affinity_propagation_.py

""" Algorithms for clustering : Meanshift,  Affinity propagation and spectral
clustering.

"""
# 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
    -----
    See examples/cluster/plot_affinity_propagation.py for an example.

    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.

    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.

    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
    -----
    See examples/cluster/plot_affinity_propagation.py for an example.

    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"

    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.
        """
        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

    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_)