486 lines
17 KiB
Python
486 lines
17 KiB
Python
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"""Affinity Propagation clustering algorithm."""
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# Author: Alexandre Gramfort alexandre.gramfort@inria.fr
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# Gael Varoquaux gael.varoquaux@normalesup.org
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# License: BSD 3 clause
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import numpy as np
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import warnings
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from ..exceptions import ConvergenceWarning
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from ..base import BaseEstimator, ClusterMixin
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from ..utils import as_float_array, check_random_state
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from ..utils.deprecation import deprecated
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from ..utils.validation import check_is_fitted, _deprecate_positional_args
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from ..metrics import euclidean_distances
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from ..metrics import pairwise_distances_argmin
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from .._config import config_context
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def _equal_similarities_and_preferences(S, preference):
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def all_equal_preferences():
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return np.all(preference == preference.flat[0])
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def all_equal_similarities():
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# Create mask to ignore diagonal of S
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mask = np.ones(S.shape, dtype=bool)
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np.fill_diagonal(mask, 0)
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return np.all(S[mask].flat == S[mask].flat[0])
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return all_equal_preferences() and all_equal_similarities()
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@_deprecate_positional_args
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def affinity_propagation(S, *, preference=None, convergence_iter=15,
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max_iter=200, damping=0.5, copy=True, verbose=False,
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return_n_iter=False, random_state='warn'):
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"""Perform Affinity Propagation Clustering of data.
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Read more in the :ref:`User Guide <affinity_propagation>`.
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Parameters
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----------
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S : array-like of shape (n_samples, n_samples)
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Matrix of similarities between points.
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preference : array-like of shape (n_samples,) or float, default=None
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Preferences for each point - points with larger values of
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preferences are more likely to be chosen as exemplars. The number of
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exemplars, i.e. of clusters, is influenced by the input preferences
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value. If the preferences are not passed as arguments, they will be
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set to the median of the input similarities (resulting in a moderate
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number of clusters). For a smaller amount of clusters, this can be set
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to the minimum value of the similarities.
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convergence_iter : int, default=15
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Number of iterations with no change in the number
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of estimated clusters that stops the convergence.
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max_iter : int, default=200
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Maximum number of iterations
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damping : float, default=0.5
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Damping factor between 0.5 and 1.
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copy : bool, default=True
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If copy is False, the affinity matrix is modified inplace by the
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algorithm, for memory efficiency.
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verbose : bool, default=False
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The verbosity level.
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return_n_iter : bool, default=False
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Whether or not to return the number of iterations.
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random_state : int, RandomState instance or None, default=0
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Pseudo-random number generator to control the starting state.
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Use an int for reproducible results across function calls.
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See the :term:`Glossary <random_state>`.
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.. versionadded:: 0.23
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this parameter was previously hardcoded as 0.
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Returns
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-------
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cluster_centers_indices : ndarray of shape (n_clusters,)
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Index of clusters centers.
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labels : ndarray of shape (n_samples,)
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Cluster labels for each point.
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n_iter : int
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Number of iterations run. Returned only if `return_n_iter` is
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set to True.
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Notes
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-----
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For an example, see :ref:`examples/cluster/plot_affinity_propagation.py
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<sphx_glr_auto_examples_cluster_plot_affinity_propagation.py>`.
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When the algorithm does not converge, it returns an empty array as
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``cluster_center_indices`` and ``-1`` as label for each training sample.
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When all training samples have equal similarities and equal preferences,
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the assignment of cluster centers and labels depends on the preference.
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If the preference is smaller than the similarities, a single cluster center
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and label ``0`` for every sample will be returned. Otherwise, every
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training sample becomes its own cluster center and is assigned a unique
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label.
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References
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----------
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Brendan J. Frey and Delbert Dueck, "Clustering by Passing Messages
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Between Data Points", Science Feb. 2007
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"""
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S = as_float_array(S, copy=copy)
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n_samples = S.shape[0]
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if S.shape[0] != S.shape[1]:
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raise ValueError("S must be a square array (shape=%s)" % repr(S.shape))
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if preference is None:
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preference = np.median(S)
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if damping < 0.5 or damping >= 1:
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raise ValueError('damping must be >= 0.5 and < 1')
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preference = np.array(preference)
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if (n_samples == 1 or
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_equal_similarities_and_preferences(S, preference)):
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# It makes no sense to run the algorithm in this case, so return 1 or
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# n_samples clusters, depending on preferences
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warnings.warn("All samples have mutually equal similarities. "
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"Returning arbitrary cluster center(s).")
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if preference.flat[0] >= S.flat[n_samples - 1]:
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return ((np.arange(n_samples), np.arange(n_samples), 0)
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if return_n_iter
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else (np.arange(n_samples), np.arange(n_samples)))
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else:
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return ((np.array([0]), np.array([0] * n_samples), 0)
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if return_n_iter
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else (np.array([0]), np.array([0] * n_samples)))
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if random_state == 'warn':
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warnings.warn(
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"'random_state' has been introduced in 0.23. It will be set to "
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"None starting from 1.0 (renaming of 0.25) which means that "
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"results will differ at every function call. Set 'random_state' "
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"to None to silence this warning, or to 0 to keep the behavior of "
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"versions <0.23.",
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FutureWarning
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)
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random_state = 0
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random_state = check_random_state(random_state)
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# Place preference on the diagonal of S
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S.flat[::(n_samples + 1)] = preference
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A = np.zeros((n_samples, n_samples))
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R = np.zeros((n_samples, n_samples)) # Initialize messages
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# Intermediate results
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tmp = np.zeros((n_samples, n_samples))
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# Remove degeneracies
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S += ((np.finfo(S.dtype).eps * S + np.finfo(S.dtype).tiny * 100) *
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random_state.randn(n_samples, n_samples))
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# Execute parallel affinity propagation updates
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e = np.zeros((n_samples, convergence_iter))
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ind = np.arange(n_samples)
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for it in range(max_iter):
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# tmp = A + S; compute responsibilities
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np.add(A, S, tmp)
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I = np.argmax(tmp, axis=1)
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Y = tmp[ind, I] # np.max(A + S, axis=1)
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tmp[ind, I] = -np.inf
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Y2 = np.max(tmp, axis=1)
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# tmp = Rnew
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np.subtract(S, Y[:, None], tmp)
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tmp[ind, I] = S[ind, I] - Y2
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# Damping
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tmp *= 1 - damping
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R *= damping
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R += tmp
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# tmp = Rp; compute availabilities
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np.maximum(R, 0, tmp)
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tmp.flat[::n_samples + 1] = R.flat[::n_samples + 1]
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# tmp = -Anew
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tmp -= np.sum(tmp, axis=0)
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dA = np.diag(tmp).copy()
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tmp.clip(0, np.inf, tmp)
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tmp.flat[::n_samples + 1] = dA
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# Damping
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tmp *= 1 - damping
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A *= damping
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A -= tmp
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# Check for convergence
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E = (np.diag(A) + np.diag(R)) > 0
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e[:, it % convergence_iter] = E
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K = np.sum(E, axis=0)
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if it >= convergence_iter:
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se = np.sum(e, axis=1)
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unconverged = (np.sum((se == convergence_iter) + (se == 0))
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!= n_samples)
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if (not unconverged and (K > 0)) or (it == max_iter):
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never_converged = False
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if verbose:
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print("Converged after %d iterations." % it)
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break
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else:
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never_converged = True
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if verbose:
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print("Did not converge")
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I = np.flatnonzero(E)
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K = I.size # Identify exemplars
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if K > 0 and not never_converged:
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c = np.argmax(S[:, I], axis=1)
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c[I] = np.arange(K) # Identify clusters
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# Refine the final set of exemplars and clusters and return results
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for k in range(K):
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ii = np.where(c == k)[0]
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j = np.argmax(np.sum(S[ii[:, np.newaxis], ii], axis=0))
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I[k] = ii[j]
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c = np.argmax(S[:, I], axis=1)
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c[I] = np.arange(K)
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labels = I[c]
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# Reduce labels to a sorted, gapless, list
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cluster_centers_indices = np.unique(labels)
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labels = np.searchsorted(cluster_centers_indices, labels)
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else:
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warnings.warn("Affinity propagation did not converge, this model "
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"will not have any cluster centers.", ConvergenceWarning)
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labels = np.array([-1] * n_samples)
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cluster_centers_indices = []
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if return_n_iter:
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return cluster_centers_indices, labels, it + 1
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else:
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return cluster_centers_indices, labels
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###############################################################################
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class AffinityPropagation(ClusterMixin, BaseEstimator):
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"""Perform Affinity Propagation Clustering of data.
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Read more in the :ref:`User Guide <affinity_propagation>`.
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Parameters
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----------
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damping : float, default=0.5
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Damping factor (between 0.5 and 1) is the extent to
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which the current value is maintained relative to
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incoming values (weighted 1 - damping). This in order
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to avoid numerical oscillations when updating these
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values (messages).
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max_iter : int, default=200
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Maximum number of iterations.
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convergence_iter : int, default=15
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Number of iterations with no change in the number
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of estimated clusters that stops the convergence.
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copy : bool, default=True
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Make a copy of input data.
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preference : array-like of shape (n_samples,) or float, default=None
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Preferences for each point - points with larger values of
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preferences are more likely to be chosen as exemplars. The number
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of exemplars, ie of clusters, is influenced by the input
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preferences value. If the preferences are not passed as arguments,
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they will be set to the median of the input similarities.
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affinity : {'euclidean', 'precomputed'}, default='euclidean'
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Which affinity to use. At the moment 'precomputed' and
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``euclidean`` are supported. 'euclidean' uses the
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negative squared euclidean distance between points.
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verbose : bool, default=False
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Whether to be verbose.
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random_state : int, RandomState instance or None, default=0
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Pseudo-random number generator to control the starting state.
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Use an int for reproducible results across function calls.
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See the :term:`Glossary <random_state>`.
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.. versionadded:: 0.23
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this parameter was previously hardcoded as 0.
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Attributes
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----------
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cluster_centers_indices_ : ndarray of shape (n_clusters,)
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Indices of cluster centers.
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cluster_centers_ : ndarray of shape (n_clusters, n_features)
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Cluster centers (if affinity != ``precomputed``).
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labels_ : ndarray of shape (n_samples,)
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Labels of each point.
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affinity_matrix_ : ndarray of shape (n_samples, n_samples)
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Stores the affinity matrix used in ``fit``.
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n_iter_ : int
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Number of iterations taken to converge.
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Notes
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-----
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For an example, see :ref:`examples/cluster/plot_affinity_propagation.py
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<sphx_glr_auto_examples_cluster_plot_affinity_propagation.py>`.
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The algorithmic complexity of affinity propagation is quadratic
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in the number of points.
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When ``fit`` does not converge, ``cluster_centers_`` becomes an empty
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array and all training samples will be labelled as ``-1``. In addition,
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``predict`` will then label every sample as ``-1``.
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When all training samples have equal similarities and equal preferences,
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the assignment of cluster centers and labels depends on the preference.
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If the preference is smaller than the similarities, ``fit`` will result in
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a single cluster center and label ``0`` for every sample. Otherwise, every
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training sample becomes its own cluster center and is assigned a unique
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label.
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References
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----------
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Brendan J. Frey and Delbert Dueck, "Clustering by Passing Messages
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Between Data Points", Science Feb. 2007
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Examples
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--------
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>>> from sklearn.cluster import AffinityPropagation
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>>> import numpy as np
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>>> X = np.array([[1, 2], [1, 4], [1, 0],
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... [4, 2], [4, 4], [4, 0]])
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>>> clustering = AffinityPropagation(random_state=5).fit(X)
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>>> clustering
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AffinityPropagation(random_state=5)
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>>> clustering.labels_
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array([0, 0, 0, 1, 1, 1])
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>>> clustering.predict([[0, 0], [4, 4]])
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array([0, 1])
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>>> clustering.cluster_centers_
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array([[1, 2],
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[4, 2]])
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"""
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@_deprecate_positional_args
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def __init__(self, *, damping=.5, max_iter=200, convergence_iter=15,
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copy=True, preference=None, affinity='euclidean',
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verbose=False, random_state='warn'):
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self.damping = damping
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self.max_iter = max_iter
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self.convergence_iter = convergence_iter
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self.copy = copy
|
||
|
|
self.verbose = verbose
|
||
|
|
self.preference = preference
|
||
|
|
self.affinity = affinity
|
||
|
|
self.random_state = random_state
|
||
|
|
|
||
|
|
# TODO: Remove in 1.1
|
||
|
|
# mypy error: Decorated property not supported
|
||
|
|
@deprecated("Attribute _pairwise was deprecated in " # type: ignore
|
||
|
|
"version 0.24 and will be removed in 1.1 (renaming of 0.26).")
|
||
|
|
@property
|
||
|
|
def _pairwise(self):
|
||
|
|
return self.affinity == "precomputed"
|
||
|
|
|
||
|
|
def _more_tags(self):
|
||
|
|
return {'pairwise': self.affinity == 'precomputed'}
|
||
|
|
|
||
|
|
def fit(self, X, y=None):
|
||
|
|
"""Fit the clustering from features, or affinity matrix.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
X : {array-like, sparse matrix} of shape (n_samples, n_features), or \
|
||
|
|
array-like of shape (n_samples, n_samples)
|
||
|
|
Training instances to cluster, or similarities / affinities between
|
||
|
|
instances if ``affinity='precomputed'``. If a sparse feature matrix
|
||
|
|
is provided, it will be converted into a sparse ``csr_matrix``.
|
||
|
|
|
||
|
|
y : Ignored
|
||
|
|
Not used, present here for API consistency by convention.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
self
|
||
|
|
|
||
|
|
"""
|
||
|
|
if self.affinity == "precomputed":
|
||
|
|
accept_sparse = False
|
||
|
|
else:
|
||
|
|
accept_sparse = 'csr'
|
||
|
|
X = self._validate_data(X, accept_sparse=accept_sparse)
|
||
|
|
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_, preference=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,
|
||
|
|
random_state=self.random_state)
|
||
|
|
|
||
|
|
if self.affinity != "precomputed":
|
||
|
|
self.cluster_centers_ = X[self.cluster_centers_indices_].copy()
|
||
|
|
|
||
|
|
return self
|
||
|
|
|
||
|
|
def predict(self, X):
|
||
|
|
"""Predict the closest cluster each sample in X belongs to.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
X : {array-like, sparse matrix} of shape (n_samples, n_features)
|
||
|
|
New data to predict. If a sparse matrix is provided, it will be
|
||
|
|
converted into a sparse ``csr_matrix``.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
labels : ndarray of shape (n_samples,)
|
||
|
|
Cluster labels.
|
||
|
|
"""
|
||
|
|
check_is_fitted(self)
|
||
|
|
X = self._validate_data(X, reset=False)
|
||
|
|
if not hasattr(self, "cluster_centers_"):
|
||
|
|
raise ValueError("Predict method is not supported when "
|
||
|
|
"affinity='precomputed'.")
|
||
|
|
|
||
|
|
if self.cluster_centers_.shape[0] > 0:
|
||
|
|
with config_context(assume_finite=True):
|
||
|
|
return pairwise_distances_argmin(X, self.cluster_centers_)
|
||
|
|
else:
|
||
|
|
warnings.warn("This model does not have any cluster centers "
|
||
|
|
"because affinity propagation did not converge. "
|
||
|
|
"Labeling every sample as '-1'.", ConvergenceWarning)
|
||
|
|
return np.array([-1] * X.shape[0])
|
||
|
|
|
||
|
|
def fit_predict(self, X, y=None):
|
||
|
|
"""Fit the clustering from features or affinity matrix, and return
|
||
|
|
cluster labels.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
X : {array-like, sparse matrix} of shape (n_samples, n_features), or \
|
||
|
|
array-like of shape (n_samples, n_samples)
|
||
|
|
Training instances to cluster, or similarities / affinities between
|
||
|
|
instances if ``affinity='precomputed'``. If a sparse feature matrix
|
||
|
|
is provided, it will be converted into a sparse ``csr_matrix``.
|
||
|
|
|
||
|
|
y : Ignored
|
||
|
|
Not used, present here for API consistency by convention.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
labels : ndarray of shape (n_samples,)
|
||
|
|
Cluster labels.
|
||
|
|
"""
|
||
|
|
return super().fit_predict(X, y)
|