"""Affinity Propagation clustering algorithm."""
# Author: Alexandre Gramfort alexandre.gramfort@inria.fr
# Gael Varoquaux gael.varoquaux@normalesup.org
# License: BSD 3 clause
import numpy as np
from ..base import BaseEstimator, ClusterMixin
from ..utils import as_float_array, check_array
from ..utils.validation import check_is_fitted
from ..metrics import euclidean_distances
from ..metrics import pairwise_distances_argmin
def affinity_propagation(S, preference=None, convergence_iter=15, max_iter=200,
damping=0.5, copy=True, verbose=False,
return_n_iter=False):
"""Perform Affinity Propagation Clustering of data
Read more in the :ref:`User Guide <affinity_propagation>`.
Parameters
----------
S : array-like, shape (n_samples, n_samples)
Matrix of similarities between points
preference : array-like, shape (n_samples,) or float, optional
Preferences for each point - points with larger values of
preferences are more likely to be chosen as exemplars. The number of
exemplars, i.e. of clusters, is influenced by the input preferences
value. If the preferences are not passed as arguments, they will be
set to the median of the input similarities (resulting in a moderate
number of clusters). For a smaller amount of clusters, this can be set
to the minimum value of the similarities.
convergence_iter : int, optional, default: 15
Number of iterations with no change in the number
of estimated clusters that stops the convergence.
max_iter : int, optional, default: 200
Maximum number of iterations
damping : float, optional, default: 0.5
Damping factor between 0.5 and 1.
copy : boolean, optional, default: True
If copy is False, the affinity matrix is modified inplace by the
algorithm, for memory efficiency
verbose : boolean, optional, default: False
The verbosity level
return_n_iter : bool, default False
Whether or not to return the number of iterations.
Returns
-------
cluster_centers_indices : array, shape (n_clusters,)
index of clusters centers
labels : array, shape (n_samples,)
cluster labels for each point
n_iter : int
number of iterations run. Returned only if `return_n_iter` is
set to True.
Notes
-----
For an example, see :ref:`examples/cluster/plot_affinity_propagation.py
<sphx_glr_auto_examples_cluster_plot_affinity_propagation.py>`.
References
----------
Brendan J. Frey and Delbert Dueck, "Clustering by Passing Messages
Between Data Points", Science Feb. 2007
"""
S = as_float_array(S, copy=copy)
n_samples = S.shape[0]
if S.shape[0] != S.shape[1]:
raise ValueError("S must be a square array (shape=%s)" % repr(S.shape))
if preference is None:
preference = np.median(S)
if damping < 0.5 or damping >= 1:
raise ValueError('damping must be >= 0.5 and < 1')
random_state = np.random.RandomState(0)
# Place preference on the diagonal of S
S.flat[::(n_samples + 1)] = preference
A = np.zeros((n_samples, n_samples))
R = np.zeros((n_samples, n_samples)) # Initialize messages
# Intermediate results
tmp = np.zeros((n_samples, n_samples))
# Remove degeneracies
S += ((np.finfo(np.double).eps * S + np.finfo(np.double).tiny * 100) *
random_state.randn(n_samples, n_samples))
# Execute parallel affinity propagation updates
e = np.zeros((n_samples, convergence_iter))
ind = np.arange(n_samples)
for it in range(max_iter):
# tmp = A + S; compute responsibilities
np.add(A, S, tmp)
I = np.argmax(tmp, axis=1)
Y = tmp[ind, I] # np.max(A + S, axis=1)
tmp[ind, I] = -np.inf
Y2 = np.max(tmp, axis=1)
# tmp = Rnew
np.subtract(S, Y[:, None], tmp)
tmp[ind, I] = S[ind, I] - Y2
# Damping
tmp *= 1 - damping
R *= damping
R += tmp
# tmp = Rp; compute availabilities
np.maximum(R, 0, tmp)
tmp.flat[::n_samples + 1] = R.flat[::n_samples + 1]
# tmp = -Anew
tmp -= np.sum(tmp, axis=0)
dA = np.diag(tmp).copy()
tmp.clip(0, np.inf, tmp)
tmp.flat[::n_samples + 1] = dA
# Damping
tmp *= 1 - damping
A *= damping
A -= tmp
# Check for convergence
E = (np.diag(A) + np.diag(R)) > 0
e[:, it % convergence_iter] = E
K = np.sum(E, axis=0)
if it >= convergence_iter:
se = np.sum(e, axis=1)
unconverged = (np.sum((se == convergence_iter) + (se == 0))
!= n_samples)
if (not unconverged and (K > 0)) or (it == max_iter):
if verbose:
print("Converged after %d iterations." % it)
break
else:
if verbose:
print("Did not converge")
I = np.where(np.diag(A + R) > 0)[0]
K = I.size # Identify exemplars
if K > 0:
c = np.argmax(S[:, I], axis=1)
c[I] = np.arange(K) # Identify clusters
# Refine the final set of exemplars and clusters and return results
for k in range(K):
ii = np.where(c == k)[0]
j = np.argmax(np.sum(S[ii[:, np.newaxis], ii], axis=0))
I[k] = ii[j]
c = np.argmax(S[:, I], axis=1)
c[I] = np.arange(K)
labels = I[c]
# Reduce labels to a sorted, gapless, list
cluster_centers_indices = np.unique(labels)
labels = np.searchsorted(cluster_centers_indices, labels)
else:
labels = np.empty((n_samples, 1))
cluster_centers_indices = None
labels.fill(np.nan)
if return_n_iter:
return cluster_centers_indices, labels, it + 1
else:
return cluster_centers_indices, labels
###############################################################################
class AffinityPropagation(BaseEstimator, ClusterMixin):
"""Perform Affinity Propagation Clustering of data.
Read more in the :ref:`User Guide <affinity_propagation>`.
Parameters
----------
damping : float, optional, default: 0.5
Damping factor (between 0.5 and 1) is the extent to
which the current value is maintained relative to
incoming values (weighted 1 - damping). This in order
to avoid numerical oscillations when updating these
values (messages).
max_iter : int, optional, default: 200
Maximum number of iterations.
convergence_iter : int, optional, default: 15
Number of iterations with no change in the number
of estimated clusters that stops the convergence.
copy : boolean, optional, default: True
Make a copy of input data.
preference : array-like, shape (n_samples,) or float, optional
Preferences for each point - points with larger values of
preferences are more likely to be chosen as exemplars. The number
of exemplars, ie of clusters, is influenced by the input
preferences value. If the preferences are not passed as arguments,
they will be set to the median of the input similarities.
affinity : string, optional, default=``euclidean``
Which affinity to use. At the moment ``precomputed`` and
``euclidean`` are supported. ``euclidean`` uses the
negative squared euclidean distance between points.
verbose : boolean, optional, default: False
Whether to be verbose.
Attributes
----------
cluster_centers_indices_ : array, shape (n_clusters,)
Indices of cluster centers
cluster_centers_ : array, shape (n_clusters, n_features)
Cluster centers (if affinity != ``precomputed``).
labels_ : array, shape (n_samples,)
Labels of each point
affinity_matrix_ : array, shape (n_samples, n_samples)
Stores the affinity matrix used in ``fit``.
n_iter_ : int
Number of iterations taken to converge.
Notes
-----
For an example, see :ref:`examples/cluster/plot_affinity_propagation.py
<sphx_glr_auto_examples_cluster_plot_affinity_propagation.py>`.
The algorithmic complexity of affinity propagation is quadratic
in the number of points.
References
----------
Brendan J. Frey and Delbert Dueck, "Clustering by Passing Messages
Between Data Points", Science Feb. 2007
"""
def __init__(self, damping=.5, max_iter=200, convergence_iter=15,
copy=True, preference=None, affinity='euclidean',
verbose=False):
self.damping = damping
self.max_iter = max_iter
self.convergence_iter = convergence_iter
self.copy = copy
self.verbose = verbose
self.preference = preference
self.affinity = affinity
@property
def _pairwise(self):
return self.affinity == "precomputed"
[docs] def fit(self, X, y=None):
""" Create affinity matrix from negative euclidean distances, then
apply affinity propagation clustering.
Parameters
----------
X : array-like, shape (n_samples, n_features) or (n_samples, n_samples)
Data matrix or, if affinity is ``precomputed``, matrix of
similarities / affinities.
y : Ignored
"""
X = check_array(X, accept_sparse='csr')
if self.affinity == "precomputed":
self.affinity_matrix_ = X
elif self.affinity == "euclidean":
self.affinity_matrix_ = -euclidean_distances(X, squared=True)
else:
raise ValueError("Affinity must be 'precomputed' or "
"'euclidean'. Got %s instead"
% str(self.affinity))
self.cluster_centers_indices_, self.labels_, self.n_iter_ = \
affinity_propagation(
self.affinity_matrix_, self.preference, max_iter=self.max_iter,
convergence_iter=self.convergence_iter, damping=self.damping,
copy=self.copy, verbose=self.verbose, return_n_iter=True)
if self.affinity != "precomputed":
self.cluster_centers_ = X[self.cluster_centers_indices_].copy()
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_indices_")
if not hasattr(self, "cluster_centers_"):
raise ValueError("Predict method is not supported when "
"affinity='precomputed'.")
return pairwise_distances_argmin(X, self.cluster_centers_)
