"""Base and mixin classes for nearest neighbors""" # Authors: Jake Vanderplas # Fabian Pedregosa # Alexandre Gramfort # Sparseness support by Lars Buitinck # # License: BSD, (C) INRIA, University of Amsterdam import warnings import numpy as np from scipy.sparse import csr_matrix, issparse from scipy.spatial.ckdtree import cKDTree from .ball_tree import BallTree from ..base import BaseEstimator from ..metrics import pairwise_distances from ..utils import safe_asarray, atleast2d_or_csr class NeighborsWarning(UserWarning): pass # Make sure that NeighborsWarning are displayed more than once warnings.simplefilter("always", NeighborsWarning) def warn_equidistant(): msg = ("kneighbors: neighbor k+1 and neighbor k have the same " "distance: results will be dependent on data order.") warnings.warn(msg, NeighborsWarning, stacklevel=3) def _check_weights(weights): """Check to make sure weights are valid""" if weights in (None, 'uniform', 'distance'): return weights elif callable(weights): return weights else: raise ValueError("weights not recognized: should be 'uniform', " "'distance', or a callable function") def _get_weights(dist, weights): """Get the weights from an array of distances and a parameter ``weights`` Parameters =========== dist: ndarray The input distances weights: {'uniform', 'distance' or a callable} The kind of weighting used Returns ======== weights_arr: array of the same shape as ``dist`` if ``weights == 'uniform'``, then returns None """ if weights in (None, 'uniform'): return None elif weights == 'distance': with np.errstate(divide='ignore'): dist = 1./dist return dist elif callable(weights): return weights(dist) else: raise ValueError("weights not recognized: should be 'uniform', " "'distance', or a callable function") class NeighborsBase(BaseEstimator): """Base class for nearest neighbors estimators.""" #FIXME: include float parameter p for using different distance metrics. # this can be passed directly to BallTree and cKDTree. Brute-force will # rely on soon-to-be-updated functionality in the pairwise module. def _init_params(self, n_neighbors=None, radius=None, algorithm='auto', leaf_size=30, warn_on_equidistant=True, p=2): self.n_neighbors = n_neighbors self.radius = radius self.algorithm = algorithm self.leaf_size = leaf_size self.warn_on_equidistant = warn_on_equidistant self.p = p if algorithm not in ['auto', 'brute', 'kd_tree', 'ball_tree']: raise ValueError("unrecognized algorithm: '%s'" % algorithm) if p < 1: raise ValueError("p must be greater than or equal to 1") self._fit_X = None self._tree = None self._fit_method = None def _fit(self, X): if isinstance(X, NeighborsBase): self._fit_X = X._fit_X self._tree = X._tree self._fit_method = X._fit_method return self elif isinstance(X, BallTree): self._fit_X = X.data self._tree = X self._fit_method = 'ball_tree' return self elif isinstance(X, cKDTree): self._fit_X = X.data self._tree = X self._fit_method = 'kd_tree' return self X = safe_asarray(X) if X.ndim != 2: raise ValueError("data type not understood") if issparse(X): if self.algorithm not in ('auto', 'brute'): warnings.warn("cannot use tree with sparse input: " "using brute force") self._fit_X = X.tocsr() self._tree = None self._fit_method = 'brute' return self self._fit_method = self.algorithm self._fit_X = X if self._fit_method == 'auto': # BallTree outperforms the others in nearly any circumstance. if self.n_neighbors < self._fit_X.shape[0] / 2: self._fit_method = 'ball_tree' else: self._fit_method = 'brute' if self._fit_method == 'kd_tree': self._tree = cKDTree(X, self.leaf_size) elif self._fit_method == 'ball_tree': self._tree = BallTree(X, self.leaf_size, p=self.p) elif self._fit_method == 'brute': self._tree = None else: raise ValueError("algorithm = '%s' not recognized" % self.algorithm) return self class KNeighborsMixin(object): """Mixin for k-neighbors searches""" def kneighbors(self, X, n_neighbors=None, return_distance=True): """Finds the K-neighbors of a point. Returns distance Parameters ---------- X : array-like, last dimension same as that of fit data The new point. n_neighbors : int Number of neighbors to get (default is the value passed to the constructor). return_distance : boolean, optional. Defaults to True. If False, distances will not be returned Returns ------- dist : array Array representing the lengths to point, only present if return_distance=True ind : array Indices of the nearest points in the population matrix. Examples -------- In the following example, we construct a NeighborsClassifier class from an array representing our data set and ask who's the closest point to [1,1,1] >>> samples = [[0., 0., 0.], [0., .5, 0.], [1., 1., .5]] >>> from sklearn.neighbors import NearestNeighbors >>> neigh = NearestNeighbors(n_neighbors=1) >>> neigh.fit(samples) # doctest: +ELLIPSIS NearestNeighbors(algorithm='auto', leaf_size=30, ...) >>> print neigh.kneighbors([1., 1., 1.]) # doctest: +ELLIPSIS (array([[ 0.5]]), array([[2]]...)) As you can see, it returns [[0.5]], and [[2]], which means that the element is at distance 0.5 and is the third element of samples (indexes start at 0). You can also query for multiple points: >>> X = [[0., 1., 0.], [1., 0., 1.]] >>> neigh.kneighbors(X, return_distance=False) # doctest: +ELLIPSIS array([[1], [2]]...) """ if self._fit_method == None: raise ValueError("must fit neighbors before querying") X = atleast2d_or_csr(X) if n_neighbors is None: n_neighbors = self.n_neighbors if self._fit_method == 'brute': if self.p == 1: dist = pairwise_distances(X, self._fit_X, 'manhattan') elif self.p == 2: dist = pairwise_distances(X, self._fit_X, 'euclidean', squared=True) elif self.p == np.inf: dist = pairwise_distances(X, self._fit_X, 'chebyshev') else: dist = pairwise_distances(X, self._fit_X, 'minkowski', p=self.p) # XXX: should be implemented with a partial sort neigh_ind = dist.argsort(axis=1) if self.warn_on_equidistant and n_neighbors < self._fit_X.shape[0]: ii = np.arange(dist.shape[0]) ind_k = neigh_ind[:, n_neighbors - 1] ind_k1 = neigh_ind[:, n_neighbors] if np.any(dist[ii, ind_k] == dist[ii, ind_k1]): warn_equidistant() neigh_ind = neigh_ind[:, :n_neighbors] if return_distance: j = np.arange(neigh_ind.shape[0])[:, None] if self.p == 2: return np.sqrt(dist[j, neigh_ind]), neigh_ind else: return dist[j, neigh_ind], neigh_ind else: return neigh_ind elif self._fit_method == 'ball_tree': result = self._tree.query(X, n_neighbors, return_distance=return_distance) if self.warn_on_equidistant and self._tree.warning_flag: warn_equidistant() return result elif self._fit_method == 'kd_tree': dist, ind = self._tree.query(X, n_neighbors, p=self.p) # kd_tree returns a 1D array for n_neighbors = 1 if n_neighbors == 1: dist = dist[:, None] ind = ind[:, None] if return_distance: return dist, ind else: return ind else: raise ValueError("internal: _fit_method not recognized") def kneighbors_graph(self, X, n_neighbors=None, mode='connectivity'): """Computes the (weighted) graph of k-Neighbors for points in X Parameters ---------- X : array-like, shape = [n_samples, n_features] Sample data n_neighbors : int Number of neighbors for each sample. (default is value passed to the constructor). mode : {'connectivity', 'distance'}, optional Type of returned matrix: 'connectivity' will return the connectivity matrix with ones and zeros, in 'distance' the edges are Euclidean distance between points. Returns ------- A : sparse matrix in CSR format, shape = [n_samples, n_samples_fit] n_samples_fit is the number of samples in the fitted data A[i, j] is assigned the weight of edge that connects i to j. Examples -------- >>> X = [[0], [3], [1]] >>> from sklearn.neighbors import NearestNeighbors >>> neigh = NearestNeighbors(n_neighbors=2) >>> neigh.fit(X) # doctest: +ELLIPSIS NearestNeighbors(algorithm='auto', leaf_size=30, ...) >>> A = neigh.kneighbors_graph(X) >>> A.todense() matrix([[ 1., 0., 1.], [ 0., 1., 1.], [ 1., 0., 1.]]) See also -------- NearestNeighbors.radius_neighbors_graph """ X = np.asarray(X) if n_neighbors is None: n_neighbors = self.n_neighbors n_samples1 = X.shape[0] n_samples2 = self._fit_X.shape[0] n_nonzero = n_samples1 * n_neighbors A_indptr = np.arange(0, n_nonzero + 1, n_neighbors) # construct CSR matrix representation of the k-NN graph if mode == 'connectivity': A_data = np.ones((n_samples1, n_neighbors)) A_ind = self.kneighbors(X, n_neighbors, return_distance=False) elif mode == 'distance': data, ind = self.kneighbors(X, n_neighbors + 1, return_distance=True) A_data, A_ind = data[:, 1:], ind[:, 1:] else: raise ValueError( 'Unsupported mode, must be one of "connectivity" ' 'or "distance" but got "%s" instead' % mode) return csr_matrix((A_data.ravel(), A_ind.ravel(), A_indptr), shape=(n_samples1, n_samples2)) class RadiusNeighborsMixin(object): """Mixin for radius-based neighbors searches""" def radius_neighbors(self, X, radius=None, return_distance=True): """Finds the neighbors of a point within a given radius. Returns distance Parameters ---------- X : array-like, last dimension same as that of fit data The new point. radius : float Limiting distance of neighbors to return. (default is the value passed to the constructor). return_distance : boolean, optional. Defaults to True. If False, distances will not be returned Returns ------- dist : array Array representing the lengths to point, only present if return_distance=True ind : array Indices of the nearest points in the population matrix. Examples -------- In the following example, we construnct a NeighborsClassifier class from an array representing our data set and ask who's the closest point to [1,1,1] >>> samples = [[0., 0., 0.], [0., .5, 0.], [1., 1., .5]] >>> from sklearn.neighbors import NearestNeighbors >>> neigh = NearestNeighbors(radius=1.6) >>> neigh.fit(samples) # doctest: +ELLIPSIS NearestNeighbors(algorithm='auto', leaf_size=30, ...) >>> print neigh.radius_neighbors([1., 1., 1.]) # doctest: +ELLIPSIS (array([[ 1.5, 0.5]]...), array([[1, 2]]...) The first array returned contains the distances to all points which are closer than 1.6, while the second array returned contains their indices. In general, multiple points can be queried at the same time. Because the number of neighbors of each point is not necessarily equal, `radius_neighbors` returns an array of objects, where each object is a 1D array of indices. """ if self._fit_method == None: raise ValueError("must fit neighbors before querying") X = atleast2d_or_csr(X) if radius is None: radius = self.radius if self._fit_method == 'brute': if self.p == 1: dist = pairwise_distances(X, self._fit_X, 'manhattan') elif self.p == 2: dist = pairwise_distances(X, self._fit_X, 'euclidean', squared=True) radius *= radius elif self.p == np.inf: dist = pairwise_distances(X, self._fit_X, 'chebyshev') else: dist = pairwise_distances(X, self._fit_X, 'minkowski', p=self.p) neigh_ind = [np.where(d < radius)[0] for d in dist] # if there are the same number of neighbors for each point, # we can do a normal array. Otherwise, we return an object # array with elements that are numpy arrays try: neigh_ind = np.asarray(neigh_ind, dtype=int) dtype_F = float except ValueError: neigh_ind = np.asarray(neigh_ind, dtype='object') dtype_F = object if return_distance: if self.p == 2: dist = np.array([np.sqrt(d[neigh_ind[i]]) \ for i, d in enumerate(dist)], dtype=dtype_F) else: dist = np.array([d[neigh_ind[i]] \ for i, d in enumerate(dist)], dtype=dtype_F) return dist, neigh_ind else: return neigh_ind elif self._fit_method == 'ball_tree': if return_distance: ind, dist = self._tree.query_radius(X, radius, return_distance=True) return dist, ind else: ind = self._tree.query_radius(X, radius, return_distance=False) return ind elif self._fit_method == 'kd_tree': Npts = self._fit_X.shape[0] dist, ind = self._tree.query(X, Npts, distance_upper_bound=radius, p=self.p) ind = [ind_i[:ind_i.searchsorted(Npts)] for ind_i in ind] # if there are the same number of neighbors for each point, # we can do a normal array. Otherwise, we return an object # array with elements that are numpy arrays try: ind = np.asarray(ind, dtype=int) dtype_F = float except ValueError: ind = np.asarray(ind, dtype='object') dtype_F = object if return_distance: dist = np.array([dist_i[:len(ind[i])] for i, dist_i in enumerate(dist)], dtype=dtype_F) return dist, ind else: return ind else: raise ValueError("internal: _fit_method not recognized") def radius_neighbors_graph(self, X, radius=None, mode='connectivity'): """Computes the (weighted) graph of Neighbors for points in X Neighborhoods are restricted the points at a distance lower than radius. Parameters ---------- X : array-like, shape = [n_samples, n_features] Sample data radius : float Radius of neighborhoods. (default is the value passed to the constructor). mode : {'connectivity', 'distance'}, optional Type of returned matrix: 'connectivity' will return the connectivity matrix with ones and zeros, in 'distance' the edges are Euclidean distance between points. 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. Examples -------- >>> X = [[0], [3], [1]] >>> from sklearn.neighbors import NearestNeighbors >>> neigh = NearestNeighbors(radius=1.5) >>> neigh.fit(X) # doctest: +ELLIPSIS NearestNeighbors(algorithm='auto', leaf_size=30, ...) >>> A = neigh.radius_neighbors_graph(X) >>> A.todense() matrix([[ 1., 0., 1.], [ 0., 1., 0.], [ 1., 0., 1.]]) See also -------- kneighbors_graph """ X = np.asarray(X) if radius is None: radius = self.radius n_samples1 = X.shape[0] n_samples2 = self._fit_X.shape[0] # construct CSR matrix representation of the NN graph if mode == 'connectivity': A_ind = self.radius_neighbors(X, radius, return_distance=False) A_data = None elif mode == 'distance': dist, A_ind = self.radius_neighbors(X, radius, return_distance=True) A_data = np.concatenate(list(dist)) else: raise ValueError( 'Unsupported mode, must be one of "connectivity", ' 'or "distance" but got %s instead' % mode) n_neighbors = np.array([len(a) for a in A_ind]) n_nonzero = np.sum(n_neighbors) if A_data is None: A_data = np.ones(n_nonzero) A_ind = np.concatenate(list(A_ind)) A_indptr = np.concatenate((np.zeros(1, dtype=int), np.cumsum(n_neighbors))) return csr_matrix((A_data, A_ind, A_indptr), shape=(n_samples1, n_samples2)) class SupervisedFloatMixin(object): def fit(self, X, y): """Fit the model using X as training data and y as target values Parameters ---------- X : {array-like, sparse matrix, BallTree, cKDTree} Training data. If array or matrix, then the shape is [n_samples, n_features] y : {array-like, sparse matrix}, shape = [n_samples] Target values, array of float values. """ self._y = np.asarray(y) return self._fit(X) class SupervisedIntegerMixin(object): def fit(self, X, y): """Fit the model using X as training data and y as target values Parameters ---------- X : {array-like, sparse matrix, BallTree, cKDTree} Training data. If array or matrix, then the shape is [n_samples, n_features] y : {array-like, sparse matrix}, shape = [n_samples] Target values, array of integer values. """ self._y = np.asarray(y) return self._fit(X) class UnsupervisedMixin(object): def fit(self, X, y=None): """Fit the model using X as training data Parameters ---------- X : {array-like, sparse matrix, BallTree, cKDTree} Training data. If array or matrix, shape = [n_samples, n_features] """ return self._fit(X)