708 lines
26 KiB
Python
708 lines
26 KiB
Python
"""Locally Linear Embedding"""
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# Author: Fabian Pedregosa -- <fabian.pedregosa@inria.fr>
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# Jake Vanderplas -- <vanderplas@astro.washington.edu>
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# License: BSD 3 clause (C) INRIA 2011
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import numpy as np
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from scipy.linalg import eigh, svd, qr, solve
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from scipy.sparse import eye, csr_matrix
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from scipy.sparse.linalg import eigsh
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from ..base import BaseEstimator, TransformerMixin
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from ..utils import check_random_state, check_array
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from ..utils.extmath import stable_cumsum
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from ..utils.validation import check_is_fitted
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from ..utils.validation import FLOAT_DTYPES
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from ..neighbors import NearestNeighbors
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def barycenter_weights(X, Z, reg=1e-3):
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"""Compute barycenter weights of X from Y along the first axis
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We estimate the weights to assign to each point in Y[i] to recover
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the point X[i]. The barycenter weights sum to 1.
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Parameters
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----------
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X : array-like, shape (n_samples, n_dim)
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Z : array-like, shape (n_samples, n_neighbors, n_dim)
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reg : float, optional
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amount of regularization to add for the problem to be
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well-posed in the case of n_neighbors > n_dim
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Returns
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-------
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B : array-like, shape (n_samples, n_neighbors)
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Notes
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-----
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See developers note for more information.
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"""
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X = check_array(X, dtype=FLOAT_DTYPES)
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Z = check_array(Z, dtype=FLOAT_DTYPES, allow_nd=True)
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n_samples, n_neighbors = X.shape[0], Z.shape[1]
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B = np.empty((n_samples, n_neighbors), dtype=X.dtype)
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v = np.ones(n_neighbors, dtype=X.dtype)
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# this might raise a LinalgError if G is singular and has trace
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# zero
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for i, A in enumerate(Z.transpose(0, 2, 1)):
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C = A.T - X[i] # broadcasting
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G = np.dot(C, C.T)
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trace = np.trace(G)
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if trace > 0:
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R = reg * trace
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else:
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R = reg
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G.flat[::Z.shape[1] + 1] += R
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w = solve(G, v, sym_pos=True)
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B[i, :] = w / np.sum(w)
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return B
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def barycenter_kneighbors_graph(X, n_neighbors, reg=1e-3, n_jobs=1):
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"""Computes the barycenter weighted graph of k-Neighbors for points in X
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Parameters
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----------
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X : {array-like, sparse matrix, BallTree, KDTree, NearestNeighbors}
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Sample data, shape = (n_samples, n_features), in the form of a
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numpy array, sparse array, precomputed tree, or NearestNeighbors
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object.
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n_neighbors : int
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Number of neighbors for each sample.
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reg : float, optional
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Amount of regularization when solving the least-squares
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problem. Only relevant if mode='barycenter'. If None, use the
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default.
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n_jobs : int, optional (default = 1)
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The number of parallel jobs to run for neighbors search.
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If ``-1``, then the number of jobs is set to the number of CPU cores.
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Returns
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-------
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A : sparse matrix in CSR format, shape = [n_samples, n_samples]
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A[i, j] is assigned the weight of edge that connects i to j.
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See also
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--------
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sklearn.neighbors.kneighbors_graph
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sklearn.neighbors.radius_neighbors_graph
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"""
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knn = NearestNeighbors(n_neighbors + 1, n_jobs=n_jobs).fit(X)
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X = knn._fit_X
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n_samples = X.shape[0]
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ind = knn.kneighbors(X, return_distance=False)[:, 1:]
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data = barycenter_weights(X, X[ind], reg=reg)
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indptr = np.arange(0, n_samples * n_neighbors + 1, n_neighbors)
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return csr_matrix((data.ravel(), ind.ravel(), indptr),
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shape=(n_samples, n_samples))
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def null_space(M, k, k_skip=1, eigen_solver='arpack', tol=1E-6, max_iter=100,
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random_state=None):
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"""
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Find the null space of a matrix M.
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Parameters
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----------
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M : {array, matrix, sparse matrix, LinearOperator}
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Input covariance matrix: should be symmetric positive semi-definite
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k : integer
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Number of eigenvalues/vectors to return
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k_skip : integer, optional
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Number of low eigenvalues to skip.
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eigen_solver : string, {'auto', 'arpack', 'dense'}
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auto : algorithm will attempt to choose the best method for input data
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arpack : use arnoldi iteration in shift-invert mode.
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For this method, M may be a dense matrix, sparse matrix,
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or general linear operator.
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Warning: ARPACK can be unstable for some problems. It is
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best to try several random seeds in order to check results.
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dense : use standard dense matrix operations for the eigenvalue
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decomposition. For this method, M must be an array
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or matrix type. This method should be avoided for
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large problems.
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tol : float, optional
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Tolerance for 'arpack' method.
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Not used if eigen_solver=='dense'.
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max_iter : maximum number of iterations for 'arpack' method
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not used if eigen_solver=='dense'
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random_state : int, RandomState instance or None, optional (default=None)
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If int, random_state is the seed used by the random number generator;
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If RandomState instance, random_state is the random number generator;
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If None, the random number generator is the RandomState instance used
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by `np.random`. Used when ``solver`` == 'arpack'.
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"""
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if eigen_solver == 'auto':
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if M.shape[0] > 200 and k + k_skip < 10:
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eigen_solver = 'arpack'
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else:
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eigen_solver = 'dense'
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if eigen_solver == 'arpack':
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random_state = check_random_state(random_state)
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# initialize with [-1,1] as in ARPACK
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v0 = random_state.uniform(-1, 1, M.shape[0])
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try:
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eigen_values, eigen_vectors = eigsh(M, k + k_skip, sigma=0.0,
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tol=tol, maxiter=max_iter,
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v0=v0)
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except RuntimeError as msg:
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raise ValueError("Error in determining null-space with ARPACK. "
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"Error message: '%s'. "
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"Note that method='arpack' can fail when the "
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"weight matrix is singular or otherwise "
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"ill-behaved. method='dense' is recommended. "
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"See online documentation for more information."
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% msg)
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return eigen_vectors[:, k_skip:], np.sum(eigen_values[k_skip:])
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elif eigen_solver == 'dense':
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if hasattr(M, 'toarray'):
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M = M.toarray()
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eigen_values, eigen_vectors = eigh(
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M, eigvals=(k_skip, k + k_skip - 1), overwrite_a=True)
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index = np.argsort(np.abs(eigen_values))
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return eigen_vectors[:, index], np.sum(eigen_values)
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else:
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raise ValueError("Unrecognized eigen_solver '%s'" % eigen_solver)
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def locally_linear_embedding(
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X, n_neighbors, n_components, reg=1e-3, eigen_solver='auto', tol=1e-6,
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max_iter=100, method='standard', hessian_tol=1E-4, modified_tol=1E-12,
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random_state=None, n_jobs=1):
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"""Perform a Locally Linear Embedding analysis on the data.
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Read more in the :ref:`User Guide <locally_linear_embedding>`.
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Parameters
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----------
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X : {array-like, sparse matrix, BallTree, KDTree, NearestNeighbors}
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Sample data, shape = (n_samples, n_features), in the form of a
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numpy array, sparse array, precomputed tree, or NearestNeighbors
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object.
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n_neighbors : integer
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number of neighbors to consider for each point.
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n_components : integer
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number of coordinates for the manifold.
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reg : float
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regularization constant, multiplies the trace of the local covariance
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matrix of the distances.
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eigen_solver : string, {'auto', 'arpack', 'dense'}
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auto : algorithm will attempt to choose the best method for input data
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arpack : use arnoldi iteration in shift-invert mode.
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For this method, M may be a dense matrix, sparse matrix,
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or general linear operator.
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Warning: ARPACK can be unstable for some problems. It is
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best to try several random seeds in order to check results.
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dense : use standard dense matrix operations for the eigenvalue
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decomposition. For this method, M must be an array
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or matrix type. This method should be avoided for
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large problems.
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tol : float, optional
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Tolerance for 'arpack' method
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Not used if eigen_solver=='dense'.
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max_iter : integer
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maximum number of iterations for the arpack solver.
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method : {'standard', 'hessian', 'modified', 'ltsa'}
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standard : use the standard locally linear embedding algorithm.
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see reference [1]_
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hessian : use the Hessian eigenmap method. This method requires
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n_neighbors > n_components * (1 + (n_components + 1) / 2.
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see reference [2]_
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modified : use the modified locally linear embedding algorithm.
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see reference [3]_
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ltsa : use local tangent space alignment algorithm
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see reference [4]_
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hessian_tol : float, optional
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Tolerance for Hessian eigenmapping method.
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Only used if method == 'hessian'
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modified_tol : float, optional
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Tolerance for modified LLE method.
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Only used if method == 'modified'
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random_state : int, RandomState instance or None, optional (default=None)
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If int, random_state is the seed used by the random number generator;
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If RandomState instance, random_state is the random number generator;
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If None, the random number generator is the RandomState instance used
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by `np.random`. Used when ``solver`` == 'arpack'.
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n_jobs : int, optional (default = 1)
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The number of parallel jobs to run for neighbors search.
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If ``-1``, then the number of jobs is set to the number of CPU cores.
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Returns
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-------
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Y : array-like, shape [n_samples, n_components]
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Embedding vectors.
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squared_error : float
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Reconstruction error for the embedding vectors. Equivalent to
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``norm(Y - W Y, 'fro')**2``, where W are the reconstruction weights.
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References
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----------
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.. [1] `Roweis, S. & Saul, L. Nonlinear dimensionality reduction
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by locally linear embedding. Science 290:2323 (2000).`
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.. [2] `Donoho, D. & Grimes, C. Hessian eigenmaps: Locally
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linear embedding techniques for high-dimensional data.
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Proc Natl Acad Sci U S A. 100:5591 (2003).`
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.. [3] `Zhang, Z. & Wang, J. MLLE: Modified Locally Linear
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Embedding Using Multiple Weights.`
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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.382
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.. [4] `Zhang, Z. & Zha, H. Principal manifolds and nonlinear
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dimensionality reduction via tangent space alignment.
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Journal of Shanghai Univ. 8:406 (2004)`
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"""
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if eigen_solver not in ('auto', 'arpack', 'dense'):
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raise ValueError("unrecognized eigen_solver '%s'" % eigen_solver)
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if method not in ('standard', 'hessian', 'modified', 'ltsa'):
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raise ValueError("unrecognized method '%s'" % method)
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nbrs = NearestNeighbors(n_neighbors=n_neighbors + 1, n_jobs=n_jobs)
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nbrs.fit(X)
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X = nbrs._fit_X
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N, d_in = X.shape
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if n_components > d_in:
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raise ValueError("output dimension must be less than or equal "
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"to input dimension")
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if n_neighbors >= N:
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raise ValueError("n_neighbors must be less than number of points")
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if n_neighbors <= 0:
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raise ValueError("n_neighbors must be positive")
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M_sparse = (eigen_solver != 'dense')
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if method == 'standard':
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W = barycenter_kneighbors_graph(
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nbrs, n_neighbors=n_neighbors, reg=reg, n_jobs=n_jobs)
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# we'll compute M = (I-W)'(I-W)
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# depending on the solver, we'll do this differently
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if M_sparse:
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M = eye(*W.shape, format=W.format) - W
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M = (M.T * M).tocsr()
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else:
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M = (W.T * W - W.T - W).toarray()
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M.flat[::M.shape[0] + 1] += 1 # W = W - I = W - I
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elif method == 'hessian':
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dp = n_components * (n_components + 1) // 2
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if n_neighbors <= n_components + dp:
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raise ValueError("for method='hessian', n_neighbors must be "
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"greater than "
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"[n_components * (n_components + 3) / 2]")
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neighbors = nbrs.kneighbors(X, n_neighbors=n_neighbors + 1,
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return_distance=False)
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neighbors = neighbors[:, 1:]
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Yi = np.empty((n_neighbors, 1 + n_components + dp), dtype=np.float64)
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Yi[:, 0] = 1
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M = np.zeros((N, N), dtype=np.float64)
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use_svd = (n_neighbors > d_in)
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for i in range(N):
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Gi = X[neighbors[i]]
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Gi -= Gi.mean(0)
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# build Hessian estimator
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if use_svd:
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U = svd(Gi, full_matrices=0)[0]
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else:
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Ci = np.dot(Gi, Gi.T)
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U = eigh(Ci)[1][:, ::-1]
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Yi[:, 1:1 + n_components] = U[:, :n_components]
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j = 1 + n_components
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for k in range(n_components):
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Yi[:, j:j + n_components - k] = (U[:, k:k + 1] *
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U[:, k:n_components])
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j += n_components - k
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Q, R = qr(Yi)
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w = Q[:, n_components + 1:]
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S = w.sum(0)
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S[np.where(abs(S) < hessian_tol)] = 1
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w /= S
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nbrs_x, nbrs_y = np.meshgrid(neighbors[i], neighbors[i])
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M[nbrs_x, nbrs_y] += np.dot(w, w.T)
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if M_sparse:
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M = csr_matrix(M)
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elif method == 'modified':
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if n_neighbors < n_components:
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raise ValueError("modified LLE requires "
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"n_neighbors >= n_components")
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neighbors = nbrs.kneighbors(X, n_neighbors=n_neighbors + 1,
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return_distance=False)
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neighbors = neighbors[:, 1:]
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# find the eigenvectors and eigenvalues of each local covariance
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# matrix. We want V[i] to be a [n_neighbors x n_neighbors] matrix,
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# where the columns are eigenvectors
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V = np.zeros((N, n_neighbors, n_neighbors))
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nev = min(d_in, n_neighbors)
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evals = np.zeros([N, nev])
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# choose the most efficient way to find the eigenvectors
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use_svd = (n_neighbors > d_in)
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if use_svd:
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for i in range(N):
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X_nbrs = X[neighbors[i]] - X[i]
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V[i], evals[i], _ = svd(X_nbrs,
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full_matrices=True)
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evals **= 2
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else:
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for i in range(N):
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X_nbrs = X[neighbors[i]] - X[i]
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C_nbrs = np.dot(X_nbrs, X_nbrs.T)
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evi, vi = eigh(C_nbrs)
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evals[i] = evi[::-1]
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V[i] = vi[:, ::-1]
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# find regularized weights: this is like normal LLE.
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# because we've already computed the SVD of each covariance matrix,
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# it's faster to use this rather than np.linalg.solve
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reg = 1E-3 * evals.sum(1)
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tmp = np.dot(V.transpose(0, 2, 1), np.ones(n_neighbors))
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tmp[:, :nev] /= evals + reg[:, None]
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tmp[:, nev:] /= reg[:, None]
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w_reg = np.zeros((N, n_neighbors))
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for i in range(N):
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w_reg[i] = np.dot(V[i], tmp[i])
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w_reg /= w_reg.sum(1)[:, None]
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# calculate eta: the median of the ratio of small to large eigenvalues
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# across the points. This is used to determine s_i, below
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rho = evals[:, n_components:].sum(1) / evals[:, :n_components].sum(1)
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eta = np.median(rho)
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# find s_i, the size of the "almost null space" for each point:
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# this is the size of the largest set of eigenvalues
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# such that Sum[v; v in set]/Sum[v; v not in set] < eta
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s_range = np.zeros(N, dtype=int)
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evals_cumsum = stable_cumsum(evals, 1)
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eta_range = evals_cumsum[:, -1:] / evals_cumsum[:, :-1] - 1
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for i in range(N):
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s_range[i] = np.searchsorted(eta_range[i, ::-1], eta)
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s_range += n_neighbors - nev # number of zero eigenvalues
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# Now calculate M.
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# This is the [N x N] matrix whose null space is the desired embedding
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M = np.zeros((N, N), dtype=np.float64)
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for i in range(N):
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s_i = s_range[i]
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# select bottom s_i eigenvectors and calculate alpha
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Vi = V[i, :, n_neighbors - s_i:]
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alpha_i = np.linalg.norm(Vi.sum(0)) / np.sqrt(s_i)
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# compute Householder matrix which satisfies
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# Hi*Vi.T*ones(n_neighbors) = alpha_i*ones(s)
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# using prescription from paper
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h = alpha_i * np.ones(s_i) - np.dot(Vi.T, np.ones(n_neighbors))
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norm_h = np.linalg.norm(h)
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if norm_h < modified_tol:
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h *= 0
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else:
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h /= norm_h
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# Householder matrix is
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# >> Hi = np.identity(s_i) - 2*np.outer(h,h)
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# Then the weight matrix is
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# >> Wi = np.dot(Vi,Hi) + (1-alpha_i) * w_reg[i,:,None]
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# We do this much more efficiently:
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Wi = (Vi - 2 * np.outer(np.dot(Vi, h), h) +
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(1 - alpha_i) * w_reg[i, :, None])
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# Update M as follows:
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# >> W_hat = np.zeros( (N,s_i) )
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# >> W_hat[neighbors[i],:] = Wi
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# >> W_hat[i] -= 1
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# >> M += np.dot(W_hat,W_hat.T)
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|
# We can do this much more efficiently:
|
|
nbrs_x, nbrs_y = np.meshgrid(neighbors[i], neighbors[i])
|
|
M[nbrs_x, nbrs_y] += np.dot(Wi, Wi.T)
|
|
Wi_sum1 = Wi.sum(1)
|
|
M[i, neighbors[i]] -= Wi_sum1
|
|
M[neighbors[i], i] -= Wi_sum1
|
|
M[i, i] += s_i
|
|
|
|
if M_sparse:
|
|
M = csr_matrix(M)
|
|
|
|
elif method == 'ltsa':
|
|
neighbors = nbrs.kneighbors(X, n_neighbors=n_neighbors + 1,
|
|
return_distance=False)
|
|
neighbors = neighbors[:, 1:]
|
|
|
|
M = np.zeros((N, N))
|
|
|
|
use_svd = (n_neighbors > d_in)
|
|
|
|
for i in range(N):
|
|
Xi = X[neighbors[i]]
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|
Xi -= Xi.mean(0)
|
|
|
|
# compute n_components largest eigenvalues of Xi * Xi^T
|
|
if use_svd:
|
|
v = svd(Xi, full_matrices=True)[0]
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|
else:
|
|
Ci = np.dot(Xi, Xi.T)
|
|
v = eigh(Ci)[1][:, ::-1]
|
|
|
|
Gi = np.zeros((n_neighbors, n_components + 1))
|
|
Gi[:, 1:] = v[:, :n_components]
|
|
Gi[:, 0] = 1. / np.sqrt(n_neighbors)
|
|
|
|
GiGiT = np.dot(Gi, Gi.T)
|
|
|
|
nbrs_x, nbrs_y = np.meshgrid(neighbors[i], neighbors[i])
|
|
M[nbrs_x, nbrs_y] -= GiGiT
|
|
M[neighbors[i], neighbors[i]] += 1
|
|
|
|
return null_space(M, n_components, k_skip=1, eigen_solver=eigen_solver,
|
|
tol=tol, max_iter=max_iter, random_state=random_state)
|
|
|
|
|
|
class LocallyLinearEmbedding(BaseEstimator, TransformerMixin):
|
|
"""Locally Linear Embedding
|
|
|
|
Read more in the :ref:`User Guide <locally_linear_embedding>`.
|
|
|
|
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, optional (default = 1)
|
|
The number of parallel jobs to run.
|
|
If ``-1``, then the number of jobs is set to the number of CPU cores.
|
|
|
|
Attributes
|
|
----------
|
|
embedding_vectors_ : array-like, shape [n_components, n_samples]
|
|
Stores the embedding vectors
|
|
|
|
reconstruction_error_ : float
|
|
Reconstruction error associated with `embedding_vectors_`
|
|
|
|
nbrs_ : NearestNeighbors object
|
|
Stores nearest neighbors instance, including BallTree or KDtree
|
|
if applicable.
|
|
|
|
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)`
|
|
"""
|
|
|
|
def __init__(self, n_neighbors=5, n_components=2, reg=1E-3,
|
|
eigen_solver='auto', tol=1E-6, max_iter=100,
|
|
method='standard', hessian_tol=1E-4, modified_tol=1E-12,
|
|
neighbors_algorithm='auto', random_state=None, n_jobs=1):
|
|
self.n_neighbors = n_neighbors
|
|
self.n_components = n_components
|
|
self.reg = reg
|
|
self.eigen_solver = eigen_solver
|
|
self.tol = tol
|
|
self.max_iter = max_iter
|
|
self.method = method
|
|
self.hessian_tol = hessian_tol
|
|
self.modified_tol = modified_tol
|
|
self.random_state = random_state
|
|
self.neighbors_algorithm = neighbors_algorithm
|
|
self.n_jobs = n_jobs
|
|
|
|
def _fit_transform(self, X):
|
|
self.nbrs_ = NearestNeighbors(self.n_neighbors,
|
|
algorithm=self.neighbors_algorithm,
|
|
n_jobs=self.n_jobs)
|
|
|
|
random_state = check_random_state(self.random_state)
|
|
X = check_array(X, dtype=float)
|
|
self.nbrs_.fit(X)
|
|
self.embedding_, self.reconstruction_error_ = \
|
|
locally_linear_embedding(
|
|
self.nbrs_, self.n_neighbors, self.n_components,
|
|
eigen_solver=self.eigen_solver, tol=self.tol,
|
|
max_iter=self.max_iter, method=self.method,
|
|
hessian_tol=self.hessian_tol, modified_tol=self.modified_tol,
|
|
random_state=random_state, reg=self.reg, n_jobs=self.n_jobs)
|
|
|
|
def fit(self, X, y=None):
|
|
"""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.
|
|
"""
|
|
self._fit_transform(X)
|
|
return self
|
|
|
|
def fit_transform(self, X, y=None):
|
|
"""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)
|
|
"""
|
|
self._fit_transform(X)
|
|
return self.embedding_
|
|
|
|
def transform(self, X):
|
|
"""
|
|
Transform new points into embedding space.
|
|
|
|
Parameters
|
|
----------
|
|
X : array-like, shape = [n_samples, n_features]
|
|
|
|
Returns
|
|
-------
|
|
X_new : array, shape = [n_samples, n_components]
|
|
|
|
Notes
|
|
-----
|
|
Because of scaling performed by this method, it is discouraged to use
|
|
it together with methods that are not scale-invariant (like SVMs)
|
|
"""
|
|
check_is_fitted(self, "nbrs_")
|
|
|
|
X = check_array(X)
|
|
ind = self.nbrs_.kneighbors(X, n_neighbors=self.n_neighbors,
|
|
return_distance=False)
|
|
weights = barycenter_weights(X, self.nbrs_._fit_X[ind],
|
|
reg=self.reg)
|
|
X_new = np.empty((X.shape[0], self.n_components))
|
|
for i in range(X.shape[0]):
|
|
X_new[i] = np.dot(self.embedding_[ind[i]].T, weights[i])
|
|
return X_new
|