ó ‡ˆ\c@s›dZddlZddlmZmZddlmZmZddl m Z ddl m Z ddl mZdd lmZd eefd „ƒYZdS( sIsomap for manifold learningiÿÿÿÿNi(t BaseEstimatortTransformerMixin(tNearestNeighborstkneighbors_graph(t check_array(tgraph_shortest_path(t KernelPCA(tKernelCenterertIsomapc BsbeZdZddddd ddd d„Zd„Zd„Zd d„Zd d „Zd „Z RS( sš Isomap Embedding Non-linear dimensionality reduction through Isometric Mapping 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 eigen_solver : ['auto'|'arpack'|'dense'] 'auto' : Attempt to choose the most efficient solver for the given problem. 'arpack' : Use Arnoldi decomposition to find the eigenvalues and eigenvectors. 'dense' : Use a direct solver (i.e. LAPACK) for the eigenvalue decomposition. tol : float Convergence tolerance passed to arpack or lobpcg. not used if eigen_solver == 'dense'. max_iter : integer Maximum number of iterations for the arpack solver. not used if eigen_solver == 'dense'. path_method : string ['auto'|'FW'|'D'] Method to use in finding shortest path. 'auto' : attempt to choose the best algorithm automatically. 'FW' : Floyd-Warshall algorithm. 'D' : Dijkstra's algorithm. neighbors_algorithm : string ['auto'|'brute'|'kd_tree'|'ball_tree'] Algorithm to use for nearest neighbors search, passed to neighbors.NearestNeighbors instance. 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. kernel_pca_ : object `KernelPCA` object used to implement the embedding. training_data_ : array-like, shape (n_samples, n_features) Stores the training data. nbrs_ : sklearn.neighbors.NearestNeighbors instance Stores nearest neighbors instance, including BallTree or KDtree if applicable. dist_matrix_ : array-like, shape (n_samples, n_samples) Stores the geodesic distance matrix of training data. Examples -------- >>> from sklearn.datasets import load_digits >>> from sklearn.manifold import Isomap >>> X, _ = load_digits(return_X_y=True) >>> X.shape (1797, 64) >>> embedding = Isomap(n_components=2) >>> X_transformed = embedding.fit_transform(X[:100]) >>> X_transformed.shape (100, 2) References ---------- .. [1] Tenenbaum, J.B.; De Silva, V.; & Langford, J.C. A global geometric framework for nonlinear dimensionality reduction. Science 290 (5500) iitautoic CsL||_||_||_||_||_||_||_||_dS(N(t n_neighborst n_componentst eigen_solverttoltmax_itert path_methodtneighbors_algorithmtn_jobs( tselfR R R R RRRR((s6lib/python2.7/site-packages/sklearn/manifold/isomap.pyt__init__hs       c Cs t|ddƒ}td|jd|jd|jƒ|_|jj|ƒ|jj|_t d|j ddd |j d |j d |j d|jƒ|_t|j|jd d d|jƒ}t|d|jdtƒ|_|jd}|d9}|jj|ƒ|_dS(Nt accept_sparsetcsrR t algorithmRR tkernelt precomputedR R Rtmodetdistancetmethodtdirectedigà¿(RRR RRtnbrs_tfitt_fit_Xttraining_data_RR R R Rt kernel_pca_RRRtFalset dist_matrix_t fit_transformt embedding_(RtXtkngtG((s6lib/python2.7/site-packages/sklearn/manifold/isomap.pyt_fit_transformts&       cCsed|jd}tƒj|ƒ}|jj}tjtj|dƒtj|dƒƒ|jdS(sCompute the reconstruction error for the embedding. Returns ------- reconstruction_error : float Notes ------- The cost function of an isomap embedding is ``E = frobenius_norm[K(D) - K(D_fit)] / n_samples`` Where D is the matrix of distances for the input data X, D_fit is the matrix of distances for the output embedding X_fit, and K is the isomap kernel: ``K(D) = -0.5 * (I - 1/n_samples) * D^2 * (I - 1/n_samples)`` gà¿ii( R#RR$R!tlambdas_tnptsqrttsumtshape(RR(tG_centertevals((s6lib/python2.7/site-packages/sklearn/manifold/isomap.pytreconstruction_errorŒs cCs|j|ƒ|S(s¤Compute the embedding vectors for data X Parameters ---------- X : {array-like, sparse matrix, BallTree, KDTree, NearestNeighbors} Sample data, shape = (n_samples, n_features), in the form of a numpy array, precomputed tree, or NearestNeighbors object. y : Ignored Returns ------- self : returns an instance of self. (R)(RR&ty((s6lib/python2.7/site-packages/sklearn/manifold/isomap.pyR¤s cCs|j|ƒ|jS(s…Fit the model from data in X and transform X. Parameters ---------- X : {array-like, sparse matrix, BallTree, KDTree} Training vector, where n_samples in the number of samples and n_features is the number of features. y : Ignored Returns ------- X_new : array-like, shape (n_samples, n_components) (R)R%(RR&R2((s6lib/python2.7/site-packages/sklearn/manifold/isomap.pyR$·s cCsËt|ƒ}|jj|dtƒ\}}tj|jd|jjdfƒ}xTt|jdƒD]?}tj |j ||||dd…dfdƒ||s