B ¦ ˆ\\ã@srdZddlZddlmZmZddlmZmZddl m Z ddl m Z ddl mZdd lmZGd d „d eeƒZdS) zIsomap for manifold learningéNé)Ú BaseEstimatorÚTransformerMixin)ÚNearestNeighborsÚkneighbors_graph)Ú check_array)Úgraph_shortest_path)Ú KernelPCA)ÚKernelCentererc@sFeZdZdZddd„Zd d „Zd d „Zdd d„Zddd„Zdd„Z dS)ÚIsomapaš 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) érÚautorNc Cs4||_||_||_||_||_||_||_||_dS)N)Ú n_neighborsÚ n_componentsÚ eigen_solverÚtolÚmax_iterÚ path_methodÚneighbors_algorithmÚn_jobs) Úselfrrrrrrrr©rú6lib/python3.7/site-packages/sklearn/manifold/isomap.pyÚ__init__hszIsomap.__init__cCs¤t|dd}t|j|j|jd|_|j |¡|jj|_t |j d|j |j |j |jd|_t|j|jd|jd}t||jdd |_|jd }|d 9}|j |¡|_dS) NZcsr)Z accept_sparse)rÚ algorithmrZ precomputed)rZkernelrrrrZdistance)ÚmoderF)ÚmethodZdirectedrgà¿)rrrrrÚnbrs_ÚfitZ_fit_XÚtraining_data_r rrrrÚ kernel_pca_rrrÚ dist_matrix_Ú fit_transformÚ embedding_)rÚXZkngÚGrrrÚ_fit_transformts&         zIsomap._fit_transformcCsNd|jd}tƒ |¡}|jj}t t |d¡t |d¡¡|jdS)aCompute 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¿rr) r!r r"r Zlambdas_ÚnpZsqrtÚsumÚshape)rr%ZG_centerZevalsrrrÚreconstruction_errorŒs zIsomap.reconstruction_errorcCs| |¡|S)a¤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$Úyrrrr¤s z Isomap.fitcCs| |¡|jS)a…Fit the model from data in X and transform X. Parameters ---------- X : {array-like, sparse matrix, BallTree, KDTree} Training vector, where n_samples in the number of samples and n_features is the number of features. y : Ignored Returns ------- X_new : array-like, shape (n_samples, n_components) )r&r#)rr$r+rrrr"·s zIsomap.fit_transformcCsšt|ƒ}|jj|dd\}}t |jd|jjdf¡}xDt|jdƒD]2}t |j ||||dd…dfd¡||<qHW|dC}|d9}|j   |¡S)a¸Transform X. This is implemented by linking the points X into the graph of geodesic distances of the training data. First the `n_neighbors` nearest neighbors of X are found in the training data, and from these the shortest geodesic distances from each point in X to each point in the training data are computed in order to construct the kernel. The embedding of X is the projection of this kernel onto the embedding vectors of the training set. Parameters ---------- X : array-like, shape (n_samples, n_features) Returns ------- X_new : array-like, shape (n_samples, n_components) T)Zreturn_distancerNrgà¿) rrZ kneighborsr'Zzerosr)rÚrangeÚminr!r Ú transform)rr$Z distancesÚindicesZG_XÚirrrr.És"zIsomap.transform)r rr rNr r N)N)N) Ú__name__Ú __module__Ú __qualname__Ú__doc__rr&r*rr"r.rrrrr sW   r )r4Znumpyr'ÚbaserrZ neighborsrrZutilsrZ utils.graphrZ decompositionr Z preprocessingr r rrrrÚs