"""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, effective_n_jobs from ._ball_tree import BallTree from ._kd_tree import KDTree from ..base import BaseEstimator, MultiOutputMixin from ..base import is_classifier from ..metrics import pairwise_distances_chunked from ..metrics.pairwise import PAIRWISE_DISTANCE_FUNCTIONS from ..utils import ( check_array, gen_even_slices, _to_object_array, ) from ..utils.deprecation import deprecated 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 delayed 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 not in (None, "uniform", "distance") and not callable(weights): raise ValueError( "weights not recognized: should be 'uniform', " "'distance', or a callable function" ) return weights 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 0.0 in point_dist: dist[point_dist_i] = point_dist == 0.0 else: dist[point_dist_i] = 1.0 / point_dist else: with np.errstate(divide="ignore"): dist = 1.0 / 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): """Return 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 : sparse matrix of shape (n_samples, n_samples) Neighbors graph as given by `kneighbors_graph` or `radius_neighbors_graph`. Matrix should be of format CSR format. Returns ------- res : bool 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 : sparse matrix of shape (n_samples, n_samples) Neighbors graph as given by `kneighbors_graph` or `radius_neighbors_graph`. Matrix should be of format CSR format. n_neighbors : int Number of neighbors required for each sample. return_distance : bool Whether or not to return the distances. Returns ------- neigh_dist : ndarray of shape (n_samples, n_neighbors) Distances to nearest neighbors. Only present if `return_distance=True`. neigh_ind : ndarray of 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 : sparse matrix of shape (n_samples, n_samples) Neighbors graph as given by `kneighbors_graph` or `radius_neighbors_graph`. Matrix should be of format CSR format. radius : float Radius of neighborhoods which should be strictly positive. return_distance : bool Whether or not to return the distances. Returns ------- neigh_dist : ndarray of shape (n_samples,) of arrays Distances to nearest neighbors. Only present if `return_distance=True`. neigh_ind : ndarray of 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 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: if self.p is not None: 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 or equal to one for minkowski metric") def _fit(self, X, y=None): if self._get_tags()["requires_y"]: if not isinstance(X, (KDTree, BallTree, NeighborsBase)): X, y = self._validate_data(X, y, accept_sparse="csr", multi_output=True) if is_classifier(self): # Classification targets require a specific format 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=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() else: self._y = y else: if not isinstance(X, (KDTree, BallTree, NeighborsBase)): X = self._validate_data(X, accept_sparse="csr") 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) w = self.effective_metric_params_.pop("w", None) if p < 1: raise ValueError( "p must be greater or equal to one for minkowski metric" ) elif p == 1 and w is None: self.effective_metric_ = "manhattan" elif p == 2 and w is None: self.effective_metric_ = "euclidean" elif p == np.inf and w is None: self.effective_metric_ = "chebyshev" else: # Use the generic minkowski metric, possibly weighted. self.effective_metric_params_["p"] = p self.effective_metric_params_["w"] = w 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.metric == "precomputed": X = _check_precomputed(X) # Precomputed matrix X must be squared if X.shape[0] != X.shape[1]: raise ValueError( "Precomputed matrix must be square." " Input is a {}x{} matrix.".format(X.shape[0], X.shape[1]) ) self.n_features_in_ = X.shape[1] n_samples = X.shape[0] if n_samples == 0: raise ValueError("n_samples must be greater than 0") 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 or small # number of features, with KDTree generally faster when available if ( self.metric == "precomputed" or self._fit_X.shape[1] > 15 or ( self.n_neighbors is not None and self.n_neighbors >= self._fit_X.shape[0] // 2 ) ): self._fit_method = "brute" else: 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" 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) elif 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 def _more_tags(self): # For cross-validation routines to split data correctly return {"pairwise": self.metric == "precomputed"} # TODO: Remove in 1.1 # mypy error: Decorated property not supported @deprecated( # type: ignore "Attribute `_pairwise` was deprecated in " "version 0.24 and will be removed in 1.1 (renaming of 0.26)." ) @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 : ndarray of shape (n_samples_chunk, n_samples) The distance matrix. start : int The index in X which the first row of dist corresponds to. n_neighbors : int Number of neighbors required for each sample. return_distance : bool Whether or not to return the distances. Returns ------- dist : array of shape (n_samples_chunk, n_neighbors) Returned only if `return_distance=True`. neigh : array of shape (n_samples_chunk, n_neighbors) The neighbors indices. """ 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): """Find 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', \ 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. n_neighbors : int, default=None Number of neighbors required for each sample. The default is the value passed to the constructor. return_distance : bool, default=True Whether or not to return the distances. Returns ------- neigh_dist : ndarray of shape (n_queries, n_neighbors) Array representing the lengths to points, only present if return_distance=True. neigh_ind : ndarray of 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) elif 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.metric == "precomputed": X = _check_precomputed(X) else: X = self._validate_data(X, accept_sparse="csr", reset=False) 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.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 parallel_kwargs = {"backend": "threading"} else: parallel_kwargs = {"prefer": "threads"} chunked_results = Parallel(n_jobs, **parallel_kwargs)( delayed(_tree_query_parallel_helper)( 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"): """Compute the (weighted) graph of k-Neighbors for points in X. Parameters ---------- X : array-like of shape (n_queries, n_features), \ or (n_queries, n_indexed) if metric == 'precomputed', \ 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. For ``metric='precomputed'`` the shape should be (n_queries, n_indexed). Otherwise the shape should be (n_queries, n_features). n_neighbors : int, default=None Number of neighbors for each sample. The default is the value passed to the constructor. mode : {'connectivity', 'distance'}, default='connectivity' Type of returned matrix: 'connectivity' will return the connectivity matrix with ones and zeros, in 'distance' the edges are distances between points, type of distance depends on the selected metric parameter in NearestNeighbors class. Returns ------- A : sparse-matrix of shape (n_queries, n_samples_fit) `n_samples_fit` is the number of samples in the fitted data. `A[i, j]` gives the weight of the edge connecting `i` to `j`. The matrix is of CSR format. See Also -------- NearestNeighbors.radius_neighbors_graph : Compute the (weighted) graph of Neighbors for points in X. 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.]]) """ 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 : ndarray of shape (n_samples_chunk, n_samples) The distance matrix. start : int The index in X which the first row of dist corresponds to. radius : float The radius considered when making the nearest neighbors search. return_distance : bool Whether or not to return the distances. Returns ------- dist : list of ndarray of shape (n_samples_chunk,) Returned only if `return_distance=True`. neigh : list of ndarray of shape (n_samples_chunk,) The neighbors indices. """ 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 ): """Find 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 of (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, default=None Limiting distance of neighbors to return. The default is the value passed to the constructor. return_distance : bool, default=True Whether or not to return the distances. sort_results : bool, default=False If True, the distances and indices will be sorted by increasing distances before being returned. If False, the results may not be sorted. If `return_distance=False`, setting `sort_results=True` will result in an error. .. versionadded:: 0.22 Returns ------- neigh_dist : ndarray of 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 : ndarray of 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. 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. 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. """ check_is_fitted(self) if X is not None: query_is_train = False if self.metric == "precomputed": X = _check_precomputed(X) else: X = self._validate_data(X, accept_sparse="csr", reset=False) else: query_is_train = True X = self._fit_X if radius is None: radius = self.radius if self._fit_method == "brute" and self.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) if sort_results: if not return_distance: raise ValueError( "return_distance must be True if sort_results is True." ) for ii in range(len(neigh_dist)): order = np.argsort(neigh_dist[ii], kind="mergesort") neigh_ind[ii] = neigh_ind[ii][order] neigh_dist[ii] = neigh_dist[ii][order] results = neigh_dist, neigh_ind 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) delayed_query = delayed(_tree_query_radius_parallel_helper) if parse_version(joblib.__version__) < parse_version("0.12"): # Deal with change of API in joblib parallel_kwargs = {"backend": "threading"} else: 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 ): """Compute 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, default=None Radius of neighborhoods. The default is the value passed to the constructor. mode : {'connectivity', 'distance'}, default='connectivity' Type of returned matrix: 'connectivity' will return the connectivity matrix with ones and zeros, in 'distance' the edges are distances between points, type of distance depends on the selected metric parameter in NearestNeighbors class. sort_results : bool, default=False If True, in each row of the result, the non-zero entries will be sorted by increasing distances. If False, the non-zero entries may not be sorted. Only used with mode='distance'. .. versionadded:: 0.22 Returns ------- A : sparse-matrix of shape (n_queries, n_samples_fit) `n_samples_fit` is the number of samples in the fitted data. `A[i, j]` gives the weight of the edge connecting `i` to `j`. The matrix is of CSR format. See Also -------- kneighbors_graph : Compute the (weighted) graph of k-Neighbors for points in X. 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.]]) """ 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))