537 lines
18 KiB
Python
537 lines
18 KiB
Python
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"""Mean shift clustering algorithm.
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Mean shift clustering aims to discover *blobs* in a smooth density of
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samples. It is a centroid based algorithm, which works by updating candidates
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for centroids to be the mean of the points within a given region. These
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candidates are then filtered in a post-processing stage to eliminate
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near-duplicates to form the final set of centroids.
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Seeding is performed using a binning technique for scalability.
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"""
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# Authors: Conrad Lee <conradlee@gmail.com>
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# Alexandre Gramfort <alexandre.gramfort@inria.fr>
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# Gael Varoquaux <gael.varoquaux@normalesup.org>
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# Martino Sorbaro <martino.sorbaro@ed.ac.uk>
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import numpy as np
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import warnings
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from numbers import Integral, Real
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from collections import defaultdict
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from ..utils._param_validation import Interval
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from ..utils.validation import check_is_fitted
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from ..utils.parallel import delayed, Parallel
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from ..utils import check_random_state, gen_batches, check_array
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from ..base import BaseEstimator, ClusterMixin
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from ..neighbors import NearestNeighbors
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from ..metrics.pairwise import pairwise_distances_argmin
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from .._config import config_context
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def estimate_bandwidth(X, *, quantile=0.3, n_samples=None, random_state=0, n_jobs=None):
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"""Estimate the bandwidth to use with the mean-shift algorithm.
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That this function takes time at least quadratic in n_samples. For large
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datasets, it's wise to set that parameter to a small value.
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Parameters
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----------
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X : array-like of shape (n_samples, n_features)
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Input points.
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quantile : float, default=0.3
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Should be between [0, 1]
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0.5 means that the median of all pairwise distances is used.
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n_samples : int, default=None
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The number of samples to use. If not given, all samples are used.
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random_state : int, RandomState instance, default=None
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The generator used to randomly select the samples from input points
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for bandwidth estimation. Use an int to make the randomness
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deterministic.
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See :term:`Glossary <random_state>`.
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n_jobs : int, default=None
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The number of parallel jobs to run for neighbors search.
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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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Returns
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-------
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bandwidth : float
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The bandwidth parameter.
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"""
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X = check_array(X)
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random_state = check_random_state(random_state)
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if n_samples is not None:
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idx = random_state.permutation(X.shape[0])[:n_samples]
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X = X[idx]
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n_neighbors = int(X.shape[0] * quantile)
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if n_neighbors < 1: # cannot fit NearestNeighbors with n_neighbors = 0
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n_neighbors = 1
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nbrs = NearestNeighbors(n_neighbors=n_neighbors, n_jobs=n_jobs)
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nbrs.fit(X)
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bandwidth = 0.0
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for batch in gen_batches(len(X), 500):
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d, _ = nbrs.kneighbors(X[batch, :], return_distance=True)
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bandwidth += np.max(d, axis=1).sum()
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return bandwidth / X.shape[0]
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# separate function for each seed's iterative loop
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def _mean_shift_single_seed(my_mean, X, nbrs, max_iter):
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# For each seed, climb gradient until convergence or max_iter
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bandwidth = nbrs.get_params()["radius"]
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stop_thresh = 1e-3 * bandwidth # when mean has converged
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completed_iterations = 0
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while True:
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# Find mean of points within bandwidth
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i_nbrs = nbrs.radius_neighbors([my_mean], bandwidth, return_distance=False)[0]
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points_within = X[i_nbrs]
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if len(points_within) == 0:
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break # Depending on seeding strategy this condition may occur
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my_old_mean = my_mean # save the old mean
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my_mean = np.mean(points_within, axis=0)
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# If converged or at max_iter, adds the cluster
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if (
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np.linalg.norm(my_mean - my_old_mean) < stop_thresh
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or completed_iterations == max_iter
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):
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break
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completed_iterations += 1
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return tuple(my_mean), len(points_within), completed_iterations
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def mean_shift(
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X,
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*,
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bandwidth=None,
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seeds=None,
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bin_seeding=False,
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min_bin_freq=1,
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cluster_all=True,
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max_iter=300,
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n_jobs=None,
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):
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"""Perform mean shift clustering of data using a flat kernel.
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Read more in the :ref:`User Guide <mean_shift>`.
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Parameters
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----------
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X : array-like of shape (n_samples, n_features)
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Input data.
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bandwidth : float, default=None
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Kernel bandwidth.
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If bandwidth is not given, it is determined using a heuristic based on
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the median of all pairwise distances. This will take quadratic time in
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the number of samples. The sklearn.cluster.estimate_bandwidth function
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can be used to do this more efficiently.
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seeds : array-like of shape (n_seeds, n_features) or None
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Point used as initial kernel locations. If None and bin_seeding=False,
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each data point is used as a seed. If None and bin_seeding=True,
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see bin_seeding.
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bin_seeding : bool, default=False
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If true, initial kernel locations are not locations of all
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points, but rather the location of the discretized version of
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points, where points are binned onto a grid whose coarseness
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corresponds to the bandwidth. Setting this option to True will speed
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up the algorithm because fewer seeds will be initialized.
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Ignored if seeds argument is not None.
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min_bin_freq : int, default=1
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To speed up the algorithm, accept only those bins with at least
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min_bin_freq points as seeds.
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cluster_all : bool, default=True
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If true, then all points are clustered, even those orphans that are
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not within any kernel. Orphans are assigned to the nearest kernel.
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If false, then orphans are given cluster label -1.
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max_iter : int, default=300
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Maximum number of iterations, per seed point before the clustering
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operation terminates (for that seed point), if has not converged yet.
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n_jobs : int, default=None
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The number of jobs to use for the computation. The following tasks benefit
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from the parallelization:
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- The search of nearest neighbors for bandwidth estimation and label
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assignments. See the details in the docstring of the
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``NearestNeighbors`` class.
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- Hill-climbing optimization for all seeds.
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See :term:`Glossary <n_jobs>` for more details.
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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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.. versionadded:: 0.17
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Parallel Execution using *n_jobs*.
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Returns
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-------
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cluster_centers : ndarray of shape (n_clusters, n_features)
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Coordinates of cluster centers.
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labels : ndarray of shape (n_samples,)
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Cluster labels for each point.
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Notes
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-----
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For an example, see :ref:`examples/cluster/plot_mean_shift.py
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<sphx_glr_auto_examples_cluster_plot_mean_shift.py>`.
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"""
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model = MeanShift(
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bandwidth=bandwidth,
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seeds=seeds,
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min_bin_freq=min_bin_freq,
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bin_seeding=bin_seeding,
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cluster_all=cluster_all,
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n_jobs=n_jobs,
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max_iter=max_iter,
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).fit(X)
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return model.cluster_centers_, model.labels_
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def get_bin_seeds(X, bin_size, min_bin_freq=1):
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"""Find seeds for mean_shift.
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Finds seeds by first binning data onto a grid whose lines are
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spaced bin_size apart, and then choosing those bins with at least
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min_bin_freq points.
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Parameters
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----------
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X : array-like of shape (n_samples, n_features)
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Input points, the same points that will be used in mean_shift.
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bin_size : float
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Controls the coarseness of the binning. Smaller values lead
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to more seeding (which is computationally more expensive). If you're
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not sure how to set this, set it to the value of the bandwidth used
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in clustering.mean_shift.
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min_bin_freq : int, default=1
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Only bins with at least min_bin_freq will be selected as seeds.
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Raising this value decreases the number of seeds found, which
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makes mean_shift computationally cheaper.
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Returns
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-------
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bin_seeds : array-like of shape (n_samples, n_features)
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Points used as initial kernel positions in clustering.mean_shift.
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"""
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if bin_size == 0:
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return X
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# Bin points
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bin_sizes = defaultdict(int)
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for point in X:
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binned_point = np.round(point / bin_size)
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bin_sizes[tuple(binned_point)] += 1
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# Select only those bins as seeds which have enough members
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bin_seeds = np.array(
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[point for point, freq in bin_sizes.items() if freq >= min_bin_freq],
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dtype=np.float32,
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)
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if len(bin_seeds) == len(X):
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warnings.warn(
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"Binning data failed with provided bin_size=%f, using data points as seeds."
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% bin_size
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)
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return X
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bin_seeds = bin_seeds * bin_size
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return bin_seeds
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class MeanShift(ClusterMixin, BaseEstimator):
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"""Mean shift clustering using a flat kernel.
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Mean shift clustering aims to discover "blobs" in a smooth density of
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samples. It is a centroid-based algorithm, which works by updating
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candidates for centroids to be the mean of the points within a given
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region. These candidates are then filtered in a post-processing stage to
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eliminate near-duplicates to form the final set of centroids.
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Seeding is performed using a binning technique for scalability.
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Read more in the :ref:`User Guide <mean_shift>`.
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Parameters
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----------
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bandwidth : float, default=None
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Bandwidth used in the flat kernel.
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If not given, the bandwidth is estimated using
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sklearn.cluster.estimate_bandwidth; see the documentation for that
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function for hints on scalability (see also the Notes, below).
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seeds : array-like of shape (n_samples, n_features), default=None
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Seeds used to initialize kernels. If not set,
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the seeds are calculated by clustering.get_bin_seeds
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with bandwidth as the grid size and default values for
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other parameters.
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bin_seeding : bool, default=False
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If true, initial kernel locations are not locations of all
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points, but rather the location of the discretized version of
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points, where points are binned onto a grid whose coarseness
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corresponds to the bandwidth. Setting this option to True will speed
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up the algorithm because fewer seeds will be initialized.
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The default value is False.
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Ignored if seeds argument is not None.
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min_bin_freq : int, default=1
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To speed up the algorithm, accept only those bins with at least
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min_bin_freq points as seeds.
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cluster_all : bool, default=True
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If true, then all points are clustered, even those orphans that are
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not within any kernel. Orphans are assigned to the nearest kernel.
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If false, then orphans are given cluster label -1.
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n_jobs : int, default=None
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The number of jobs to use for the computation. The following tasks benefit
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from the parallelization:
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- The search of nearest neighbors for bandwidth estimation and label
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assignments. See the details in the docstring of the
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``NearestNeighbors`` class.
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- Hill-climbing optimization for all seeds.
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See :term:`Glossary <n_jobs>` for more details.
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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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max_iter : int, default=300
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Maximum number of iterations, per seed point before the clustering
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operation terminates (for that seed point), if has not converged yet.
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.. versionadded:: 0.22
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Attributes
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----------
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cluster_centers_ : ndarray of shape (n_clusters, n_features)
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Coordinates of cluster centers.
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labels_ : ndarray of shape (n_samples,)
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Labels of each point.
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n_iter_ : int
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Maximum number of iterations performed on each seed.
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.. versionadded:: 0.22
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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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KMeans : K-Means clustering.
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Notes
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-----
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Scalability:
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Because this implementation uses a flat kernel and
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a Ball Tree to look up members of each kernel, the complexity will tend
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towards O(T*n*log(n)) in lower dimensions, with n the number of samples
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and T the number of points. In higher dimensions the complexity will
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tend towards O(T*n^2).
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Scalability can be boosted by using fewer seeds, for example by using
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a higher value of min_bin_freq in the get_bin_seeds function.
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Note that the estimate_bandwidth function is much less scalable than the
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mean shift algorithm and will be the bottleneck if it is used.
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References
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----------
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Dorin Comaniciu and Peter Meer, "Mean Shift: A robust approach toward
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feature space analysis". IEEE Transactions on Pattern Analysis and
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Machine Intelligence. 2002. pp. 603-619.
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Examples
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--------
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>>> from sklearn.cluster import MeanShift
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>>> import numpy as np
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>>> X = np.array([[1, 1], [2, 1], [1, 0],
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... [4, 7], [3, 5], [3, 6]])
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>>> clustering = MeanShift(bandwidth=2).fit(X)
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>>> clustering.labels_
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array([1, 1, 1, 0, 0, 0])
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>>> clustering.predict([[0, 0], [5, 5]])
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array([1, 0])
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>>> clustering
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MeanShift(bandwidth=2)
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"""
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_parameter_constraints: dict = {
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"bandwidth": [Interval(Real, 0, None, closed="neither"), None],
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"seeds": ["array-like", None],
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"bin_seeding": ["boolean"],
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"min_bin_freq": [Interval(Integral, 1, None, closed="left")],
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"cluster_all": ["boolean"],
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"n_jobs": [Integral, None],
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"max_iter": [Interval(Integral, 0, None, closed="left")],
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}
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def __init__(
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self,
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*,
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bandwidth=None,
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seeds=None,
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bin_seeding=False,
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min_bin_freq=1,
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cluster_all=True,
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n_jobs=None,
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max_iter=300,
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):
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self.bandwidth = bandwidth
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self.seeds = seeds
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self.bin_seeding = bin_seeding
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self.cluster_all = cluster_all
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self.min_bin_freq = min_bin_freq
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self.n_jobs = n_jobs
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self.max_iter = max_iter
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def fit(self, X, y=None):
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"""Perform clustering.
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Parameters
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----------
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X : array-like of shape (n_samples, n_features)
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Samples to cluster.
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y : Ignored
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Not used, present for API consistency by convention.
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Returns
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-------
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self : object
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Fitted instance.
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"""
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self._validate_params()
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X = self._validate_data(X)
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bandwidth = self.bandwidth
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if bandwidth is None:
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bandwidth = estimate_bandwidth(X, n_jobs=self.n_jobs)
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seeds = self.seeds
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if seeds is None:
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if self.bin_seeding:
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seeds = get_bin_seeds(X, bandwidth, self.min_bin_freq)
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else:
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seeds = X
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n_samples, n_features = X.shape
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center_intensity_dict = {}
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# We use n_jobs=1 because this will be used in nested calls under
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# parallel calls to _mean_shift_single_seed so there is no need for
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# for further parallelism.
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nbrs = NearestNeighbors(radius=bandwidth, n_jobs=1).fit(X)
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# execute iterations on all seeds in parallel
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all_res = Parallel(n_jobs=self.n_jobs)(
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delayed(_mean_shift_single_seed)(seed, X, nbrs, self.max_iter)
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for seed in seeds
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)
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# copy results in a dictionary
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for i in range(len(seeds)):
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if all_res[i][1]: # i.e. len(points_within) > 0
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center_intensity_dict[all_res[i][0]] = all_res[i][1]
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self.n_iter_ = max([x[2] for x in all_res])
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if not center_intensity_dict:
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# nothing near seeds
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raise ValueError(
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"No point was within bandwidth=%f of any seed. Try a different seeding"
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" strategy or increase the bandwidth."
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% bandwidth
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)
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# POST PROCESSING: remove near duplicate points
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# If the distance between two kernels is less than the bandwidth,
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# then we have to remove one because it is a duplicate. Remove the
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# one with fewer points.
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sorted_by_intensity = sorted(
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center_intensity_dict.items(),
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key=lambda tup: (tup[1], tup[0]),
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reverse=True,
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)
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sorted_centers = np.array([tup[0] for tup in sorted_by_intensity])
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unique = np.ones(len(sorted_centers), dtype=bool)
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nbrs = NearestNeighbors(radius=bandwidth, n_jobs=self.n_jobs).fit(
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sorted_centers
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)
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for i, center in enumerate(sorted_centers):
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if unique[i]:
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neighbor_idxs = nbrs.radius_neighbors([center], return_distance=False)[
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0
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]
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unique[neighbor_idxs] = 0
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unique[i] = 1 # leave the current point as unique
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cluster_centers = sorted_centers[unique]
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# ASSIGN LABELS: a point belongs to the cluster that it is closest to
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nbrs = NearestNeighbors(n_neighbors=1, n_jobs=self.n_jobs).fit(cluster_centers)
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labels = np.zeros(n_samples, dtype=int)
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distances, idxs = nbrs.kneighbors(X)
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if self.cluster_all:
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labels = idxs.flatten()
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else:
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labels.fill(-1)
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bool_selector = distances.flatten() <= bandwidth
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labels[bool_selector] = idxs.flatten()[bool_selector]
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self.cluster_centers_, self.labels_ = cluster_centers, labels
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return self
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def predict(self, X):
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"""Predict the closest cluster each sample in X belongs to.
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Parameters
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----------
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X : array-like of shape (n_samples, n_features)
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New data to predict.
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Returns
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-------
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labels : ndarray of shape (n_samples,)
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Index of the cluster each sample belongs to.
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"""
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check_is_fitted(self)
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X = self._validate_data(X, reset=False)
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with config_context(assume_finite=True):
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return pairwise_distances_argmin(X, self.cluster_centers_)
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