpw_regrhoetas_range evals_cumsum eta_ranges_iVialpha_ihnorm_hWiWi_sum1Xir,GiGiTr4r4r5locally_linear_embeddings4n    &     ( D           ,( 4  , "      6     $ rc @sXeZdZdZdddddddd d dd d d d dZddZdddZdddZddZd S)LocallyLinearEmbeddingafLocally 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. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.382 .. [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 rrHrFrGrcrdreN) r*rr(r[rMr\rfrgrhneighbors_algorithmr]r8c CsL||_||_||_||_||_||_||_||_| |_| |_ | |_ | |_ dSN) r*rr(r[rMr\rfrgrhr]rr8) selfr*rr(r[rMr\rfrgrhrr]r8r4r4r5__init__s zLocallyLinearEmbedding.__init__cCst|j|j|jd|_t|j}|j|td}|j |t |j|j|j |j |j |j|j|j|j||j|jd \|_|_|jjd|_dS)N)r* algorithmr8r) r%r*rr[rMr\rfrgrhr]r(r8r)rr*rr8nbrs_rr]_validate_datafloatr;rrr[rMr\rfrgrhr( embedding_reconstruction_error_r_n_features_out)rr%r]r4r4r5_fit_transforms.  z%LocallyLinearEmbedding._fit_transformcCs|||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%yr4r4r5r;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. )rrrr4r4r5 fit_transforms z$LocallyLinearEmbedding.fit_transformcCst||j|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)resetrmr:r)rrrr>r*r6r<r(rrrrrsr rr!)rr%r.weightsX_newr-r4r4r5 transform s"z LocallyLinearEmbedding.transformr) __name__ __module__ __qualname____doc__rrr;rrr4r4r4r5r&s(    r)r)rN)rrErFrGN)#rnumpyr scipy.linalgrrrr scipy.sparserrscipy.sparse.linalgrbaser r r r utilsrr utils._arpackr utils.extmathrutils.validationrrrrr6rDrbrrr4r4r4r5sD        6+ Q  b