# sklearn.neighbors.BallTree¶

class sklearn.neighbors.BallTree

BallTree for fast generalized N-point problems

BallTree(X, leaf_size=40, metric=’minkowski’, **kwargs)

Parameters
Xarray-like of shape (n_samples, n_features)

n_samples is the number of points in the data set, and n_features is the dimension of the parameter space. Note: if X is a C-contiguous array of doubles then data will not be copied. Otherwise, an internal copy will be made.

leaf_sizepositive integer (default = 40)

Number of points at which to switch to brute-force. Changing leaf_size will not affect the results of a query, but can significantly impact the speed of a query and the memory required to store the constructed tree. The amount of memory needed to store the tree scales as approximately n_samples / leaf_size. For a specified leaf_size, a leaf node is guaranteed to satisfy leaf_size <= n_points <= 2 * leaf_size, except in the case that n_samples < leaf_size.

metricstring or DistanceMetric object

the distance metric to use for the tree. Default=’minkowski’ with p=2 (that is, a euclidean metric). See the documentation of the DistanceMetric class for a list of available metrics. ball_tree.valid_metrics gives a list of the metrics which are valid for BallTree.

Additional keywords are passed to the distance metric class.
Note: Callable functions in the metric parameter are NOT supported for KDTree
and Ball Tree. Function call overhead will result in very poor performance.
Attributes
datamemory view

The training data

Examples

Query for k-nearest neighbors

>>> import numpy as np
>>> rng = np.random.RandomState(0)
>>> X = rng.random_sample((10, 3))  # 10 points in 3 dimensions
>>> tree = BallTree(X, leaf_size=2)              # doctest: +SKIP
>>> dist, ind = tree.query(X[:1], k=3)                # doctest: +SKIP
>>> print(ind)  # indices of 3 closest neighbors
[0 3 1]
>>> print(dist)  # distances to 3 closest neighbors
[ 0.          0.19662693  0.29473397]


Pickle and Unpickle a tree. Note that the state of the tree is saved in the pickle operation: the tree needs not be rebuilt upon unpickling.

>>> import numpy as np
>>> import pickle
>>> rng = np.random.RandomState(0)
>>> X = rng.random_sample((10, 3))  # 10 points in 3 dimensions
>>> tree = BallTree(X, leaf_size=2)        # doctest: +SKIP
>>> s = pickle.dumps(tree)                     # doctest: +SKIP
>>> tree_copy = pickle.loads(s)                # doctest: +SKIP
>>> dist, ind = tree_copy.query(X[:1], k=3)     # doctest: +SKIP
>>> print(ind)  # indices of 3 closest neighbors
[0 3 1]
>>> print(dist)  # distances to 3 closest neighbors
[ 0.          0.19662693  0.29473397]


Query for neighbors within a given radius

>>> import numpy as np
>>> rng = np.random.RandomState(0)
>>> X = rng.random_sample((10, 3))  # 10 points in 3 dimensions
>>> tree = BallTree(X, leaf_size=2)     # doctest: +SKIP
3
>>> ind = tree.query_radius(X[:1], r=0.3)  # doctest: +SKIP
>>> print(ind)  # indices of neighbors within distance 0.3
[3 0 1]


Compute a gaussian kernel density estimate:

>>> import numpy as np
>>> rng = np.random.RandomState(42)
>>> X = rng.random_sample((100, 3))
>>> tree = BallTree(X)                # doctest: +SKIP
>>> tree.kernel_density(X[:3], h=0.1, kernel='gaussian')
array([ 6.94114649,  7.83281226,  7.2071716 ])


Compute a two-point auto-correlation function

>>> import numpy as np
>>> rng = np.random.RandomState(0)
>>> X = rng.random_sample((30, 3))
>>> r = np.linspace(0, 1, 5)
>>> tree = BallTree(X)                # doctest: +SKIP
>>> tree.two_point_correlation(X, r)
array([ 30,  62, 278, 580, 820])


Methods

 kernel_density(self, X, h[, kernel, atol, …]) Compute the kernel density estimate at points X with the given kernel, using the distance metric specified at tree creation. query(X[, k, return_distance, dualtree, …]) query the tree for the k nearest neighbors query_radius(self, X, r, count_only = False): Compute the two-point correlation function
 get_arrays get_n_calls get_tree_stats reset_n_calls
__init__(self, /, *args, **kwargs)

Initialize self. See help(type(self)) for accurate signature.

kernel_density(self, X, h, kernel='gaussian', atol=0, rtol=1E-8, breadth_first=True, return_log=False)

Compute the kernel density estimate at points X with the given kernel, using the distance metric specified at tree creation.

Parameters
Xarray-like of shape (n_samples, n_features)

An array of points to query. Last dimension should match dimension of training data.

hfloat

the bandwidth of the kernel

kernelstring

specify the kernel to use. Options are - ‘gaussian’ - ‘tophat’ - ‘epanechnikov’ - ‘exponential’ - ‘linear’ - ‘cosine’ Default is kernel = ‘gaussian’

atol, rtolfloat (default = 0)

Specify the desired relative and absolute tolerance of the result. If the true result is K_true, then the returned result K_ret satisfies abs(K_true - K_ret) < atol + rtol * K_ret The default is zero (i.e. machine precision) for both.

if True, use a breadth-first search. If False (default) use a depth-first search. Breadth-first is generally faster for compact kernels and/or high tolerances.

return_logboolean (default = False)

return the logarithm of the result. This can be more accurate than returning the result itself for narrow kernels.

Returns
densityndarray

The array of (log)-density evaluations, shape = X.shape[:-1]

query(X, k=1, return_distance=True, dualtree=False, breadth_first=False)

query the tree for the k nearest neighbors

Parameters
Xarray-like of shape (n_samples, n_features)

An array of points to query

kinteger (default = 1)

The number of nearest neighbors to return

return_distanceboolean (default = True)

if True, return a tuple (d, i) of distances and indices if False, return array i

dualtreeboolean (default = False)

if True, use the dual tree formalism for the query: a tree is built for the query points, and the pair of trees is used to efficiently search this space. This can lead to better performance as the number of points grows large.

if True, then query the nodes in a breadth-first manner. Otherwise, query the nodes in a depth-first manner.

sort_resultsboolean (default = True)

if True, then distances and indices of each point are sorted on return, so that the first column contains the closest points. Otherwise, neighbors are returned in an arbitrary order.

Returns
iif return_distance == False
(d,i)if return_distance == True
darray of doubles - shape: x.shape[:-1] + (k,)

each entry gives the list of distances to the neighbors of the corresponding point

iarray of integers - shape: x.shape[:-1] + (k,)

each entry gives the list of indices of neighbors of the corresponding point

query_radius()

query_radius(self, X, r, count_only = False):

query the tree for neighbors within a radius r

Parameters
Xarray-like of shape (n_samples, n_features)

An array of points to query

rdistance within which neighbors are returned

r can be a single value, or an array of values of shape x.shape[:-1] if different radii are desired for each point.

return_distanceboolean (default = False)

if True, return distances to neighbors of each point if False, return only neighbors Note that unlike the query() method, setting return_distance=True here adds to the computation time. Not all distances need to be calculated explicitly for return_distance=False. Results are not sorted by default: see sort_results keyword.

count_onlyboolean (default = False)

if True, return only the count of points within distance r if False, return the indices of all points within distance r If return_distance==True, setting count_only=True will result in an error.

sort_resultsboolean (default = 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.

Returns
countif count_only == True
indif count_only == False and return_distance == False
(ind, dist)if count_only == False and return_distance == True
countarray of integers, shape = X.shape[:-1]

each entry gives the number of neighbors within a distance r of the corresponding point.

indarray of objects, shape = X.shape[:-1]

each element is a numpy integer array listing the indices of neighbors of the corresponding point. Note that unlike the results of a k-neighbors query, the returned neighbors are not sorted by distance by default.

distarray of objects, shape = X.shape[:-1]

each element is a numpy double array listing the distances corresponding to indices in i.

two_point_correlation()

Compute the two-point correlation function

Parameters
Xarray-like of shape (n_samples, n_features)

An array of points to query. Last dimension should match dimension of training data.

rarray_like

A one-dimensional array of distances

dualtreeboolean (default = False)

If true, use a dualtree algorithm. Otherwise, use a single-tree algorithm. Dual tree algorithms can have better scaling for large N.

Returns
countsndarray

counts[i] contains the number of pairs of points with distance less than or equal to r[i]