dbscan_.py

# -*- 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 import check_array, check_consistent_length
from ..neighbors import NearestNeighbors

from ._dbscan_inner import dbscan_inner


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 or sparse (CSR) matrix of shape (n_samples, n_features), or \
            array of shape (n_samples, n_samples)
        A feature array, or array of distances between samples if
        ``metric='precomputed'``.

    eps : float, optional
        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, optional
        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. X may be a sparse matrix, in which case only "nonzero"
        elements may be considered neighbors for DBSCAN.

    metric_params : dict, optional
        Additional keyword arguments for the metric function.

        .. versionadded:: 0.19

    algorithm : {'auto', 'ball_tree', 'kd_tree', 'brute'}, optional
        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, 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.

    p : float, optional
        The power of the Minkowski metric to be used to calculate distance
        between points.

    sample_weight : array, shape (n_samples,), optional
        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 or None, optional (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.

    Returns
    -------
    core_samples : array [n_core_samples]
        Indices of core samples.

    labels : array [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.
    """
    if not eps > 0.0:
        raise ValueError("eps must be positive.")

    X = check_array(X, accept_sparse='csr')
    if sample_weight is not None:
        sample_weight = np.asarray(sample_weight)
        check_consistent_length(X, sample_weight)

    # 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 metric == 'precomputed' and sparse.issparse(X):
        neighborhoods = np.empty(X.shape[0], dtype=object)
        X.sum_duplicates()  # XXX: modifies X's internals in-place

        # 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

        X_mask = X.data <= eps
        masked_indices = X.indices.astype(np.intp, copy=False)[X_mask]
        masked_indptr = np.concatenate(([0], np.cumsum(X_mask)))
        masked_indptr = masked_indptr[X.indptr[1:-1]]

        # split into rows
        neighborhoods[:] = np.split(masked_indices, masked_indptr)
    else:
        neighbors_model = NearestNeighbors(radius=eps, algorithm=algorithm,
                                           leaf_size=leaf_size,
                                           metric=metric,
                                           metric_params=metric_params, p=p,
                                           n_jobs=n_jobs)
        neighbors_model.fit(X)
        # This has worst case O(n^2) memory complexity
        neighborhoods = neighbors_model.radius_neighbors(X, eps,
                                                         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 >= min_samples, dtype=np.uint8)
    dbscan_inner(core_samples, neighborhoods, labels)
    return np.where(core_samples)[0], labels


class DBSCAN(BaseEstimator, ClusterMixin):
    """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, optional
        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, optional
        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. X may be a sparse matrix, 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, optional
        Additional keyword arguments for the metric function.

        .. versionadded:: 0.19

    algorithm : {'auto', 'ball_tree', 'kd_tree', 'brute'}, optional
        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, 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.

    p : float, optional
        The power of the Minkowski metric to be used to calculate distance
        between points.

    n_jobs : int or None, optional (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_ : array, shape = [n_core_samples]
        Indices of core samples.

    components_ : array, shape = [n_core_samples, n_features]
        Copy of each core sample found by training.

    labels_ : array, 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 # doctest: +NORMALIZE_WHITESPACE
    DBSCAN(algorithm='auto', eps=3, leaf_size=30, metric='euclidean',
        metric_params=None, min_samples=2, n_jobs=None, p=None)

    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.
    """

    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 or sparse (CSR) matrix of shape (n_samples, n_features), or \
                array of shape (n_samples, n_samples)
            A feature array, or array of distances between samples if
            ``metric='precomputed'``.
        sample_weight : array, shape (n_samples,), optional
            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.

        y : Ignored

        """
        X = check_array(X, accept_sparse='csr')
        clust = dbscan(X, sample_weight=sample_weight,
                       **self.get_params())
        self.core_sample_indices_, self.labels_ = clust
        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):
        """Performs clustering on X and returns cluster labels.

        Parameters
        ----------
        X : array or sparse (CSR) matrix of shape (n_samples, n_features), or \
                array of shape (n_samples, n_samples)
            A feature array, or array of distances between samples if
            ``metric='precomputed'``.
        sample_weight : array, shape (n_samples,), optional
            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.

        y : Ignored

        Returns
        -------
        y : ndarray, shape (n_samples,)
            cluster labels
        """
        self.fit(X, sample_weight=sample_weight)
        return self.labels_