"""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 import warnings from abc import ABCMeta, abstractmethod import numpy as np from scipy.sparse import csr_matrix, issparse from .ball_tree import BallTree from .kd_tree import KDTree from ..base import BaseEstimator from ..metrics import pairwise_distances from ..metrics.pairwise import PAIRWISE_DISTANCE_FUNCTIONS from ..utils import check_X_y, check_array, _get_n_jobs, gen_even_slices from ..utils.fixes import argpartition from ..utils.multiclass import check_classification_targets from ..externals import six from ..externals.joblib import Parallel, delayed from ..exceptions import NotFittedError from ..exceptions import DataConversionWarning 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()) 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") class NeighborsBase(six.with_metaclass(ABCMeta, BaseEstimator)): """Base class for nearest neighbors estimators.""" @abstractmethod def __init__(self): pass def _init_params(self, n_neighbors=None, radius=None, algorithm='auto', leaf_size=30, metric='minkowski', p=2, metric_params=None, n_jobs=1): 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 if algorithm not in ['auto', 'brute', 'kd_tree', 'ball_tree']: raise ValueError("unrecognized algorithm: '%s'" % algorithm) if algorithm == 'auto': if metric == 'precomputed': alg_check = 'brute' else: alg_check = 'ball_tree' else: alg_check = algorithm if callable(metric): if algorithm == 'kd_tree': # callable metric is only valid for brute force and ball_tree raise ValueError( "kd_tree algorithm does not support callable metric '%s'" % metric) elif metric not in VALID_METRICS[alg_check]: raise ValueError("Metric '%s' not valid for algorithm '%s'" % (metric, algorithm)) 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 = 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") self._fit_X = None self._tree = None self._fit_method = None def _fit(self, X): 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 return self elif isinstance(X, BallTree): self._fit_X = X.data self._tree = X self._fit_method = 'ball_tree' return self elif isinstance(X, KDTree): self._fit_X = X.data self._tree = X self._fit_method = 'kd_tree' return self X = check_array(X, accept_sparse='csr') 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']: raise ValueError("metric '%s' not valid for sparse input" % self.effective_metric_) self._fit_X = X.copy() self._tree = None self._fit_method = 'brute' return self self._fit_method = self.algorithm self._fit_X = X 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' else: 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 ) return self @property def _pairwise(self): # For cross-validation routines to split data correctly return self.metric == 'precomputed' class KNeighborsMixin(object): """Mixin for k-neighbors searches""" 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_query, n_features), \ or (n_query, 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 ------- dist : array Array representing the lengths to points, 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 is None: raise NotFittedError("Must fit neighbors before querying.") if n_neighbors is None: n_neighbors = self.n_neighbors if X is not None: query_is_train = False 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 train_size = self._fit_X.shape[0] if n_neighbors > train_size: raise ValueError( "Expected n_neighbors <= n_samples, " " but n_samples = %d, n_neighbors = %d" % (train_size, n_neighbors) ) n_samples, _ = X.shape sample_range = np.arange(n_samples)[:, None] n_jobs = _get_n_jobs(self.n_jobs) if self._fit_method == 'brute': # for efficiency, use squared euclidean distances if self.effective_metric_ == 'euclidean': dist = pairwise_distances(X, self._fit_X, 'euclidean', n_jobs=n_jobs, squared=True) else: dist = pairwise_distances( X, self._fit_X, self.effective_metric_, n_jobs=n_jobs, **self.effective_metric_params_) neigh_ind = 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 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) result = Parallel(n_jobs, backend='threading')( delayed(self._tree.query, check_pickle=False)( X[s], n_neighbors, return_distance) for s in gen_even_slices(X.shape[0], n_jobs) ) if return_distance: dist, neigh_ind = tuple(zip(*result)) result = np.vstack(dist), np.vstack(neigh_ind) else: result = np.vstack(result) else: raise ValueError("internal: _fit_method not recognized") if not query_is_train: return result 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: dist, neigh_ind = result else: neigh_ind = result 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_samples, n_neighbors - 1)) if return_distance: dist = np.reshape( dist[sample_mask], (n_samples, n_neighbors - 1)) return 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_query, n_features), \ or (n_query, 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 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.toarray() array([[ 1., 0., 1.], [ 0., 1., 1.], [ 1., 0., 1.]]) See also -------- NearestNeighbors.radius_neighbors_graph """ if n_neighbors is None: n_neighbors = self.n_neighbors # kneighbors does the None handling. if X is not None: X = check_array(X, accept_sparse='csr') n_samples1 = X.shape[0] else: n_samples1 = self._fit_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': 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) kneighbors_graph = csr_matrix((A_data, A_ind.ravel(), A_indptr), shape=(n_samples1, n_samples2)) return kneighbors_graph class RadiusNeighborsMixin(object): """Mixin for radius-based neighbors searches""" def radius_neighbors(self, X=None, radius=None, return_distance=True): """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 Returns ------- 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. 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) # doctest: +ELLIPSIS NearestNeighbors(algorithm='auto', leaf_size=30, ...) >>> rng = neigh.radius_neighbors([[1., 1., 1.]]) >>> print(np.asarray(rng[0][0])) # doctest: +ELLIPSIS [ 1.5 0.5] >>> print(np.asarray(rng[1][0])) # doctest: +ELLIPSIS [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. """ if self._fit_method is None: raise NotFittedError("Must fit neighbors before querying.") if X is not None: query_is_train = False X = check_array(X, accept_sparse='csr') else: query_is_train = True X = self._fit_X if radius is None: radius = self.radius n_samples = X.shape[0] if self._fit_method == 'brute': # for efficiency, use squared euclidean distances if self.effective_metric_ == 'euclidean': dist = pairwise_distances(X, self._fit_X, 'euclidean', n_jobs=self.n_jobs, squared=True) radius *= radius else: dist = pairwise_distances(X, self._fit_X, self.effective_metric_, n_jobs=self.n_jobs, **self.effective_metric_params_) neigh_ind_list = [np.where(d <= radius)[0] for d in dist] # See https://github.com/numpy/numpy/issues/5456 # if you want to understand why this is initialized this way. neigh_ind = np.empty(n_samples, dtype='object') neigh_ind[:] = neigh_ind_list if return_distance: dist_array = np.empty(n_samples, dtype='object') if self.effective_metric_ == 'euclidean': dist_list = [np.sqrt(d[neigh_ind[i]]) for i, d in enumerate(dist)] else: dist_list = [d[neigh_ind[i]] for i, d in enumerate(dist)] dist_array[:] = dist_list results = dist_array, neigh_ind else: results = 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) results = self._tree.query_radius(X, radius, return_distance=return_distance) if return_distance: results = results[::-1] 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: 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: dist[ind] = dist[ind][mask] if return_distance: return dist, neigh_ind return neigh_ind def radius_neighbors_graph(self, X=None, 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], 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 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.toarray() array([[ 1., 0., 1.], [ 0., 1., 0.], [ 1., 0., 1.]]) See also -------- kneighbors_graph """ if X is not None: X = check_array(X, accept_sparse=['csr', 'csc', 'coo']) n_samples2 = self._fit_X.shape[0] 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) A_data = np.concatenate(list(dist)) else: raise ValueError( 'Unsupported mode, must be one of "connectivity", ' 'or "distance" but got %s instead' % mode) n_samples1 = A_ind.shape[0] 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_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, 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 = check_X_y(X, y, "csr", multi_output=True) self._y = 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, 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 = check_X_y(X, y, "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) class UnsupervisedMixin(object): 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)