ó ‡ˆ\c @sCdZddlZddlmZmZmZmZddlm Z m Z ddl m Z ddl mZmZmZddlmZmZdd lmZdd lmZdd lmZdd lmZd d„Zd ed„Zdddded„Zd ddddddeed„ Zdeeefd„ƒYZ dS(sLocally Linear EmbeddingiÿÿÿÿN(teightsvdtqrtsolve(teyet csr_matrix(teigshi(t BaseEstimatortTransformerMixint_UnstableArchMixin(tcheck_random_statet check_array(t stable_cumsum(tcheck_is_fitted(t FLOAT_DTYPES(tNearestNeighborsgü©ñÒMbP?cCs^t|dtƒ}t|dtdtƒ}|jd|jd}}tj||fd|jƒ}tj|d|jƒ}xÜt|j dddƒƒD]¿\}}|j ||} tj | | j ƒ} tj | ƒ} | dkrñ|| } n|} | j dd|jdd…c| 7 n_dim Returns ------- B : array-like, shape (n_samples, n_neighbors) Notes ----- See developers note for more information. tdtypetallow_ndiiiNtsym_pos(R RtTruetshapetnptemptyRtonest enumeratet transposetTtdotttracetflatRtsum(tXtZtregt n_samplest n_neighborstBtvtitAtCtGRtRtw((s>lib/python2.7/site-packages/sklearn/manifold/locally_linear.pytbarycenter_weightss (  ''c CsÁt|dd|ƒj|ƒ}|j}|jd}|j|dtƒdd…dd…f}t|||d|ƒ}tjd||d|ƒ}t |j ƒ|j ƒ|fd||fƒS(s4Computes 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, optional Amount of regularization when solving the least-squares problem. Only relevant if mode='barycenter'. If None, use the default. n_jobs : int or None, optional (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 itn_jobsitreturn_distanceNR!R( Rtfitt_fit_XRt kneighborstFalseR,RtarangeRtravel( RR#R!R-tknnR"tindtdatatindptr((s>lib/python2.7/site-packages/sklearn/manifold/locally_linear.pytbarycenter_kneighbors_graphCs!  +itarpackgíµ ÷Æ°>idc Cs¢|dkrA|jddkr8||dkr8d}qAd}n|dkrýt|ƒ}|jdd|jdƒ}y5t|||d d d |d |d |ƒ\}} Wn#tk rÏ} td| ƒ‚nX| dd…|d…ftj||ƒfS|dkrŽt|dƒr'|j ƒ}nt |d|||dfdt ƒ\}} tj tj |ƒƒ} | dd…| ftj|ƒfStd|ƒ‚dS(sŽ 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 : integer Number of eigenvalues/vectors to return k_skip : integer, optional Number of low eigenvalues to skip. eigen_solver : string, {'auto', 'arpack', 'dense'} 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, optional Tolerance for 'arpack' method. Not used if eigen_solver=='dense'. max_iter : int Maximum number of iterations for 'arpack' method. Not used if eigen_solver=='dense' random_state : int, RandomState instance or None, optional (default=None) If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Used when ``solver`` == 'arpack'. tautoiiÈi R:tdenseiÿÿÿÿitsigmagttoltmaxitertv0sðError in determining null-space with ARPACK. Error message: '%s'. Note that method='arpack' can fail when the weight matrix is singular or otherwise ill-behaved. method='dense' is recommended. See online documentation for more information.Nttoarrayteigvalst overwrite_asUnrecognized eigen_solver '%s'(RR tuniformRt RuntimeErrort ValueErrorRRthasattrRARRtargsorttabs( tMtktk_skipt eigen_solverR>tmax_itert random_stateR@t eigen_valuest eigen_vectorstmsgtindex((s>lib/python2.7/site-packages/sklearn/manifold/locally_linear.pyt null_spacens.+ #     - )#R;tstandardg-Cëâ6?gê-™—q=c ; Cs |d"krtd|ƒ‚n|d#kr>td |ƒ‚ntd |d d | ƒ} | j|ƒ| j}|j\} }||kr—td ƒ‚n|| kr¼td| |fƒ‚n|dkr×tdƒ‚n|dk}|dkrt| d |d|d | ƒ}|rEtd|j|jŒ|}|j|j ƒ}qó |j||j|j ƒ}|j dd|jdd …cd 7tj||jƒ}t|ƒd dd…ddd…f}|dd…d|…f|dd…d d |…ftj|8|8jƒ}t|ƒd dd…ddd…f}9tj||d fƒ}|9dd…d|…f|dd…d d…f`. 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 : integer number of neighbors to consider for each point. n_components : integer number of coordinates for the manifold. reg : float regularization constant, multiplies the trace of the local covariance matrix of the distances. eigen_solver : string, {'auto', 'arpack', 'dense'} 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, optional Tolerance for 'arpack' method Not used if eigen_solver=='dense'. max_iter : integer maximum number of iterations for the arpack solver. method : {'standard', 'hessian', 'modified', 'ltsa'} 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, optional Tolerance for Hessian eigenmapping method. Only used if method == 'hessian' modified_tol : float, optional Tolerance for modified LLE method. Only used if method == 'modified' random_state : int, RandomState instance or None, optional (default=None) If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Used when ``solver`` == 'arpack'. n_jobs : int or None, optional (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)` R;R:R<sunrecognized eigen_solver '%s'RUthessiantmodifiedtltsasunrecognized method '%s'R#iR-s>output dimension must be less than or equal to input dimensionsHExpected n_neighbors <= n_samples, but n_samples = %d, n_neighbors = %disn_neighbors must be positiveR!tformatNis^for method='hessian', n_neighbors must be greater than [n_components * (n_components + 3) / 2]R.Rt full_matricesiÿÿÿÿs1modified LLE requires n_neighbors >= n_componentsgü©ñÒMbP?gð?RLRMR>RNRO(R;R:R<(RURVRWRX(,RFRR/R0RR9RRYRttocsrRARR1R2RRtfloat64tzerostrangetmeanRRRRRtwhereRItmeshgridRtminRRRtNonetmediantintR t searchsortedtlinalgtnormtsqrttfulltouterRT(;RR#t n_componentsR!RMR>RNtmethodt hessian_tolt modified_tolROR-tnbrstNtd_intM_sparsetWRJtdpt neighborstYituse_svdR&tGitUtCitjRKtQR*R+tStnbrs_xtnbrs_ytVtnevtevalstX_nbrst_tC_nbrstevitvittmptw_regtrhotetats_ranget evals_cumsumt eta_rangets_itVitalpha_ithtnorm_htWitWi_sum1tXiR%tGiGiT((s>lib/python2.7/site-packages/sklearn/manifold/locally_linear.pytlocally_linear_embedding¼sd         *  & )6 ;   )      '*62"#H:- #(.   #" %   )2# %tLocallyLinearEmbeddingc BseeZdZddddddddd dddd „ Zd „Zdd „Zdd „Zd„ZRS(soLocally Linear Embedding Read more in the :ref:`User Guide `. Parameters ---------- n_neighbors : integer number of neighbors to consider for each point. n_components : integer number of coordinates for the manifold reg : float regularization constant, multiplies the trace of the local covariance matrix of the distances. eigen_solver : string, {'auto', 'arpack', 'dense'} 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, optional Tolerance for 'arpack' method Not used if eigen_solver=='dense'. max_iter : integer maximum number of iterations for the arpack solver. Not used if eigen_solver=='dense'. method : string ('standard', 'hessian', 'modified' or 'ltsa') 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, optional Tolerance for Hessian eigenmapping method. Only used if ``method == 'hessian'`` modified_tol : float, optional Tolerance for modified LLE method. Only used if ``method == 'modified'`` neighbors_algorithm : string ['auto'|'brute'|'kd_tree'|'ball_tree'] algorithm to use for nearest neighbors search, passed to neighbors.NearestNeighbors instance random_state : int, RandomState instance or None, optional (default=None) If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Used when ``eigen_solver`` == 'arpack'. n_jobs : int or None, optional (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_` nbrs_ : NearestNeighbors object Stores nearest neighbors instance, including BallTree or KDtree if applicable. 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) 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)` iigü©ñÒMbP?R;gíµ ÷Æ°>idRUg-Cëâ6?gê-™—q=c Csp||_||_||_||_||_||_||_||_| |_| |_ | |_ | |_ dS(N( R#RlR!RMR>RNRmRnRoROtneighbors_algorithmR-( tselfR#RlR!RMR>RNRmRnRoR›ROR-((s>lib/python2.7/site-packages/sklearn/manifold/locally_linear.pyt__init__|s           cCsÎt|jd|jd|jƒ|_t|jƒ}t|dtƒ}|jj |ƒt |j|j|j d|j d|j d|jd|jd|jd |jd |d |jd|jƒ \|_|_dS( Nt algorithmR-RRMR>RNRmRnRoROR!(RR#R›R-tnbrs_R ROR tfloatR/R™RlRMR>RNRmRnRoR!t embedding_treconstruction_error_(RœRRO((s>lib/python2.7/site-packages/sklearn/manifold/locally_linear.pyt_fit_transforms  cCs|j|ƒ|S(s Compute the embedding vectors for data X Parameters ---------- X : array-like of shape [n_samples, n_features] training set. y : Ignored Returns ------- self : returns an instance of self. (R£(RœRty((s>lib/python2.7/site-packages/sklearn/manifold/locally_linear.pyR/s cCs|j|ƒ|jS(s-Compute the embedding vectors for data X and transform X. Parameters ---------- X : array-like of shape [n_samples, n_features] training set. y : Ignored Returns ------- X_new : array-like, shape (n_samples, n_components) (R£R¡(RœRR¤((s>lib/python2.7/site-packages/sklearn/manifold/locally_linear.pyt fit_transform®s cCsÅt|dƒt|ƒ}|jj|d|jdtƒ}t||jj|d|jƒ}t j |j d|j fƒ}xCt |j dƒD].}t j|j||j||ƒ||lib/python2.7/site-packages/sklearn/manifold/locally_linear.pyt transform¿s    ,N( t__name__t __module__t__doc__RcRR£R/R¥R¨(((s>lib/python2.7/site-packages/sklearn/manifold/locally_linear.pyRš sq      (!R«tnumpyRt scipy.linalgRRRRt scipy.sparseRRtscipy.sparse.linalgRtbaseRRR tutilsR R t utils.extmathR tutils.validationR RRvRR,RcR9RTR™Rš(((s>lib/python2.7/site-packages/sklearn/manifold/locally_linear.pyts( " /+  N  ÿK