skhubness.neighbors.kneighbors_graph(X, n_neighbors, mode='connectivity', algorithm: str = 'auto', algorithm_params: dict = None, hubness: str = None, hubness_params: dict = None, metric='minkowski', p=2, metric_params=None, include_self=False, n_jobs=None)[source]

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

Read more in the scikit-learn User Guide

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

Sample data, in the form of a numpy array or a precomputed BallTree.

n_neighbors: int

Number of neighbors for each sample.

mode: {‘connectivity’, ‘distance’}, optional

Type of returned matrix: ‘connectivity’ will return the connectivity matrix with ones and zeros, and ‘distance’ will return the distances between neighbors according to the given metric.

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

Algorithm used to compute the nearest neighbors:

  • ‘hnsw’ will use HNSW

  • ‘lsh’ will use PuffinnLSH

  • ‘falconn_lsh’ will use FalconnLSH

  • ‘ball_tree’ will use BallTree

  • ‘kd_tree’ will use KDTree

  • ‘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.

algorithm_params: dict, optional

Override default parameters of the NN algorithm. For example, with algorithm=’lsh’ and algorithm_params={n_candidates: 100} one hundred approximate neighbors are retrieved with LSH. If parameter hubness is set, the candidate neighbors are further reordered with hubness reduction. Finally, n_neighbors objects are used from the (optionally reordered) candidates.

hubness: {‘mutual_proximity’, ‘local_scaling’, ‘dis_sim_local’, None}, optional

Hubness reduction algorithm

  • ‘mutual_proximity’ or ‘mp’ will use MutualProximity

  • ‘local_scaling’ or ‘ls’ will use LocalScaling

  • ‘dis_sim_local’ or ‘dsl’ will use DisSimLocal

If None, no hubness reduction will be performed (=vanilla kNN).

hubness_params: dict, optional

Override default parameters of the selected hubness reduction algorithm. For example, with hubness=’mp’ and hubness_params={‘method’: ‘normal’} a mutual proximity variant is used, which models distance distributions with independent Gaussians.

metric: string, default ‘minkowski’

The distance metric used to calculate the k-Neighbors for each sample point. The DistanceMetric class gives a list of available metrics. The default distance is ‘euclidean’ (‘minkowski’ metric with the p param equal to 2.)

p: int, default 2

Power parameter for the Minkowski metric. When p = 1, this is equivalent to using manhattan_distance (l1), and euclidean_distance (l2) for p = 2. For arbitrary p, minkowski_distance (l_p) is used.

metric_params: dict, optional

additional keyword arguments for the metric function.

include_self: bool, default=False.

Whether or not to mark each sample as the first nearest neighbor to itself. If None, then True is used for mode=’connectivity’ and False for mode=’distance’ as this will preserve backwards compatibility.

n_jobs: int or None, optional (default=None)

The number of parallel jobs to run for neighbors search. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

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.


>>> X = [[0], [3], [1]]
>>> from skhubness.neighbors import kneighbors_graph
>>> A = kneighbors_graph(X, 2, mode='connectivity', include_self=True)
>>> A.toarray()
array([[1., 0., 1.],
       [0., 1., 1.],
       [1., 0., 1.]])