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