"""Base and mixin classes for nearest neighbors""" # Authors: Jake Vanderplas # Fabian Pedregosa # Alexandre Gramfort # Sparseness support by Lars Buitinck # Multi-output support by Arnaud Joly # # License: BSD 3 clause (C) INRIA, University of Amsterdam from functools import partial import warnings from abc import ABCMeta, abstractmethod import numbers import numpy as np from scipy.sparse import csr_matrix, issparse import joblib from joblib import Parallel, delayed, effective_n_jobs from ._ball_tree import BallTree from ._kd_tree import KDTree from ..base import BaseEstimator, MultiOutputMixin from ..metrics import pairwise_distances_chunked from ..metrics.pairwise import PAIRWISE_DISTANCE_FUNCTIONS from ..utils import check_array, gen_even_slices from ..utils import _to_object_array from ..utils.multiclass import check_classification_targets from ..utils.validation import check_is_fitted from ..utils.validation import check_non_negative from ..utils.fixes import parse_version from ..exceptions import DataConversionWarning, EfficiencyWarning VALID_METRICS = dict(ball_tree=BallTree.valid_metrics, kd_tree=KDTree.valid_metrics, # The following list comes from the # sklearn.metrics.pairwise doc string brute=(list(PAIRWISE_DISTANCE_FUNCTIONS.keys()) + ['braycurtis', 'canberra', 'chebyshev', 'correlation', 'cosine', 'dice', 'hamming', 'jaccard', 'kulsinski', 'mahalanobis', 'matching', 'minkowski', 'rogerstanimoto', 'russellrao', 'seuclidean', 'sokalmichener', 'sokalsneath', 'sqeuclidean', 'yule', 'wminkowski'])) VALID_METRICS_SPARSE = dict(ball_tree=[], kd_tree=[], brute=(PAIRWISE_DISTANCE_FUNCTIONS.keys() - {'haversine', 'nan_euclidean'})) 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': # if user attempts to classify a point that was zero distance from one # or more training points, those training points are weighted as 1.0 # and the other points as 0.0 if dist.dtype is np.dtype(object): for point_dist_i, point_dist in enumerate(dist): # check if point_dist is iterable # (ex: RadiusNeighborClassifier.predict may set an element of # dist to 1e-6 to represent an 'outlier') if hasattr(point_dist, '__contains__') and 0. in point_dist: dist[point_dist_i] = point_dist == 0. else: dist[point_dist_i] = 1. / point_dist else: with np.errstate(divide='ignore'): dist = 1. / dist inf_mask = np.isinf(dist) inf_row = np.any(inf_mask, axis=1) dist[inf_row] = inf_mask[inf_row] return dist elif callable(weights): return weights(dist) else: raise ValueError("weights not recognized: should be 'uniform', " "'distance', or a callable function") def _is_sorted_by_data(graph): """Returns whether the graph's non-zero entries are sorted by data The non-zero entries are stored in graph.data and graph.indices. For each row (or sample), the non-zero entries can be either: - sorted by indices, as after graph.sort_indices() - sorted by data, as after _check_precomputed(graph) - not sorted. Parameters ---------- graph : CSR sparse matrix, shape (n_samples, n_samples) Neighbors graph as given by kneighbors_graph or radius_neighbors_graph Returns ------- res : boolean Whether input graph is sorted by data """ assert graph.format == 'csr' out_of_order = graph.data[:-1] > graph.data[1:] line_change = np.unique(graph.indptr[1:-1] - 1) line_change = line_change[line_change < out_of_order.shape[0]] return (out_of_order.sum() == out_of_order[line_change].sum()) def _check_precomputed(X): """Check precomputed distance matrix If the precomputed distance matrix is sparse, it checks that the non-zero entries are sorted by distances. If not, the matrix is copied and sorted. Parameters ---------- X : {sparse matrix, array-like}, (n_samples, n_samples) Distance matrix to other samples. X may be a sparse matrix, in which case only non-zero elements may be considered neighbors. Returns ------- X : {sparse matrix, array-like}, (n_samples, n_samples) Distance matrix to other samples. X may be a sparse matrix, in which case only non-zero elements may be considered neighbors. """ if not issparse(X): X = check_array(X) check_non_negative(X, whom="precomputed distance matrix.") return X else: graph = X if graph.format not in ('csr', 'csc', 'coo', 'lil'): raise TypeError('Sparse matrix in {!r} format is not supported due to ' 'its handling of explicit zeros'.format(graph.format)) copied = graph.format != 'csr' graph = check_array(graph, accept_sparse='csr') check_non_negative(graph, whom="precomputed distance matrix.") if not _is_sorted_by_data(graph): warnings.warn('Precomputed sparse input was not sorted by data.', EfficiencyWarning) if not copied: graph = graph.copy() # if each sample has the same number of provided neighbors row_nnz = np.diff(graph.indptr) if row_nnz.max() == row_nnz.min(): n_samples = graph.shape[0] distances = graph.data.reshape(n_samples, -1) order = np.argsort(distances, kind='mergesort') order += np.arange(n_samples)[:, None] * row_nnz[0] order = order.ravel() graph.data = graph.data[order] graph.indices = graph.indices[order] else: for start, stop in zip(graph.indptr, graph.indptr[1:]): order = np.argsort(graph.data[start:stop], kind='mergesort') graph.data[start:stop] = graph.data[start:stop][order] graph.indices[start:stop] = graph.indices[start:stop][order] return graph def _kneighbors_from_graph(graph, n_neighbors, return_distance): """Decompose a nearest neighbors sparse graph into distances and indices Parameters ---------- graph : CSR sparse matrix, shape (n_samples, n_samples) Neighbors graph as given by kneighbors_graph or radius_neighbors_graph n_neighbors : int Number of neighbors required for each sample. return_distance : boolean If False, distances will not be returned Returns ------- neigh_dist : array, shape (n_samples, n_neighbors) Distances to nearest neighbors. Only present if return_distance=True. neigh_ind : array, shape (n_samples, n_neighbors) Indices of nearest neighbors. """ n_samples = graph.shape[0] assert graph.format == 'csr' # number of neighbors by samples row_nnz = np.diff(graph.indptr) row_nnz_min = row_nnz.min() if n_neighbors is not None and row_nnz_min < n_neighbors: raise ValueError( '%d neighbors per samples are required, but some samples have only' ' %d neighbors in precomputed graph matrix. Decrease number of ' 'neighbors used or recompute the graph with more neighbors.' % (n_neighbors, row_nnz_min)) def extract(a): # if each sample has the same number of provided neighbors if row_nnz.max() == row_nnz_min: return a.reshape(n_samples, -1)[:, :n_neighbors] else: idx = np.tile(np.arange(n_neighbors), (n_samples, 1)) idx += graph.indptr[:-1, None] return a.take(idx, mode='clip').reshape(n_samples, n_neighbors) if return_distance: return extract(graph.data), extract(graph.indices) else: return extract(graph.indices) def _radius_neighbors_from_graph(graph, radius, return_distance): """Decompose a nearest neighbors sparse graph into distances and indices Parameters ---------- graph : CSR sparse matrix, shape (n_samples, n_samples) Neighbors graph as given by kneighbors_graph or radius_neighbors_graph radius : float > 0 Radius of neighborhoods. return_distance : boolean If False, distances will not be returned Returns ------- neigh_dist : array, shape (n_samples,) of arrays Distances to nearest neighbors. Only present if return_distance=True. neigh_ind :array, shape (n_samples,) of arrays Indices of nearest neighbors. """ assert graph.format == 'csr' no_filter_needed = bool(graph.data.max() <= radius) if no_filter_needed: data, indices, indptr = graph.data, graph.indices, graph.indptr else: mask = graph.data <= radius if return_distance: data = np.compress(mask, graph.data) indices = np.compress(mask, graph.indices) indptr = np.concatenate(([0], np.cumsum(mask)))[graph.indptr] indices = indices.astype(np.intp, copy=no_filter_needed) if return_distance: neigh_dist = _to_object_array(np.split(data, indptr[1:-1])) neigh_ind = _to_object_array(np.split(indices, indptr[1:-1])) if return_distance: return neigh_dist, neigh_ind else: return neigh_ind class NeighborsBase(MultiOutputMixin, BaseEstimator, metaclass=ABCMeta): """Base class for nearest neighbors estimators.""" @abstractmethod def __init__(self, n_neighbors=None, radius=None, algorithm='auto', leaf_size=30, metric='minkowski', p=2, metric_params=None, n_jobs=None): self.n_neighbors = n_neighbors self.radius = radius self.algorithm = algorithm self.leaf_size = leaf_size self.metric = metric self.metric_params = metric_params self.p = p self.n_jobs = n_jobs self._check_algorithm_metric() def _check_algorithm_metric(self): if self.algorithm not in ['auto', 'brute', 'kd_tree', 'ball_tree']: raise ValueError("unrecognized algorithm: '%s'" % self.algorithm) if self.algorithm == 'auto': if self.metric == 'precomputed': alg_check = 'brute' elif (callable(self.metric) or self.metric in VALID_METRICS['ball_tree']): alg_check = 'ball_tree' else: alg_check = 'brute' else: alg_check = self.algorithm if callable(self.metric): if self.algorithm == 'kd_tree': # callable metric is only valid for brute force and ball_tree raise ValueError( "kd_tree does not support callable metric '%s'" "Function call overhead will result" "in very poor performance." % self.metric) elif self.metric not in VALID_METRICS[alg_check]: raise ValueError("Metric '%s' not valid. Use " "sorted(sklearn.neighbors.VALID_METRICS['%s']) " "to get valid options. " "Metric can also be a callable function." % (self.metric, alg_check)) if self.metric_params is not None and 'p' in self.metric_params: warnings.warn("Parameter p is found in metric_params. " "The corresponding parameter from __init__ " "is ignored.", SyntaxWarning, stacklevel=3) effective_p = self.metric_params['p'] else: effective_p = self.p if self.metric in ['wminkowski', 'minkowski'] and effective_p < 1: raise ValueError("p must be greater than one for minkowski metric") def _fit(self, X): self._check_algorithm_metric() if self.metric_params is None: self.effective_metric_params_ = {} else: self.effective_metric_params_ = self.metric_params.copy() effective_p = self.effective_metric_params_.get('p', self.p) if self.metric in ['wminkowski', 'minkowski']: self.effective_metric_params_['p'] = effective_p self.effective_metric_ = self.metric # For minkowski distance, use more efficient methods where available if self.metric == 'minkowski': p = self.effective_metric_params_.pop('p', 2) if p < 1: raise ValueError("p must be greater than one " "for minkowski metric") elif p == 1: self.effective_metric_ = 'manhattan' elif p == 2: self.effective_metric_ = 'euclidean' elif p == np.inf: self.effective_metric_ = 'chebyshev' else: self.effective_metric_params_['p'] = p if isinstance(X, NeighborsBase): self._fit_X = X._fit_X self._tree = X._tree self._fit_method = X._fit_method self.n_samples_fit_ = X.n_samples_fit_ return self elif isinstance(X, BallTree): self._fit_X = X.data self._tree = X self._fit_method = 'ball_tree' self.n_samples_fit_ = X.data.shape[0] return self elif isinstance(X, KDTree): self._fit_X = X.data self._tree = X self._fit_method = 'kd_tree' self.n_samples_fit_ = X.data.shape[0] return self if self.effective_metric_ == 'precomputed': X = _check_precomputed(X) self.n_features_in_ = X.shape[1] else: X = self._validate_data(X, accept_sparse='csr') n_samples = X.shape[0] if n_samples == 0: raise ValueError("n_samples must be greater than 0") # Precomputed matrix X must be squared if self.metric == 'precomputed' and X.shape[0] != X.shape[1]: raise ValueError("Precomputed matrix must be a square matrix." " Input is a {}x{} matrix." .format(X.shape[0], X.shape[1])) if issparse(X): if self.algorithm not in ('auto', 'brute'): warnings.warn("cannot use tree with sparse input: " "using brute force") if self.effective_metric_ not in VALID_METRICS_SPARSE['brute'] \ and not callable(self.effective_metric_): raise ValueError("Metric '%s' not valid for sparse input. " "Use sorted(sklearn.neighbors." "VALID_METRICS_SPARSE['brute']) " "to get valid options. " "Metric can also be a callable function." % (self.effective_metric_)) self._fit_X = X.copy() self._tree = None self._fit_method = 'brute' self.n_samples_fit_ = X.shape[0] return self self._fit_method = self.algorithm self._fit_X = X self.n_samples_fit_ = X.shape[0] if self._fit_method == 'auto': # A tree approach is better for small number of neighbors, # and KDTree is generally faster when available if ((self.n_neighbors is None or self.n_neighbors < self._fit_X.shape[0] // 2) and self.metric != 'precomputed'): if self.effective_metric_ in VALID_METRICS['kd_tree']: self._fit_method = 'kd_tree' elif (callable(self.effective_metric_) or self.effective_metric_ in VALID_METRICS['ball_tree']): self._fit_method = 'ball_tree' else: self._fit_method = 'brute' else: self._fit_method = 'brute' if self._fit_method == 'ball_tree': self._tree = BallTree(X, self.leaf_size, metric=self.effective_metric_, **self.effective_metric_params_) elif self._fit_method == 'kd_tree': self._tree = KDTree(X, self.leaf_size, metric=self.effective_metric_, **self.effective_metric_params_) elif self._fit_method == 'brute': self._tree = None else: raise ValueError("algorithm = '%s' not recognized" % self.algorithm) if self.n_neighbors is not None: if self.n_neighbors <= 0: raise ValueError( "Expected n_neighbors > 0. Got %d" % self.n_neighbors ) else: if not isinstance(self.n_neighbors, numbers.Integral): raise TypeError( "n_neighbors does not take %s value, " "enter integer value" % type(self.n_neighbors)) return self @property def _pairwise(self): # For cross-validation routines to split data correctly return self.metric == 'precomputed' def _tree_query_parallel_helper(tree, *args, **kwargs): """Helper for the Parallel calls in KNeighborsMixin.kneighbors The Cython method tree.query is not directly picklable by cloudpickle under PyPy. """ return tree.query(*args, **kwargs) class KNeighborsMixin: """Mixin for k-neighbors searches""" def _kneighbors_reduce_func(self, dist, start, n_neighbors, return_distance): """Reduce a chunk of distances to the nearest neighbors Callback to :func:`sklearn.metrics.pairwise.pairwise_distances_chunked` Parameters ---------- dist : array of shape (n_samples_chunk, n_samples) start : int The index in X which the first row of dist corresponds to. n_neighbors : int return_distance : bool Returns ------- dist : array of shape (n_samples_chunk, n_neighbors), optional Returned only if return_distance neigh : array of shape (n_samples_chunk, n_neighbors) """ sample_range = np.arange(dist.shape[0])[:, None] neigh_ind = np.argpartition(dist, n_neighbors - 1, axis=1) neigh_ind = neigh_ind[:, :n_neighbors] # argpartition doesn't guarantee sorted order, so we sort again neigh_ind = neigh_ind[ sample_range, np.argsort(dist[sample_range, neigh_ind])] if return_distance: if self.effective_metric_ == 'euclidean': result = np.sqrt(dist[sample_range, neigh_ind]), neigh_ind else: result = dist[sample_range, neigh_ind], neigh_ind else: result = neigh_ind return result def kneighbors(self, X=None, n_neighbors=None, return_distance=True): """Finds the K-neighbors of a point. Returns indices of and distances to the neighbors of each point. Parameters ---------- X : array-like, shape (n_queries, n_features), \ or (n_queries, n_indexed) if metric == 'precomputed' The query point or points. If not provided, neighbors of each indexed point are returned. In this case, the query point is not considered its own neighbor. 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 ------- neigh_dist : array, shape (n_queries, n_neighbors) Array representing the lengths to points, only present if return_distance=True neigh_ind : array, shape (n_queries, n_neighbors) Indices of the nearest points in the population matrix. Examples -------- In the following example, we construct a NearestNeighbors 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) NearestNeighbors(n_neighbors=1) >>> print(neigh.kneighbors([[1., 1., 1.]])) (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) array([[1], [2]]...) """ check_is_fitted(self) if n_neighbors is None: n_neighbors = self.n_neighbors elif n_neighbors <= 0: raise ValueError( "Expected n_neighbors > 0. Got %d" % n_neighbors ) else: if not isinstance(n_neighbors, numbers.Integral): raise TypeError( "n_neighbors does not take %s value, " "enter integer value" % type(n_neighbors)) if X is not None: query_is_train = False if self.effective_metric_ == 'precomputed': X = _check_precomputed(X) else: X = check_array(X, accept_sparse='csr') else: query_is_train = True X = self._fit_X # Include an extra neighbor to account for the sample itself being # returned, which is removed later n_neighbors += 1 n_samples_fit = self.n_samples_fit_ if n_neighbors > n_samples_fit: raise ValueError( "Expected n_neighbors <= n_samples, " " but n_samples = %d, n_neighbors = %d" % (n_samples_fit, n_neighbors) ) n_jobs = effective_n_jobs(self.n_jobs) chunked_results = None if (self._fit_method == 'brute' and self.effective_metric_ == 'precomputed' and issparse(X)): results = _kneighbors_from_graph( X, n_neighbors=n_neighbors, return_distance=return_distance) elif self._fit_method == 'brute': reduce_func = partial(self._kneighbors_reduce_func, n_neighbors=n_neighbors, return_distance=return_distance) # for efficiency, use squared euclidean distances if self.effective_metric_ == 'euclidean': kwds = {'squared': True} else: kwds = self.effective_metric_params_ chunked_results = list(pairwise_distances_chunked( X, self._fit_X, reduce_func=reduce_func, metric=self.effective_metric_, n_jobs=n_jobs, **kwds)) elif self._fit_method in ['ball_tree', 'kd_tree']: if issparse(X): raise ValueError( "%s does not work with sparse matrices. Densify the data, " "or set algorithm='brute'" % self._fit_method) old_joblib = ( parse_version(joblib.__version__) < parse_version('0.12')) if old_joblib: # Deal with change of API in joblib check_pickle = False if old_joblib else None delayed_query = delayed(_tree_query_parallel_helper, check_pickle=check_pickle) parallel_kwargs = {"backend": "threading"} else: delayed_query = delayed(_tree_query_parallel_helper) parallel_kwargs = {"prefer": "threads"} chunked_results = Parallel(n_jobs, **parallel_kwargs)( delayed_query( self._tree, X[s], n_neighbors, return_distance) for s in gen_even_slices(X.shape[0], n_jobs) ) else: raise ValueError("internal: _fit_method not recognized") if chunked_results is not None: if return_distance: neigh_dist, neigh_ind = zip(*chunked_results) results = np.vstack(neigh_dist), np.vstack(neigh_ind) else: results = np.vstack(chunked_results) if not query_is_train: return results else: # If the query data is the same as the indexed data, we would like # to ignore the first nearest neighbor of every sample, i.e # the sample itself. if return_distance: neigh_dist, neigh_ind = results else: neigh_ind = results n_queries, _ = X.shape sample_range = np.arange(n_queries)[:, None] sample_mask = neigh_ind != sample_range # Corner case: When the number of duplicates are more # than the number of neighbors, the first NN will not # be the sample, but a duplicate. # In that case mask the first duplicate. dup_gr_nbrs = np.all(sample_mask, axis=1) sample_mask[:, 0][dup_gr_nbrs] = False neigh_ind = np.reshape( neigh_ind[sample_mask], (n_queries, n_neighbors - 1)) if return_distance: neigh_dist = np.reshape( neigh_dist[sample_mask], (n_queries, n_neighbors - 1)) return neigh_dist, neigh_ind return neigh_ind def kneighbors_graph(self, X=None, n_neighbors=None, mode='connectivity'): """Computes the (weighted) graph of k-Neighbors for points in X Parameters ---------- X : array-like, shape (n_queries, n_features), \ or (n_queries, n_indexed) if metric == 'precomputed' The query point or points. If not provided, neighbors of each indexed point are returned. In this case, the query point is not considered its own neighbor. 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 graph in CSR format, shape = [n_queries, 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) NearestNeighbors(n_neighbors=2) >>> A = neigh.kneighbors_graph(X) >>> A.toarray() array([[1., 0., 1.], [0., 1., 1.], [1., 0., 1.]]) See also -------- NearestNeighbors.radius_neighbors_graph """ check_is_fitted(self) if n_neighbors is None: n_neighbors = self.n_neighbors # check the input only in self.kneighbors # construct CSR matrix representation of the k-NN graph if mode == 'connectivity': A_ind = self.kneighbors(X, n_neighbors, return_distance=False) n_queries = A_ind.shape[0] A_data = np.ones(n_queries * n_neighbors) elif mode == 'distance': A_data, A_ind = self.kneighbors( X, n_neighbors, return_distance=True) A_data = np.ravel(A_data) else: raise ValueError( 'Unsupported mode, must be one of "connectivity" ' 'or "distance" but got "%s" instead' % mode) n_queries = A_ind.shape[0] n_samples_fit = self.n_samples_fit_ n_nonzero = n_queries * n_neighbors A_indptr = np.arange(0, n_nonzero + 1, n_neighbors) kneighbors_graph = csr_matrix((A_data, A_ind.ravel(), A_indptr), shape=(n_queries, n_samples_fit)) return kneighbors_graph def _tree_query_radius_parallel_helper(tree, *args, **kwargs): """Helper for the Parallel calls in RadiusNeighborsMixin.radius_neighbors The Cython method tree.query_radius is not directly picklable by cloudpickle under PyPy. """ return tree.query_radius(*args, **kwargs) class RadiusNeighborsMixin: """Mixin for radius-based neighbors searches""" def _radius_neighbors_reduce_func(self, dist, start, radius, return_distance): """Reduce a chunk of distances to the nearest neighbors Callback to :func:`sklearn.metrics.pairwise.pairwise_distances_chunked` Parameters ---------- dist : array of shape (n_samples_chunk, n_samples) start : int The index in X which the first row of dist corresponds to. radius : float return_distance : bool Returns ------- dist : list of n_samples_chunk 1d arrays, optional Returned only if return_distance neigh : list of n_samples_chunk 1d arrays """ neigh_ind = [np.where(d <= radius)[0] for d in dist] if return_distance: if self.effective_metric_ == 'euclidean': dist = [np.sqrt(d[neigh_ind[i]]) for i, d in enumerate(dist)] else: dist = [d[neigh_ind[i]] for i, d in enumerate(dist)] results = dist, neigh_ind else: results = neigh_ind return results def radius_neighbors(self, X=None, radius=None, return_distance=True, sort_results=False): """Finds the neighbors within a given radius of a point or points. Return the indices and distances of each point from the dataset lying in a ball with size ``radius`` around the points of the query array. Points lying on the boundary are included in the results. The result points are *not* necessarily sorted by distance to their query point. Parameters ---------- X : array-like, (n_samples, n_features), optional The query point or points. If not provided, neighbors of each indexed point are returned. In this case, the query point is not considered its own neighbor. 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. sort_results : boolean, optional. Defaults to False. If True, the distances and indices will be sorted before being returned. If False, the results will not be sorted. If return_distance == False, setting sort_results = True will result in an error. .. versionadded:: 0.22 Returns ------- neigh_dist : array, shape (n_samples,) of arrays Array representing the distances to each point, only present if return_distance=True. The distance values are computed according to the ``metric`` constructor parameter. neigh_ind : array, shape (n_samples,) of arrays An array of arrays of indices of the approximate nearest points from the population matrix that lie within a ball of size ``radius`` around the query points. 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]: >>> import numpy as np >>> samples = [[0., 0., 0.], [0., .5, 0.], [1., 1., .5]] >>> from sklearn.neighbors import NearestNeighbors >>> neigh = NearestNeighbors(radius=1.6) >>> neigh.fit(samples) NearestNeighbors(radius=1.6) >>> rng = neigh.radius_neighbors([[1., 1., 1.]]) >>> print(np.asarray(rng[0][0])) [1.5 0.5] >>> print(np.asarray(rng[1][0])) [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. Notes ----- Because the number of neighbors of each point is not necessarily equal, the results for multiple query points cannot be fit in a standard data array. For efficiency, `radius_neighbors` returns arrays of objects, where each object is a 1D array of indices or distances. """ check_is_fitted(self) if X is not None: query_is_train = False if self.effective_metric_ == 'precomputed': X = _check_precomputed(X) else: X = check_array(X, accept_sparse='csr') else: query_is_train = True X = self._fit_X if radius is None: radius = self.radius if (self._fit_method == 'brute' and self.effective_metric_ == 'precomputed' and issparse(X)): results = _radius_neighbors_from_graph( X, radius=radius, return_distance=return_distance) elif self._fit_method == 'brute': # for efficiency, use squared euclidean distances if self.effective_metric_ == 'euclidean': radius *= radius kwds = {'squared': True} else: kwds = self.effective_metric_params_ reduce_func = partial(self._radius_neighbors_reduce_func, radius=radius, return_distance=return_distance) chunked_results = pairwise_distances_chunked( X, self._fit_X, reduce_func=reduce_func, metric=self.effective_metric_, n_jobs=self.n_jobs, **kwds) if return_distance: neigh_dist_chunks, neigh_ind_chunks = zip(*chunked_results) neigh_dist_list = sum(neigh_dist_chunks, []) neigh_ind_list = sum(neigh_ind_chunks, []) neigh_dist = _to_object_array(neigh_dist_list) neigh_ind = _to_object_array(neigh_ind_list) results = neigh_dist, neigh_ind else: neigh_ind_list = sum(chunked_results, []) results = _to_object_array(neigh_ind_list) elif self._fit_method in ['ball_tree', 'kd_tree']: if issparse(X): raise ValueError( "%s does not work with sparse matrices. Densify the data, " "or set algorithm='brute'" % self._fit_method) n_jobs = effective_n_jobs(self.n_jobs) if parse_version(joblib.__version__) < parse_version('0.12'): # Deal with change of API in joblib delayed_query = delayed(_tree_query_radius_parallel_helper, check_pickle=False) parallel_kwargs = {"backend": "threading"} else: delayed_query = delayed(_tree_query_radius_parallel_helper) parallel_kwargs = {"prefer": "threads"} chunked_results = Parallel(n_jobs, **parallel_kwargs)( delayed_query(self._tree, X[s], radius, return_distance, sort_results=sort_results) for s in gen_even_slices(X.shape[0], n_jobs) ) if return_distance: neigh_ind, neigh_dist = tuple(zip(*chunked_results)) results = np.hstack(neigh_dist), np.hstack(neigh_ind) else: results = np.hstack(chunked_results) else: raise ValueError("internal: _fit_method not recognized") if not query_is_train: return results else: # If the query data is the same as the indexed data, we would like # to ignore the first nearest neighbor of every sample, i.e # the sample itself. if return_distance: neigh_dist, neigh_ind = results else: neigh_ind = results for ind, ind_neighbor in enumerate(neigh_ind): mask = ind_neighbor != ind neigh_ind[ind] = ind_neighbor[mask] if return_distance: neigh_dist[ind] = neigh_dist[ind][mask] if return_distance: return neigh_dist, neigh_ind return neigh_ind def radius_neighbors_graph(self, X=None, radius=None, mode='connectivity', sort_results=False): """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 of shape (n_samples, n_features), default=None The query point or points. If not provided, neighbors of each indexed point are returned. In this case, the query point is not considered its own neighbor. 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. sort_results : boolean, optional. Defaults to False. If True, the distances and indices will be sorted before being returned. If False, the results will not be sorted. Only used with mode='distance'. .. versionadded:: 0.22 Returns ------- A : sparse graph in CSR format, shape = [n_queries, 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(radius=1.5) >>> neigh.fit(X) NearestNeighbors(radius=1.5) >>> A = neigh.radius_neighbors_graph(X) >>> A.toarray() array([[1., 0., 1.], [0., 1., 0.], [1., 0., 1.]]) See also -------- kneighbors_graph """ check_is_fitted(self) # check the input only in self.radius_neighbors if radius is None: radius = self.radius # 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, sort_results=sort_results) A_data = np.concatenate(list(dist)) else: raise ValueError( 'Unsupported mode, must be one of "connectivity", ' 'or "distance" but got %s instead' % mode) n_queries = A_ind.shape[0] n_samples_fit = self.n_samples_fit_ n_neighbors = np.array([len(a) for a in A_ind]) A_ind = np.concatenate(list(A_ind)) if A_data is None: A_data = np.ones(len(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_queries, n_samples_fit)) class SupervisedFloatMixin: 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, KDTree} Training data. If array or matrix, shape [n_samples, n_features], or [n_samples, n_samples] if metric='precomputed'. y : {array-like, sparse matrix} Target values, array of float values, shape = [n_samples] or [n_samples, n_outputs] """ if not isinstance(X, (KDTree, BallTree)): X, y = self._validate_data(X, y, accept_sparse="csr", multi_output=True) self._y = y return self._fit(X) def _more_tags(self): return {'requires_y': True} class SupervisedIntegerMixin: 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, KDTree} Training data. If array or matrix, shape [n_samples, n_features], or [n_samples, n_samples] if metric='precomputed'. y : {array-like, sparse matrix} Target values of shape = [n_samples] or [n_samples, n_outputs] """ if not isinstance(X, (KDTree, BallTree)): X, y = self._validate_data(X, y, accept_sparse="csr", multi_output=True) if y.ndim == 1 or y.ndim == 2 and y.shape[1] == 1: if y.ndim != 1: warnings.warn("A column-vector y was passed when a 1d array " "was expected. Please change the shape of y to " "(n_samples, ), for example using ravel().", DataConversionWarning, stacklevel=2) self.outputs_2d_ = False y = y.reshape((-1, 1)) else: self.outputs_2d_ = True check_classification_targets(y) self.classes_ = [] self._y = np.empty(y.shape, dtype=np.int) for k in range(self._y.shape[1]): classes, self._y[:, k] = np.unique(y[:, k], return_inverse=True) self.classes_.append(classes) if not self.outputs_2d_: self.classes_ = self.classes_[0] self._y = self._y.ravel() return self._fit(X) def _more_tags(self): return {'requires_y': True} class UnsupervisedMixin: def fit(self, X, y=None): """Fit the model using X as training data Parameters ---------- X : {array-like, sparse matrix, BallTree, KDTree} Training data. If array or matrix, shape [n_samples, n_features], or [n_samples, n_samples] if metric='precomputed'. """ return self._fit(X)