8.20.1. sklearn.neighbors.NearestNeighbors¶

class sklearn.neighbors.NearestNeighbors(n_neighbors=5, radius=1.0, algorithm='auto', leaf_size=30, warn_on_equidistant=True)¶

Unsupervised learner for implementing neighbor searches.

Parameters :

n_neighbors : int, optional (default = 5)

Number of neighbors to use by default for k_neighbors queries.

radius : float, optional (default = 1.0)

Range of parameter space to use by default for :meth`radius_neighbors` queries.

algorithm : {‘auto’, ‘ball_tree’, ‘kd_tree’, ‘brute’}, optional

Algorithm used to compute the nearest neighbors:

‘ball_tree’ will use BallTree

‘kd_tree’ will use scipy.spatial.cKDtree

‘brute’ will use a brute-force search.

‘auto’ will attempt to decide the most appropriate algorithm based on the values passed to fit method.

Note: fitting on sparse input will override the setting of this parameter, using brute force.

leaf_size : int, optional (default = 30)

Leaf size passed to BallTree or cKDTree. This can affect the speed of the construction and query, as well as the memory required to store the tree. The optimal value depends on the nature of the problem.

warn_on_equidistant : boolean, optional. Defaults to True.

Generate a warning if equidistant neighbors are discarded. For classification or regression based on k-neighbors, if neighbor k and neighbor k+1 have identical distances but different labels, then the result will be dependent on the ordering of the training data. If the fit method is 'kd_tree', no warnings will be generated.

Notes

See Nearest Neighbors in the online documentation for a discussion of the choice of algorithm and leaf_size.

http://en.wikipedia.org/wiki/K-nearest_neighbor_algorithm

Examples

>>> from sklearn.neighbors import NearestNeighbors
>>> samples = [[0, 0, 2], [1, 0, 0], [0, 0, 1]]

>>> neigh = NearestNeighbors(2, 0.4)
>>> neigh.fit(samples)  
NearestNeighbors(...)

>>> neigh.kneighbors([[0, 0, 1.3]], 2, return_distance=False)
array([[2, 0]])

>>> neigh.radius_neighbors([0, 0, 1.3], 0.4, return_distance=False)
array([[2]])

Methods

`fit`(X[, y])	Fit the model using X as training data
`kneighbors`(X[, n_neighbors, return_distance])	Finds the K-neighbors of a point.
`kneighbors_graph`(X[, n_neighbors, mode])	Computes the (weighted) graph of k-Neighbors for points in X
`radius_neighbors`(X[, radius, return_distance])	Finds the neighbors of a point within a given radius.
`radius_neighbors_graph`(X[, radius, mode])	Computes the (weighted) graph of Neighbors for points in X
`set_params`(**params)	Set the parameters of the estimator.

__init__(n_neighbors=5, radius=1.0, algorithm='auto', leaf_size=30, warn_on_equidistant=True)¶

fit(X, y=None)¶

Fit the model using X as training data

Parameters :

X : {array-like, sparse matrix, BallTree, cKDTree}

Training data. If array or matrix, shape = [n_samples, n_features]

kneighbors(X, n_neighbors=None, return_distance=True)¶

Finds the K-neighbors of a point.

Returns distance

Parameters :

X : array-like, last dimension same as that of fit data

The new point.

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 point, 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) 
NearestNeighbors(algorithm='auto', leaf_size=30, ...)
>>> 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]]...)

kneighbors_graph(X, n_neighbors=None, mode='connectivity')¶

Computes the (weighted) graph of k-Neighbors for points in X

Parameters :

X : array-like, shape = [n_samples, n_features]

Sample data

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) 
NearestNeighbors(algorithm='auto', leaf_size=30, ...)
>>> A = neigh.kneighbors_graph(X)
>>> A.todense()
matrix([[ 1.,  0.,  1.],
        [ 0.,  1.,  1.],
        [ 1.,  0.,  1.]])

radius_neighbors(X, radius=None, return_distance=True)¶

Finds the neighbors of a point within a given radius.

Returns distance

Parameters :

X : array-like, last dimension same as that of fit data

The new point.

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

Array representing the lengths to point, only present if return_distance=True

ind : array

Indices of the nearest points in the population matrix.

Examples

In the following example, we construnct 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(radius=1.6)
>>> neigh.fit(samples) 
NearestNeighbors(algorithm='auto', leaf_size=30, ...)
>>> print neigh.radius_neighbors([1., 1., 1.]) 
(array([[ 1.5,  0.5]]...), array([[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. Because the number of neighbors of each point is not necessarily equal, radius_neighbors returns an array of objects, where each object is a 1D array of indices.

radius_neighbors_graph(X, 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]

Sample data

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.

Citing

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8.20.1. sklearn.neighbors.NearestNeighbors¶