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# -*- coding: utf-8 -*-
"""
DBSCAN: Density-Based Spatial Clustering of Applications with Noise
"""
# Author: Robert Layton <robertlayton@gmail.com>
# Joel Nothman <joel.nothman@gmail.com>
# Lars Buitinck
#
# License: BSD 3 clause
import numpy as np
import warnings
from scipy import sparse
from ..base import BaseEstimator, ClusterMixin
from ..utils.validation import _check_sample_weight, _deprecate_positional_args
from ..neighbors import NearestNeighbors
from ._dbscan_inner import dbscan_inner
@_deprecate_positional_args
def dbscan(X, eps=0.5, *, min_samples=5, metric='minkowski',
metric_params=None, algorithm='auto', leaf_size=30, p=2,
sample_weight=None, n_jobs=None):
"""Perform DBSCAN clustering from vector array or distance matrix.
Read more in the :ref:`User Guide <dbscan>`.
Parameters
----------
X : {array-like, sparse (CSR) matrix} of shape (n_samples, n_features) or \
(n_samples, n_samples)
A feature array, or array of distances between samples if
``metric='precomputed'``.
eps : float, default=0.5
The maximum distance between two samples for one to be considered
as in the neighborhood of the other. This is not a maximum bound
on the distances of points within a cluster. This is the most
important DBSCAN parameter to choose appropriately for your data set
and distance function.
min_samples : int, default=5
The number of samples (or total weight) in a neighborhood for a point
to be considered as a core point. This includes the point itself.
metric : string, or callable
The metric to use when calculating distance between instances in a
feature array. If metric is a string or callable, it must be one of
the options allowed by :func:`sklearn.metrics.pairwise_distances` for
its metric parameter.
If metric is "precomputed", X is assumed to be a distance matrix and
must be square during fit.
X may be a :term:`sparse graph <sparse graph>`,
in which case only "nonzero" elements may be considered neighbors.
metric_params : dict, default=None
Additional keyword arguments for the metric function.
.. versionadded:: 0.19
algorithm : {'auto', 'ball_tree', 'kd_tree', 'brute'}, default='auto'
The algorithm to be used by the NearestNeighbors module
to compute pointwise distances and find nearest neighbors.
See NearestNeighbors module documentation for details.
leaf_size : int, 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.
p : float, default=2
The power of the Minkowski metric to be used to calculate distance
between points.
sample_weight : array-like of shape (n_samples,), default=None
Weight of each sample, such that a sample with a weight of at least
``min_samples`` is by itself a core sample; a sample with negative
weight may inhibit its eps-neighbor from being core.
Note that weights are absolute, and default to 1.
n_jobs : int, default=None
The number of parallel jobs to run for neighbors search. ``None`` means
1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means
using all processors. See :term:`Glossary <n_jobs>` for more details.
If precomputed distance are used, parallel execution is not available
and thus n_jobs will have no effect.
Returns
-------
core_samples : ndarray of shape (n_core_samples,)
Indices of core samples.
labels : ndarray of shape (n_samples,)
Cluster labels for each point. Noisy samples are given the label -1.
See also
--------
DBSCAN
An estimator interface for this clustering algorithm.
OPTICS
A similar estimator interface clustering at multiple values of eps. Our
implementation is optimized for memory usage.
Notes
-----
For an example, see :ref:`examples/cluster/plot_dbscan.py
<sphx_glr_auto_examples_cluster_plot_dbscan.py>`.
This implementation bulk-computes all neighborhood queries, which increases
the memory complexity to O(n.d) where d is the average number of neighbors,
while original DBSCAN had memory complexity O(n). It may attract a higher
memory complexity when querying these nearest neighborhoods, depending
on the ``algorithm``.
One way to avoid the query complexity is to pre-compute sparse
neighborhoods in chunks using
:func:`NearestNeighbors.radius_neighbors_graph
<sklearn.neighbors.NearestNeighbors.radius_neighbors_graph>` with
``mode='distance'``, then using ``metric='precomputed'`` here.
Another way to reduce memory and computation time is to remove
(near-)duplicate points and use ``sample_weight`` instead.
:func:`cluster.optics <sklearn.cluster.optics>` provides a similar
clustering with lower memory usage.
References
----------
Ester, M., H. P. Kriegel, J. Sander, and X. Xu, "A Density-Based
Algorithm for Discovering Clusters in Large Spatial Databases with Noise".
In: Proceedings of the 2nd International Conference on Knowledge Discovery
and Data Mining, Portland, OR, AAAI Press, pp. 226-231. 1996
Schubert, E., Sander, J., Ester, M., Kriegel, H. P., & Xu, X. (2017).
DBSCAN revisited, revisited: why and how you should (still) use DBSCAN.
ACM Transactions on Database Systems (TODS), 42(3), 19.
"""
est = DBSCAN(eps=eps, min_samples=min_samples, metric=metric,
metric_params=metric_params, algorithm=algorithm,
leaf_size=leaf_size, p=p, n_jobs=n_jobs)
est.fit(X, sample_weight=sample_weight)
return est.core_sample_indices_, est.labels_
class DBSCAN(ClusterMixin, BaseEstimator):
"""Perform DBSCAN clustering from vector array or distance matrix.
DBSCAN - Density-Based Spatial Clustering of Applications with Noise.
Finds core samples of high density and expands clusters from them.
Good for data which contains clusters of similar density.
Read more in the :ref:`User Guide <dbscan>`.
Parameters
----------
eps : float, default=0.5
The maximum distance between two samples for one to be considered
as in the neighborhood of the other. This is not a maximum bound
on the distances of points within a cluster. This is the most
important DBSCAN parameter to choose appropriately for your data set
and distance function.
min_samples : int, default=5
The number of samples (or total weight) in a neighborhood for a point
to be considered as a core point. This includes the point itself.
metric : string, or callable, default='euclidean'
The metric to use when calculating distance between instances in a
feature array. If metric is a string or callable, it must be one of
the options allowed by :func:`sklearn.metrics.pairwise_distances` for
its metric parameter.
If metric is "precomputed", X is assumed to be a distance matrix and
must be square. X may be a :term:`Glossary <sparse graph>`, in which
case only "nonzero" elements may be considered neighbors for DBSCAN.
.. versionadded:: 0.17
metric *precomputed* to accept precomputed sparse matrix.
metric_params : dict, default=None
Additional keyword arguments for the metric function.
.. versionadded:: 0.19
algorithm : {'auto', 'ball_tree', 'kd_tree', 'brute'}, default='auto'
The algorithm to be used by the NearestNeighbors module
to compute pointwise distances and find nearest neighbors.
See NearestNeighbors module documentation for details.
leaf_size : int, 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.
p : float, default=None
The power of the Minkowski metric to be used to calculate distance
between points.
n_jobs : int, default=None
The number of parallel jobs to run.
``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
``-1`` means using all processors. See :term:`Glossary <n_jobs>`
for more details.
Attributes
----------
core_sample_indices_ : ndarray of shape (n_core_samples,)
Indices of core samples.
components_ : ndarray of shape (n_core_samples, n_features)
Copy of each core sample found by training.
labels_ : ndarray of shape (n_samples)
Cluster labels for each point in the dataset given to fit().
Noisy samples are given the label -1.
Examples
--------
>>> from sklearn.cluster import DBSCAN
>>> import numpy as np
>>> X = np.array([[1, 2], [2, 2], [2, 3],
... [8, 7], [8, 8], [25, 80]])
>>> clustering = DBSCAN(eps=3, min_samples=2).fit(X)
>>> clustering.labels_
array([ 0, 0, 0, 1, 1, -1])
>>> clustering
DBSCAN(eps=3, min_samples=2)
See also
--------
OPTICS
A similar clustering at multiple values of eps. Our implementation
is optimized for memory usage.
Notes
-----
For an example, see :ref:`examples/cluster/plot_dbscan.py
<sphx_glr_auto_examples_cluster_plot_dbscan.py>`.
This implementation bulk-computes all neighborhood queries, which increases
the memory complexity to O(n.d) where d is the average number of neighbors,
while original DBSCAN had memory complexity O(n). It may attract a higher
memory complexity when querying these nearest neighborhoods, depending
on the ``algorithm``.
One way to avoid the query complexity is to pre-compute sparse
neighborhoods in chunks using
:func:`NearestNeighbors.radius_neighbors_graph
<sklearn.neighbors.NearestNeighbors.radius_neighbors_graph>` with
``mode='distance'``, then using ``metric='precomputed'`` here.
Another way to reduce memory and computation time is to remove
(near-)duplicate points and use ``sample_weight`` instead.
:class:`cluster.OPTICS` provides a similar clustering with lower memory
usage.
References
----------
Ester, M., H. P. Kriegel, J. Sander, and X. Xu, "A Density-Based
Algorithm for Discovering Clusters in Large Spatial Databases with Noise".
In: Proceedings of the 2nd International Conference on Knowledge Discovery
and Data Mining, Portland, OR, AAAI Press, pp. 226-231. 1996
Schubert, E., Sander, J., Ester, M., Kriegel, H. P., & Xu, X. (2017).
DBSCAN revisited, revisited: why and how you should (still) use DBSCAN.
ACM Transactions on Database Systems (TODS), 42(3), 19.
"""
@_deprecate_positional_args
def __init__(self, eps=0.5, *, min_samples=5, metric='euclidean',
metric_params=None, algorithm='auto', leaf_size=30, p=None,
n_jobs=None):
self.eps = eps
self.min_samples = min_samples
self.metric = metric
self.metric_params = metric_params
self.algorithm = algorithm
self.leaf_size = leaf_size
self.p = p
self.n_jobs = n_jobs
def fit(self, X, y=None, sample_weight=None):
"""Perform DBSCAN clustering from features, or distance matrix.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features), or \
(n_samples, n_samples)
Training instances to cluster, or distances between instances if
``metric='precomputed'``. If a sparse matrix is provided, it will
be converted into a sparse ``csr_matrix``.
sample_weight : array-like of shape (n_samples,), default=None
Weight of each sample, such that a sample with a weight of at least
``min_samples`` is by itself a core sample; a sample with a
negative weight may inhibit its eps-neighbor from being core.
Note that weights are absolute, and default to 1.
y : Ignored
Not used, present here for API consistency by convention.
Returns
-------
self
"""
X = self._validate_data(X, accept_sparse='csr')
if not self.eps > 0.0:
raise ValueError("eps must be positive.")
if sample_weight is not None:
sample_weight = _check_sample_weight(sample_weight, X)
# Calculate neighborhood for all samples. This leaves the original
# point in, which needs to be considered later (i.e. point i is in the
# neighborhood of point i. While True, its useless information)
if self.metric == 'precomputed' and sparse.issparse(X):
# set the diagonal to explicit values, as a point is its own
# neighbor
with warnings.catch_warnings():
warnings.simplefilter('ignore', sparse.SparseEfficiencyWarning)
X.setdiag(X.diagonal()) # XXX: modifies X's internals in-place
neighbors_model = NearestNeighbors(
radius=self.eps, algorithm=self.algorithm,
leaf_size=self.leaf_size, metric=self.metric,
metric_params=self.metric_params, p=self.p, n_jobs=self.n_jobs)
neighbors_model.fit(X)
# This has worst case O(n^2) memory complexity
neighborhoods = neighbors_model.radius_neighbors(X,
return_distance=False)
if sample_weight is None:
n_neighbors = np.array([len(neighbors)
for neighbors in neighborhoods])
else:
n_neighbors = np.array([np.sum(sample_weight[neighbors])
for neighbors in neighborhoods])
# Initially, all samples are noise.
labels = np.full(X.shape[0], -1, dtype=np.intp)
# A list of all core samples found.
core_samples = np.asarray(n_neighbors >= self.min_samples,
dtype=np.uint8)
dbscan_inner(core_samples, neighborhoods, labels)
self.core_sample_indices_ = np.where(core_samples)[0]
self.labels_ = labels
if len(self.core_sample_indices_):
# fix for scipy sparse indexing issue
self.components_ = X[self.core_sample_indices_].copy()
else:
# no core samples
self.components_ = np.empty((0, X.shape[1]))
return self
def fit_predict(self, X, y=None, sample_weight=None):
"""Perform DBSCAN clustering from features or distance matrix,
and return cluster labels.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features), or \
(n_samples, n_samples)
Training instances to cluster, or distances between instances if
``metric='precomputed'``. If a sparse matrix is provided, it will
be converted into a sparse ``csr_matrix``.
sample_weight : array-like of shape (n_samples,), default=None
Weight of each sample, such that a sample with a weight of at least
``min_samples`` is by itself a core sample; a sample with a
negative weight may inhibit its eps-neighbor from being core.
Note that weights are absolute, and default to 1.
y : Ignored
Not used, present here for API consistency by convention.
Returns
-------
labels : ndarray of shape (n_samples,)
Cluster labels. Noisy samples are given the label -1.
"""
self.fit(X, sample_weight=sample_weight)
return self.labels_