479 lines
18 KiB
Python
479 lines
18 KiB
Python
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"""
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DBSCAN: Density-Based Spatial Clustering of Applications with Noise
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"""
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# Author: Robert Layton <robertlayton@gmail.com>
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# Joel Nothman <joel.nothman@gmail.com>
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# Lars Buitinck
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#
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# License: BSD 3 clause
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import warnings
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from numbers import Integral, Real
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import numpy as np
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from scipy import sparse
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from ..base import BaseEstimator, ClusterMixin, _fit_context
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from ..metrics.pairwise import _VALID_METRICS
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from ..neighbors import NearestNeighbors
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from ..utils._param_validation import Interval, StrOptions, validate_params
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from ..utils.validation import _check_sample_weight
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from ._dbscan_inner import dbscan_inner
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@validate_params(
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{
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"X": ["array-like", "sparse matrix"],
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"sample_weight": ["array-like", None],
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},
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prefer_skip_nested_validation=False,
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)
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def dbscan(
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X,
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eps=0.5,
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*,
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min_samples=5,
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metric="minkowski",
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metric_params=None,
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algorithm="auto",
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leaf_size=30,
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p=2,
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sample_weight=None,
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n_jobs=None,
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):
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"""Perform DBSCAN clustering from vector array or distance matrix.
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Read more in the :ref:`User Guide <dbscan>`.
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Parameters
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----------
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X : {array-like, sparse (CSR) matrix} of shape (n_samples, n_features) or \
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(n_samples, n_samples)
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A feature array, or array of distances between samples if
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``metric='precomputed'``.
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eps : float, default=0.5
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The maximum distance between two samples for one to be considered
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as in the neighborhood of the other. This is not a maximum bound
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on the distances of points within a cluster. This is the most
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important DBSCAN parameter to choose appropriately for your data set
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and distance function.
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min_samples : int, default=5
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The number of samples (or total weight) in a neighborhood for a point
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to be considered as a core point. This includes the point itself.
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metric : str or callable, default='minkowski'
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The metric to use when calculating distance between instances in a
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feature array. If metric is a string or callable, it must be one of
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the options allowed by :func:`sklearn.metrics.pairwise_distances` for
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its metric parameter.
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If metric is "precomputed", X is assumed to be a distance matrix and
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must be square during fit.
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X may be a :term:`sparse graph <sparse graph>`,
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in which case only "nonzero" elements may be considered neighbors.
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metric_params : dict, default=None
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Additional keyword arguments for the metric function.
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.. versionadded:: 0.19
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algorithm : {'auto', 'ball_tree', 'kd_tree', 'brute'}, default='auto'
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The algorithm to be used by the NearestNeighbors module
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to compute pointwise distances and find nearest neighbors.
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See NearestNeighbors module documentation for details.
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leaf_size : int, default=30
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Leaf size passed to BallTree or cKDTree. This can affect the speed
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of the construction and query, as well as the memory required
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to store the tree. The optimal value depends
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on the nature of the problem.
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p : float, default=2
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The power of the Minkowski metric to be used to calculate distance
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between points.
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sample_weight : array-like of shape (n_samples,), default=None
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Weight of each sample, such that a sample with a weight of at least
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``min_samples`` is by itself a core sample; a sample with negative
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weight may inhibit its eps-neighbor from being core.
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Note that weights are absolute, and default to 1.
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n_jobs : int, default=None
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The number of parallel jobs to run for neighbors search. ``None`` means
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1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means
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using all processors. See :term:`Glossary <n_jobs>` for more details.
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If precomputed distance are used, parallel execution is not available
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and thus n_jobs will have no effect.
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Returns
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-------
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core_samples : ndarray of shape (n_core_samples,)
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Indices of core samples.
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labels : ndarray of shape (n_samples,)
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Cluster labels for each point. Noisy samples are given the label -1.
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See Also
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--------
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DBSCAN : An estimator interface for this clustering algorithm.
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OPTICS : A similar estimator interface clustering at multiple values of
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eps. Our implementation is optimized for memory usage.
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Notes
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-----
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For an example, see :ref:`examples/cluster/plot_dbscan.py
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<sphx_glr_auto_examples_cluster_plot_dbscan.py>`.
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This implementation bulk-computes all neighborhood queries, which increases
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the memory complexity to O(n.d) where d is the average number of neighbors,
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while original DBSCAN had memory complexity O(n). It may attract a higher
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memory complexity when querying these nearest neighborhoods, depending
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on the ``algorithm``.
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One way to avoid the query complexity is to pre-compute sparse
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neighborhoods in chunks using
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:func:`NearestNeighbors.radius_neighbors_graph
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<sklearn.neighbors.NearestNeighbors.radius_neighbors_graph>` with
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``mode='distance'``, then using ``metric='precomputed'`` here.
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Another way to reduce memory and computation time is to remove
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(near-)duplicate points and use ``sample_weight`` instead.
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:class:`~sklearn.cluster.OPTICS` provides a similar clustering with lower
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memory usage.
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References
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----------
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Ester, M., H. P. Kriegel, J. Sander, and X. Xu, `"A Density-Based
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Algorithm for Discovering Clusters in Large Spatial Databases with Noise"
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<https://www.dbs.ifi.lmu.de/Publikationen/Papers/KDD-96.final.frame.pdf>`_.
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In: Proceedings of the 2nd International Conference on Knowledge Discovery
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and Data Mining, Portland, OR, AAAI Press, pp. 226-231. 1996
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Schubert, E., Sander, J., Ester, M., Kriegel, H. P., & Xu, X. (2017).
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:doi:`"DBSCAN revisited, revisited: why and how you should (still) use DBSCAN."
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<10.1145/3068335>`
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ACM Transactions on Database Systems (TODS), 42(3), 19.
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Examples
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--------
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>>> from sklearn.cluster import dbscan
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>>> X = [[1, 2], [2, 2], [2, 3], [8, 7], [8, 8], [25, 80]]
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>>> core_samples, labels = dbscan(X, eps=3, min_samples=2)
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>>> core_samples
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array([0, 1, 2, 3, 4])
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>>> labels
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array([ 0, 0, 0, 1, 1, -1])
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"""
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est = DBSCAN(
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eps=eps,
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min_samples=min_samples,
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metric=metric,
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metric_params=metric_params,
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algorithm=algorithm,
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leaf_size=leaf_size,
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p=p,
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n_jobs=n_jobs,
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)
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est.fit(X, sample_weight=sample_weight)
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return est.core_sample_indices_, est.labels_
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class DBSCAN(ClusterMixin, BaseEstimator):
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"""Perform DBSCAN clustering from vector array or distance matrix.
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DBSCAN - Density-Based Spatial Clustering of Applications with Noise.
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Finds core samples of high density and expands clusters from them.
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Good for data which contains clusters of similar density.
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This implementation has a worst case memory complexity of :math:`O({n}^2)`,
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which can occur when the `eps` param is large and `min_samples` is low,
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while the original DBSCAN only uses linear memory.
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For further details, see the Notes below.
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Read more in the :ref:`User Guide <dbscan>`.
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Parameters
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----------
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eps : float, default=0.5
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The maximum distance between two samples for one to be considered
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as in the neighborhood of the other. This is not a maximum bound
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on the distances of points within a cluster. This is the most
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important DBSCAN parameter to choose appropriately for your data set
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and distance function.
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min_samples : int, default=5
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The number of samples (or total weight) in a neighborhood for a point to
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be considered as a core point. This includes the point itself. If
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`min_samples` is set to a higher value, DBSCAN will find denser clusters,
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whereas if it is set to a lower value, the found clusters will be more
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sparse.
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metric : str, or callable, default='euclidean'
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The metric to use when calculating distance between instances in a
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feature array. If metric is a string or callable, it must be one of
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the options allowed by :func:`sklearn.metrics.pairwise_distances` for
|
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its metric parameter.
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If metric is "precomputed", X is assumed to be a distance matrix and
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must be square. X may be a :term:`sparse graph`, in which
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case only "nonzero" elements may be considered neighbors for DBSCAN.
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.. versionadded:: 0.17
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metric *precomputed* to accept precomputed sparse matrix.
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metric_params : dict, default=None
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Additional keyword arguments for the metric function.
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.. versionadded:: 0.19
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algorithm : {'auto', 'ball_tree', 'kd_tree', 'brute'}, default='auto'
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The algorithm to be used by the NearestNeighbors module
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to compute pointwise distances and find nearest neighbors.
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See NearestNeighbors module documentation for details.
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leaf_size : int, default=30
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Leaf size passed to BallTree or cKDTree. This can affect the speed
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of the construction and query, as well as the memory required
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|
|
to store the tree. The optimal value depends
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on the nature of the problem.
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|
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p : float, default=None
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The power of the Minkowski metric to be used to calculate distance
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between points. If None, then ``p=2`` (equivalent to the Euclidean
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distance).
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n_jobs : int, default=None
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The number of parallel jobs to run.
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``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
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``-1`` means using all processors. See :term:`Glossary <n_jobs>`
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for more details.
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Attributes
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----------
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core_sample_indices_ : ndarray of shape (n_core_samples,)
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Indices of core samples.
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components_ : ndarray of shape (n_core_samples, n_features)
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Copy of each core sample found by training.
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labels_ : ndarray of shape (n_samples)
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Cluster labels for each point in the dataset given to fit().
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Noisy samples are given the label -1.
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n_features_in_ : int
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Number of features seen during :term:`fit`.
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.. versionadded:: 0.24
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feature_names_in_ : ndarray of shape (`n_features_in_`,)
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Names of features seen during :term:`fit`. Defined only when `X`
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has feature names that are all strings.
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.. versionadded:: 1.0
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See Also
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--------
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OPTICS : A similar clustering at multiple values of eps. Our implementation
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|
is optimized for memory usage.
|
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|
|
|
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Notes
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-----
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|
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For an example, see :ref:`examples/cluster/plot_dbscan.py
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|
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<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
|
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|
|
memory complexity when querying these nearest neighborhoods, depending
|
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|
|
on the ``algorithm``.
|
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|
|
|
||
|
|
One way to avoid the query complexity is to pre-compute sparse
|
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|
|
neighborhoods in chunks using
|
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|
|
:func:`NearestNeighbors.radius_neighbors_graph
|
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|
|
<sklearn.neighbors.NearestNeighbors.radius_neighbors_graph>` with
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|
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``mode='distance'``, then using ``metric='precomputed'`` here.
|
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|
|
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|
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Another way to reduce memory and computation time is to remove
|
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|
|
(near-)duplicate points and use ``sample_weight`` instead.
|
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|
|
|
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|
|
:class:`~sklearn.cluster.OPTICS` provides a similar clustering with lower memory
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|
|
usage.
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|
|
|
||
|
|
References
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|
|
----------
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|
|
Ester, M., H. P. Kriegel, J. Sander, and X. Xu, `"A Density-Based
|
||
|
|
Algorithm for Discovering Clusters in Large Spatial Databases with Noise"
|
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|
|
<https://www.dbs.ifi.lmu.de/Publikationen/Papers/KDD-96.final.frame.pdf>`_.
|
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|
|
In: Proceedings of the 2nd International Conference on Knowledge Discovery
|
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|
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and Data Mining, Portland, OR, AAAI Press, pp. 226-231. 1996
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|
|
|
||
|
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Schubert, E., Sander, J., Ester, M., Kriegel, H. P., & Xu, X. (2017).
|
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|
|
:doi:`"DBSCAN revisited, revisited: why and how you should (still) use DBSCAN."
|
||
|
|
<10.1145/3068335>`
|
||
|
|
ACM Transactions on Database Systems (TODS), 42(3), 19.
|
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|
|
|
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|
|
Examples
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|
|
--------
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>>> from sklearn.cluster import DBSCAN
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>>> import numpy as np
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>>> X = np.array([[1, 2], [2, 2], [2, 3],
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... [8, 7], [8, 8], [25, 80]])
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>>> clustering = DBSCAN(eps=3, min_samples=2).fit(X)
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>>> clustering.labels_
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array([ 0, 0, 0, 1, 1, -1])
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>>> clustering
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DBSCAN(eps=3, min_samples=2)
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"""
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_parameter_constraints: dict = {
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"eps": [Interval(Real, 0.0, None, closed="neither")],
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"min_samples": [Interval(Integral, 1, None, closed="left")],
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"metric": [
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StrOptions(set(_VALID_METRICS) | {"precomputed"}),
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callable,
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],
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"metric_params": [dict, None],
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"algorithm": [StrOptions({"auto", "ball_tree", "kd_tree", "brute"})],
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"leaf_size": [Interval(Integral, 1, None, closed="left")],
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"p": [Interval(Real, 0.0, None, closed="left"), None],
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"n_jobs": [Integral, None],
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}
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def __init__(
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self,
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eps=0.5,
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*,
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min_samples=5,
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metric="euclidean",
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metric_params=None,
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algorithm="auto",
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leaf_size=30,
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p=None,
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n_jobs=None,
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):
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self.eps = eps
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self.min_samples = min_samples
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self.metric = metric
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self.metric_params = metric_params
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self.algorithm = algorithm
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self.leaf_size = leaf_size
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||
|
|
self.p = p
|
||
|
|
self.n_jobs = n_jobs
|
||
|
|
|
||
|
|
@_fit_context(
|
||
|
|
# DBSCAN.metric is not validated yet
|
||
|
|
prefer_skip_nested_validation=False
|
||
|
|
)
|
||
|
|
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``.
|
||
|
|
|
||
|
|
y : Ignored
|
||
|
|
Not used, present here for API consistency by convention.
|
||
|
|
|
||
|
|
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.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
self : object
|
||
|
|
Returns a fitted instance of self.
|
||
|
|
"""
|
||
|
|
X = self._validate_data(X, accept_sparse="csr")
|
||
|
|
|
||
|
|
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
|
||
|
|
X = X.copy() # copy to avoid in-place modification
|
||
|
|
with warnings.catch_warnings():
|
||
|
|
warnings.simplefilter("ignore", sparse.SparseEfficiencyWarning)
|
||
|
|
X.setdiag(X.diagonal())
|
||
|
|
|
||
|
|
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):
|
||
|
|
"""Compute clusters from a data or distance matrix and predict 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``.
|
||
|
|
|
||
|
|
y : Ignored
|
||
|
|
Not used, present here for API consistency by convention.
|
||
|
|
|
||
|
|
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.
|
||
|
|
|
||
|
|
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_
|
||
|
|
|
||
|
|
def _more_tags(self):
|
||
|
|
return {"pairwise": self.metric == "precomputed"}
|