"""Affinity Propagation clustering algorithm.""" # Authors: The scikit-learn developers # SPDX-License-Identifier: BSD-3-Clause import warnings from numbers import Integral, Real import numpy as np from .._config import config_context from ..base import BaseEstimator, ClusterMixin, _fit_context from ..exceptions import ConvergenceWarning from ..metrics import euclidean_distances, pairwise_distances_argmin from ..utils import check_random_state from ..utils._param_validation import Interval, StrOptions, validate_params from ..utils.validation import check_is_fitted, validate_data 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() def _affinity_propagation( S, *, preference, convergence_iter, max_iter, damping, verbose, return_n_iter, random_state, ): """Main affinity propagation algorithm.""" n_samples = S.shape[0] 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)) ) # 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.standard_normal(size=(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: if never_converged: warnings.warn( ( "Affinity propagation did not converge, this model " "may return degenerate cluster centers and labels." ), ConvergenceWarning, ) 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 and 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 ############################################################################### # Public API @validate_params( { "S": ["array-like"], "return_n_iter": ["boolean"], }, prefer_skip_nested_validation=False, ) 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=None, ): """Perform Affinity Propagation Clustering of data. Read more in the :ref:`User Guide `. Parameters ---------- S : array-like of shape (n_samples, n_samples) Matrix of similarities between points. 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, 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, default=15 Number of iterations with no change in the number of estimated clusters that stops the convergence. max_iter : int, default=200 Maximum number of iterations. damping : float, default=0.5 Damping factor between 0.5 and 1. copy : bool, default=True If copy is False, the affinity matrix is modified inplace by the algorithm, for memory efficiency. verbose : bool, default=False The verbosity level. return_n_iter : bool, default=False Whether or not to return the number of iterations. random_state : int, RandomState instance or None, default=None 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 : ndarray of shape (n_clusters,) Index of clusters centers. labels : ndarray of 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 usage, see :ref:`sphx_glr_auto_examples_cluster_plot_affinity_propagation.py`. You may also check out, :ref:`sphx_glr_auto_examples_applications_plot_stock_market.py` When the algorithm does not converge, it will still return a arrays of ``cluster_center_indices`` and labels if there are any exemplars/clusters, however they may be degenerate and should be used with caution. 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 Examples -------- >>> import numpy as np >>> from sklearn.cluster import affinity_propagation >>> from sklearn.metrics.pairwise import euclidean_distances >>> X = np.array([[1, 2], [1, 4], [1, 0], ... [4, 2], [4, 4], [4, 0]]) >>> S = -euclidean_distances(X, squared=True) >>> cluster_centers_indices, labels = affinity_propagation(S, random_state=0) >>> cluster_centers_indices array([0, 3]) >>> labels array([0, 0, 0, 1, 1, 1]) """ estimator = AffinityPropagation( damping=damping, max_iter=max_iter, convergence_iter=convergence_iter, copy=copy, preference=preference, affinity="precomputed", verbose=verbose, random_state=random_state, ).fit(S) if return_n_iter: return estimator.cluster_centers_indices_, estimator.labels_, estimator.n_iter_ return estimator.cluster_centers_indices_, estimator.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 in the range `[0.5, 1.0)` 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, RandomState instance or None, default=None 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. n_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 1.0 See Also -------- AgglomerativeClustering : Recursively merges the pair of clusters that minimally increases a given linkage distance. FeatureAgglomeration : Similar to AgglomerativeClustering, but recursively merges features instead of samples. KMeans : K-Means clustering. MiniBatchKMeans : Mini-Batch K-Means clustering. MeanShift : Mean shift clustering using a flat kernel. SpectralClustering : Apply clustering to a projection of the normalized Laplacian. Notes ----- For an example usage, see :ref:`sphx_glr_auto_examples_cluster_plot_affinity_propagation.py`. The algorithmic complexity of affinity propagation is quadratic in the number of points. When the algorithm does not converge, it will still return a arrays of ``cluster_center_indices`` and labels if there are any exemplars/clusters, however they may be degenerate and should be used with caution. When ``fit`` does not converge, ``cluster_centers_`` is still populated however it may be degenerate. In such a case, proceed with caution. If ``fit`` does not converge and fails to produce any ``cluster_centers_`` then ``predict`` will 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]]) """ _parameter_constraints: dict = { "damping": [Interval(Real, 0.5, 1.0, closed="left")], "max_iter": [Interval(Integral, 1, None, closed="left")], "convergence_iter": [Interval(Integral, 1, None, closed="left")], "copy": ["boolean"], "preference": [ "array-like", Interval(Real, None, None, closed="neither"), None, ], "affinity": [StrOptions({"euclidean", "precomputed"})], "verbose": ["verbose"], "random_state": ["random_state"], } def __init__( self, *, damping=0.5, max_iter=200, convergence_iter=15, copy=True, preference=None, affinity="euclidean", verbose=False, random_state=None, ): 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 def __sklearn_tags__(self): tags = super().__sklearn_tags__() tags.input_tags.pairwise = self.affinity == "precomputed" tags.input_tags.sparse = self.affinity != "precomputed" return tags @_fit_context(prefer_skip_nested_validation=True) 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 Returns the instance itself. """ if self.affinity == "precomputed": X = validate_data(self, X, copy=self.copy, force_writeable=True) self.affinity_matrix_ = X else: # self.affinity == "euclidean" X = validate_data(self, X, accept_sparse="csr") self.affinity_matrix_ = -euclidean_distances(X, squared=True) if self.affinity_matrix_.shape[0] != self.affinity_matrix_.shape[1]: raise ValueError( "The matrix of similarities must be a square array. " f"Got {self.affinity_matrix_.shape} instead." ) if self.preference is None: preference = np.median(self.affinity_matrix_) else: preference = self.preference preference = np.asarray(preference) random_state = check_random_state(self.random_state) ( self.cluster_centers_indices_, self.labels_, self.n_iter_, ) = _affinity_propagation( self.affinity_matrix_, max_iter=self.max_iter, convergence_iter=self.convergence_iter, preference=preference, damping=self.damping, verbose=self.verbose, return_n_iter=True, random_state=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 = validate_data(self, X, reset=False, accept_sparse="csr") 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 clustering from features/affinity matrix; 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)