"""Base and mixin classes for nearest neighbors"""
# Authors: Jake Vanderplas <vanderplas@astro.washington.edu>
# Fabian Pedregosa <fabian.pedregosa@inria.fr>
# Alexandre Gramfort <alexandre.gramfort@inria.fr>
# Sparseness support by Lars Buitinck
# Multi-output support by Arnaud Joly <a.joly@ulg.ac.be>
#
# 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.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'
elif callable(metric) or metric in VALID_METRICS['ball_tree']:
alg_check = 'ball_tree'
else:
alg_check = 'brute'
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'
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
)
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 = 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
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)
