sklearn.cluster.compute_optics_graph(X, *, min_samples, max_eps, metric, p, metric_params, algorithm, leaf_size, n_jobs)[source]#

Compute the OPTICS reachability graph.

Read more in the User Guide.

X{ndarray, sparse matrix} of shape (n_samples, n_features), or (n_samples, n_samples) if metric=’precomputed’

A feature array, or array of distances between samples if metric=’precomputed’.

min_samplesint > 1 or float between 0 and 1

The number of samples in a neighborhood for a point to be considered as a core point. Expressed as an absolute number or a fraction of the number of samples (rounded to be at least 2).

max_epsfloat, default=np.inf

The maximum distance between two samples for one to be considered as in the neighborhood of the other. Default value of np.inf will identify clusters across all scales; reducing max_eps will result in shorter run times.

metricstr or callable, default=’minkowski’

Metric to use for distance computation. Any metric from scikit-learn or scipy.spatial.distance can be used.

If metric is a callable function, it is called on each pair of instances (rows) and the resulting value recorded. The callable should take two arrays as input and return one value indicating the distance between them. This works for Scipy’s metrics, but is less efficient than passing the metric name as a string. If metric is “precomputed”, X is assumed to be a distance matrix and must be square.

Valid values for metric are:

  • from scikit-learn: [‘cityblock’, ‘cosine’, ‘euclidean’, ‘l1’, ‘l2’, ‘manhattan’]

  • from scipy.spatial.distance: [‘braycurtis’, ‘canberra’, ‘chebyshev’, ‘correlation’, ‘dice’, ‘hamming’, ‘jaccard’, ‘kulsinski’, ‘mahalanobis’, ‘minkowski’, ‘rogerstanimoto’, ‘russellrao’, ‘seuclidean’, ‘sokalmichener’, ‘sokalsneath’, ‘sqeuclidean’, ‘yule’]

See the documentation for scipy.spatial.distance for details on these metrics.


'kulsinski' is deprecated from SciPy 1.9 and will be removed in SciPy 1.11.

pfloat, default=2

Parameter for the Minkowski metric from pairwise_distances. 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_paramsdict, default=None

Additional keyword arguments for the metric function.

algorithm{‘auto’, ‘ball_tree’, ‘kd_tree’, ‘brute’}, default=’auto’

Algorithm used to compute the nearest neighbors:

  • ‘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. (default)

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

leaf_sizeint, default=30

Leaf size passed to BallTree or KDTree. 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.

n_jobsint, 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.

ordering_array of shape (n_samples,)

The cluster ordered list of sample indices.

core_distances_array of shape (n_samples,)

Distance at which each sample becomes a core point, indexed by object order. Points which will never be core have a distance of inf. Use clust.core_distances_[clust.ordering_] to access in cluster order.

reachability_array of shape (n_samples,)

Reachability distances per sample, indexed by object order. Use clust.reachability_[clust.ordering_] to access in cluster order.

predecessor_array of shape (n_samples,)

Point that a sample was reached from, indexed by object order. Seed points have a predecessor of -1.



Ankerst, Mihael, Markus M. Breunig, Hans-Peter Kriegel, and Jörg Sander. “OPTICS: ordering points to identify the clustering structure.” ACM SIGMOD Record 28, no. 2 (1999): 49-60.


>>> import numpy as np
>>> from sklearn.cluster import compute_optics_graph
>>> X = np.array([[1, 2], [2, 5], [3, 6],
...               [8, 7], [8, 8], [7, 3]])
>>> ordering, core_distances, reachability, predecessor = compute_optics_graph(
...     X,
...     min_samples=2,
...     max_eps=np.inf,
...     metric="minkowski",
...     p=2,
...     metric_params=None,
...     algorithm="auto",
...     leaf_size=30,
...     n_jobs=None,
... )
>>> ordering
array([0, 1, 2, 5, 3, 4])
>>> core_distances
array([3.16..., 1.41..., 1.41..., 1.        , 1.        ,
>>> reachability
array([       inf, 3.16..., 1.41..., 4.12..., 1.        ,
       5.        ])
>>> predecessor
array([-1,  0,  1,  5,  3,  2])