Mpjx SrSSKJrJr SSKrSSKJrJrJ r J r SSK J r J r SSKJr SSKJrJrJrJrJr SSKJr SS KJrJr SS KJr SS KJrJrJ r SS K!J"r" SS K#J$r$J%r% SSK&J'r'J(r(J)r) S(Sjr*S)Sjr+S*Sjr,SSSSSSSSSS. Sjr-\ "S\/\"\SSSS9/\"\SSSS9/\"\SSSS9/\"1Sk5/\"\SSSS9/\"\SSSS9/\"1S k5/\"\SSSS9/\"\SSSS9/S!/S\/S". S#S$9SSSSSSSSSS. S%j5r."S&S'\\\\5r/g)+zLocally Linear Embedding)IntegralRealN)eighqrsolvesvd) csr_array lil_array)eigsh) BaseEstimatorClassNamePrefixFeaturesOutMixinTransformerMixin _fit_context_UnstableArchMixin)NearestNeighbors) check_arraycheck_random_state)_init_arpack_v0)Interval StrOptionsvalidate_params)_align_api_if_sparse)SCIPY_VERSION_BELOW_1_15_sparse_eye_array) FLOAT_DTYPEScheck_is_fitted validate_dataMbP?cl[U[S9n[U[S9n[U[S9nURupEURSU:Xde[R "XE4UR S9n[R"XPR S9n[U5HupXn XU- n [R"XR5n [R"U 5n U S:aX=-nOUnU RSSUS-2==U- ss'[XSS9nU[R"U5- XhSS24'M U$)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/pdf-tiff/venv/lib/python3.13/site-packages/sklearn/manifold/_locally_linear.pybarycenter_weightsr@s6 A\*AA\*A'-G$]]I 771: "" " ))9A  77+AG$ F !H FF1ccN  19 AA !+/!"a'" ! 'bffQi-Q$% HcT[US-US9RU5nURnURnUR USS9SS2SS24n[ XXbS9n[ R"SXQ-S-U5n[UR5UR5U4XU4S9n [U 5$) aComputes 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 ravelr) r0r5r3rDknnr4r9dataindptrcsrs r?barycenter_kneighbors_graphrRSsB {Qv F J J1 MC A""I ..E. 21ab5 9C aC 1D YYq)1A5{ CF TZZ\399;7 ?U VC  $$rAr"ư>dc ZUS:Xa URSS:a X-S:aSnOSnUS:XaN[URSU5n[XU-SXEUS9upU S S 2US 24[ R "XS 54$US:Xa}[US 5(aUR5n[XX-S - 4S S9up[ R"[ R"U55n U S S 2U 4[ R "U54$[ SU-5e![an [ S U -5U eS n A ff=f)a 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_solverr\max_iter random_stater^ eigen_values eigen_vectorseindexs r? null_spacerq~sGTv 771:  R#L"Lx QWWQZ 6 */v:Sc+ 'LQZ("&&g1F*GGG  1i  A&*  Q7T' #  266,/0QX&|(<<<9LHII' 69: :    sD D*D%%D*rVstandard-C6?-q=) r3rjr\rkmethod hessian_tol modified_tolrlrDc [US-U S9n U RU5 U RnURupX.:a [ S5eX:a[ SX4-5eUS:gnU(a[ O[ RnUS:Xa[XX;S9nU(a>[URURURS.6U- nURU-nGOURU-UR- U- R5nURSSURS S-2==S- ss'GOyUS :XGa X"S--S -nXU-::a [ S 5eU RXS-S S9nUSS2SS24n[ R "USU-U-4[ R"S9nSUSS2S 4'U"X4[ R"S9nX:n[%U 5GHrnUUUnUUR'S 5-nU(a[)US S9S nO9[ R*"UUR5n[-U5SSS2SSS24nUSS2SU24USS2SSU-24'SU-n[%U5H4nUSS2UUS-24USS2UU24-USS2UUU-U- 24'UUU- - nM6 [/U5unnUSS2US-S24nUR1S 5n SU [ R2"[5U 5U:5'UU -n[ R6"UUUU5un!n"UU!U"4==[ R*"UUR5- ss'GMu GOeUS:XGaX:a [ S5eU RXS-S S9nUSS2SS24n[ R"XU45n#[9X5n$[ R"U U$/5n%X:nU(a:[%U 5H%nUUUUU- n&[)U&SS9uU#U'U%U'n'M' U%S -n%Oi[%U 5HZnUUUUU- n&[ R*"U&U&R5n([-U(5un)n*U)SSS2U%U'U*SS2SSS24U#U'M\ SU%R1S5-n[ R*"U#R;S S S5[ R<"U55n+U+SS2SU$24==U%USS2S4--ss'U+SS2U$S24==USS2S4-ss'[ R"X45n,[%U 5H#n[ R*"U#UU+U5U,U'M% U,U,R1S5SS2S4-n,U%SS2US24R1S5U%SS2SU24R1S5- n-[ R>"U-5n.[ R"U [@S9n/[ RB"U%S5n0U0SS2SS24U0SS2SS24- S- n1[%U 5H%n[ RD"U1USSS24U.5U/U'M' U/UU$- - n/U"X4[ R"S9n[%U 5GHnU/Un2U#USS2UU2- S24n3[ RFRIU3R1S 55[ RJ"U25- n4[ RL"U2U45[ R*"U3R[ R<"U55- n5[ RFRIU55n6U6U :aU5S -n5OU5U6-n5U3S [ RN"[ R*"U3U55U55-- SU4- U,USS2S4--n7[ R6"UUUU5un!n"UU!U"4==[ R*"U7U7R5- ss'U7R1S5n8[P(a'UU/UU4==U8-ss'UUUU/4==U8-ss'O$UUUU4==U8-ss'UUUU4==U8-ss'UUU4==U2- ss'GM GOUS:XGa{U RXS-S S9nUSS2SS24nU"X4[ R"S9nX:n[%U 5GH3nUUUn9U9U9R'S 5-n9U(a[)U9SS9S n:O9[ R*"U9U9R5n[-U5SSS2SSS24n:[ R"XS-45nU:SS2SU24USS2SS24'S[ RJ"U5- USS2S 4'[ R*"UUR5n;[ R6"UUUU5un!n"UU!U"4==U;-ss'UUUUU4==[ R<"US9- ss'GM6 U(a[SWRU55n[WWUSUUUU S9$)Nr"rCz>output dimension must be less than or equal to input dimensionzFExpected n_neighbors < n_samples, but n_samples = %d, n_neighbors = %drZrr)r5r3rD)formatr!rhessianz^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)rirjr\rkrl),rrHrIr&rcr r'zerosrRrryr!r,r_r.rKr(float64rangemeanrr+rrr/whererfmeshgridmin transposer)medianr%cumsum searchsortedlinalgnormsqrtfullouterrrtocsrrq)Snbrs_xnbrs_yVnevevalsX_nbrs_C_nbrsevivitmpw_regrhoetas_range evals_cumsum eta_ranges_iVialpha_ihnorm_hWiWi_sum1Xir7GiGiTs< r?_locally_linear_embeddingrs   a GDHHQK AggGA L   T   w&H+3i  ' s  !177188177KaOAaAq133"++-A FF$aggaj1n$ % * % 9  A- .! 3 + +:  OO ?E$ ae$ XX{A $4r$9:"** M1a4 #QF"** =$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: :   %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(yy*  BC(<3B3+??!C qA1dd7);SAGAJ;$$ $QF"** =qA!*C1as*,,-BiinnRVVAY/"''#,>G W%rttRWW[5I(JJAYY^^A&F $QV a"((266"a=!444G uQPQSWZGX7XXB [[1y|DNFF ffn BDD!1 1 ffQiG''1#y|#$/$)A,#$/$!Yq\/"g-")A,/"g-" adGsNGQT 6 OO ?E$ ae$ #QF"** =$qA9Q<B "''!* B$/2VVB%HQK4R4(;q(89:B!]l]*+Bq!"uIRWW[11Bq!tHFF2rtt$E[[1y|DNFF ffn  &  ilIaL( )RWW;-G G )),  +  ! ! rAz array-likeleftclosed>rVrZrY>rrzrrrrl r0r5rr3rjr\rkrurvrwrlrDTprefer_skip_nested_validationc *[UUUUUUUUUU U U S9 $)a_Perform 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 % ! ! !!  rAcV\rSrSr%Sr\"\SSSS9/\"\SSSS9/\"\SSSS9/\"1Sk5/\"\SSSS9/\"\SSSS9/\"1S k5/\"\SSSS9/\"\SSSS9/\"1S k5/S /S\/S . r \ \ S 'SSSSSSSSSSSSS . Sjr Sr \"SS9SSj5r\"SS9SSj5rSrSrg) LocallyLinearEmbeddingi`aLocally 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>rVrZrY>rrzrrr>rVbrutekd_tree ball_treerl) r5rr3rjr\rkrurvrwneighbors_algorithmrlrD_parameter_constraintsr{rrVrSrTrrrsrtc XlX lX0lX@lXPlX`lXplXlXlXl Xl Xl gN) r5rr3rjr\rkrurvrwrlrrD) selfr5rr3rjr\rkrurvrwrrlrDs r?__init__LocallyLinearEmbedding.__init__sG '((  &((#6  rAc6[URURURS9Ul[ UR 5n[X[S9nURRU5 [URURURURURURURUR UR"UUR$URS9 uUlUlUR&R*SUlg)N)r5 algorithmrDr ) r0r5rrjr\rkrurvrwrlr3rDr")rr5rrDnbrs_rrlrfloatrHrrrjr\rkrurvrwr3 embedding_reconstruction_error_r&_n_features_out)rr0rls r?_fit_transform%LocallyLinearEmbedding._fit_transforms%((..;;  *$*;*;< $ / q6Ojj((****]];;((**%;; 7 33 $44Q7rATrc(URU5 U$)a!Compute 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?rHLocallyLinearEmbedding.fit0s" A rAc<URU5 UR$)aDCompute the embedding vectors for data X and transform X. Parameters ---------- X : array-like of shape (n_samples, n_features) Training set. y : Ignored Not used, present here for API consistency by convention. Returns ------- X_new : array-like, shape (n_samples, n_components) Returns the instance itself. )rrrs r? fit_transform$LocallyLinearEmbedding.fit_transformDs" ArAc[U5 [XSS9nURRXRSS9n[ XRR X RS9n[R"URSUR45n[URS5H7n[R"URX%RX55XE'M9 U$)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)resetr|rFr)rrrrKr5r@rIr3r'r(r&rrr+rr,)rr0r9weightsX_newr8s r? transform LocallyLinearEmbedding.transformXs&  $ /jj## ++U$ %Q (9(93HHM!''!*d&7&789qwwqz"Avvdoocf577DEH# rA)rrjrrvrkrurwrrDr5rrrlrr3r\r)__name__ __module__ __qualname____firstlineno____doc__rrrrrdict__annotations__rrrrHrr__static_attributes__rAr?rr`s* BJ!1d6BC!(AtFCDq$v67#$?@Aq$v67h4?@IJK q$v>?!$4?@ *+T UV'(" $D $  ":8456&56&rAr)r)rN)r"rYrSrTN)0rnumbersrrnumpyr' scipy.linalgrrrr scipy.sparser r scipy.sparse.linalgr sklearn.baser r rrrsklearn.neighborsr sklearn.utilsrrsklearn.utils._arpackrsklearn.utils._param_validationrrrsklearn.utils._sparsersklearn.utils.fixesrrsklearn.utils.validationrrrr@rRrqrrrrrAr?rs #---%/91QQ6KQQ3 l(%XQUIJb    yx, - 1d6BC!(AtFCDq$v67#$?@Aq$v67h4?@IJK q$v>?!$4?@'(" #',    F#"FRU# UrA