"""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 import warnings from ..exceptions import ConvergenceWarning from ..base import BaseEstimator, ClusterMixin from ..utils import as_float_array, check_array, check_random_state from ..utils.validation import check_is_fitted, _deprecate_positional_args from ..metrics import euclidean_distances from ..metrics import pairwise_distances_argmin def _equal_similarities_and_preferences(S, preference): def all_equal_preferences(): return np.all(preference == preference.flat[0]) def all_equal_similarities(): # Create mask to ignore diagonal of S mask = np.ones(S.shape, dtype=bool) np.fill_diagonal(mask, 0) return np.all(S[mask].flat == S[mask].flat[0]) return all_equal_preferences() and all_equal_similarities() @_deprecate_positional_args def affinity_propagation(S, *, preference=None, convergence_iter=15, max_iter=200, damping=0.5, copy=True, verbose=False, return_n_iter=False, random_state='warn'): """Perform Affinity Propagation Clustering of data Read more in the :ref:`User Guide `. 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. random_state : int or np.random.RandomStateInstance, default: 0 Pseudo-random number generator to control the starting state. Use an int for reproducible results across function calls. See the :term:`Glossary `. .. versionadded:: 0.23 this parameter was previously hardcoded as 0. 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 `. When the algorithm does not converge, it returns an empty array as ``cluster_center_indices`` and ``-1`` as label for each training sample. When all training samples have equal similarities and equal preferences, the assignment of cluster centers and labels depends on the preference. If the preference is smaller than the similarities, a single cluster center and label ``0`` for every sample will be returned. Otherwise, every training sample becomes its own cluster center and is assigned a unique label. 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') preference = np.array(preference) if (n_samples == 1 or _equal_similarities_and_preferences(S, preference)): # It makes no sense to run the algorithm in this case, so return 1 or # n_samples clusters, depending on preferences warnings.warn("All samples have mutually equal similarities. " "Returning arbitrary cluster center(s).") if preference.flat[0] >= S.flat[n_samples - 1]: return ((np.arange(n_samples), np.arange(n_samples), 0) if return_n_iter else (np.arange(n_samples), np.arange(n_samples))) else: return ((np.array([0]), np.array([0] * n_samples), 0) if return_n_iter else (np.array([0]), np.array([0] * n_samples))) if random_state == 'warn': warnings.warn(("'random_state' has been introduced in 0.23. " "It will be set to None starting from 0.25 which " "means that results will differ at every function " "call. Set 'random_state' to None to silence this " "warning, or to 0 to keep the behavior of versions " "<0.23."), FutureWarning) random_state = 0 random_state = check_random_state(random_state) # 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(S.dtype).eps * S + np.finfo(S.dtype).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): never_converged = False if verbose: print("Converged after %d iterations." % it) break else: never_converged = True if verbose: print("Did not converge") I = np.flatnonzero(E) K = I.size # Identify exemplars if K > 0 and not never_converged: 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: warnings.warn("Affinity propagation did not converge, this model " "will not have any cluster centers.", ConvergenceWarning) labels = np.array([-1] * n_samples) cluster_centers_indices = [] if return_n_iter: return cluster_centers_indices, labels, it + 1 else: return cluster_centers_indices, labels ############################################################################### class AffinityPropagation(ClusterMixin, BaseEstimator): """Perform Affinity Propagation Clustering of data. Read more in the :ref:`User Guide `. Parameters ---------- damping : float, 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, default=200 Maximum number of iterations. convergence_iter : int, default=15 Number of iterations with no change in the number of estimated clusters that stops the convergence. copy : bool, default=True Make a copy of input data. preference : array-like of shape (n_samples,) or float, default=None 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 : {'euclidean', 'precomputed'}, default='euclidean' Which affinity to use. At the moment 'precomputed' and ``euclidean`` are supported. 'euclidean' uses the negative squared euclidean distance between points. verbose : bool, default=False Whether to be verbose. random_state : int or np.random.RandomStateInstance, default: 0 Pseudo-random number generator to control the starting state. Use an int for reproducible results across function calls. See the :term:`Glossary `. .. versionadded:: 0.23 this parameter was previously hardcoded as 0. Attributes ---------- cluster_centers_indices_ : ndarray of shape (n_clusters,) Indices of cluster centers cluster_centers_ : ndarray of shape (n_clusters, n_features) Cluster centers (if affinity != ``precomputed``). labels_ : ndarray of shape (n_samples,) Labels of each point affinity_matrix_ : ndarray of 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 `. The algorithmic complexity of affinity propagation is quadratic in the number of points. When ``fit`` does not converge, ``cluster_centers_`` becomes an empty array and all training samples will be labelled as ``-1``. In addition, ``predict`` will then label every sample as ``-1``. When all training samples have equal similarities and equal preferences, the assignment of cluster centers and labels depends on the preference. If the preference is smaller than the similarities, ``fit`` will result in a single cluster center and label ``0`` for every sample. Otherwise, every training sample becomes its own cluster center and is assigned a unique label. References ---------- Brendan J. Frey and Delbert Dueck, "Clustering by Passing Messages Between Data Points", Science Feb. 2007 Examples -------- >>> from sklearn.cluster import AffinityPropagation >>> import numpy as np >>> X = np.array([[1, 2], [1, 4], [1, 0], ... [4, 2], [4, 4], [4, 0]]) >>> clustering = AffinityPropagation(random_state=5).fit(X) >>> clustering AffinityPropagation(random_state=5) >>> clustering.labels_ array([0, 0, 0, 1, 1, 1]) >>> clustering.predict([[0, 0], [4, 4]]) array([0, 1]) >>> clustering.cluster_centers_ array([[1, 2], [4, 2]]) """ @_deprecate_positional_args def __init__(self, *, damping=.5, max_iter=200, convergence_iter=15, copy=True, preference=None, affinity='euclidean', verbose=False, random_state='warn'): 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 self.random_state = random_state @property def _pairwise(self): return self.affinity == "precomputed" def fit(self, X, y=None): """Fit the clustering from features, or affinity matrix. Parameters ---------- X : array-like or sparse matrix, shape (n_samples, n_features), or \ array-like, 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 or sparse matrix, 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, shape (n_samples,) Cluster labels. """ check_is_fitted(self) X = check_array(X) if not hasattr(self, "cluster_centers_"): raise ValueError("Predict method is not supported when " "affinity='precomputed'.") if self.cluster_centers_.shape[0] > 0: 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 or sparse matrix, shape (n_samples, n_features), or \ array-like, 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, shape (n_samples,) Cluster labels. """ return super().fit_predict(X, y)