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matrice de liaison de regroupement agglomératif sklearn

J'essaie de dessiner un lien complet scipy.cluster.hierarchy.dendrogram , et j'ai trouvé que scipy.cluster.hierarchy.linkage est plus lent que sklearn.AgglomerativeClustering .

Pourtant, sklearn.AgglomerativeClustering ne renvoie pas la distance entre les clusters et le nombre d'observations originales, qui scipy.cluster.hierarchy.dendrogram Besoins. Y a-t-il un moyen de les prendre?

27
Presian Abarov

J'ai fait un scipt pour le faire sans modifier sklearn et sans fonctions récursives. Avant d'utiliser, notez que:

  • La distance de fusion peut parfois diminuer par rapport à la distance de fusion des enfants. J'ai ajouté trois façons de gérer ces cas: prendre le maximum, ne rien faire ou augmenter avec la norme l2. La logique de la norme l2 n'a pas encore été vérifiée. Veuillez vérifier ce qui vous convient le mieux.

Importez les packages:

from sklearn.cluster import AgglomerativeClustering
import numpy as np
import matplotlib.pyplot as plt
from scipy.cluster.hierarchy import dendrogram

Fonction de calcul des poids et des distances:

def get_distances(X,model,mode='l2'):
    distances = []
    weights = []
    children=model.children_
    dims = (X.shape[1],1)
    distCache = {}
    weightCache = {}
    for childs in children:
        c1 = X[childs[0]].reshape(dims)
        c2 = X[childs[1]].reshape(dims)
        c1Dist = 0
        c1W = 1
        c2Dist = 0
        c2W = 1
        if childs[0] in distCache.keys():
            c1Dist = distCache[childs[0]]
            c1W = weightCache[childs[0]]
        if childs[1] in distCache.keys():
            c2Dist = distCache[childs[1]]
            c2W = weightCache[childs[1]]
        d = np.linalg.norm(c1-c2)
        cc = ((c1W*c1)+(c2W*c2))/(c1W+c2W)

        X = np.vstack((X,cc.T))

        newChild_id = X.shape[0]-1

        # How to deal with a higher level cluster merge with lower distance:
        if mode=='l2':  # Increase the higher level cluster size suing an l2 norm
            added_dist = (c1Dist**2+c2Dist**2)**0.5 
            dNew = (d**2 + added_dist**2)**0.5
        Elif mode == 'max':  # If the previrous clusters had higher distance, use that one
            dNew = max(d,c1Dist,c2Dist)
        Elif mode == 'actual':  # Plot the actual distance.
            dNew = d


        wNew = (c1W + c2W)
        distCache[newChild_id] = dNew
        weightCache[newChild_id] = wNew

        distances.append(dNew)
        weights.append( wNew)
    return distances, weights

Faire des échantillons de données de 2 clusters avec 2 sous-clusters:

# Make 4 distributions, two of which form a bigger cluster
X1_1 = np.random.randn(25,2)+[8,1.5]
X1_2 = np.random.randn(25,2)+[8,-1.5]
X2_1 = np.random.randn(25,2)-[8,3]
X2_2 = np.random.randn(25,2)-[8,-3]

# Merge the four distributions
X = np.vstack([X1_1,X1_2,X2_1,X2_2])

# Plot the clusters
colors = ['r']*25 + ['b']*25 + ['g']*25 + ['y']*25
plt.scatter(X[:,0],X[:,1],c=colors)

Exemples de données:

Clusters sample data

Ajuster le modèle de clustering

model = AgglomerativeClustering(n_clusters=2,linkage="ward")
model.fit(X)

Appelez la fonction pour trouver les distances et passez-la au dendogramme

distance, weight = get_distances(X,model)
linkage_matrix = np.column_stack([model.children_, distance, weight]).astype(float)
plt.figure(figsize=(20,10))
dendrogram(linkage_matrix)
plt.show()

Dendogramme de sortie: enter image description here

5
Arjan Groen

C'est possible, mais ce n'est pas joli. Il nécessite (au minimum) une petite réécriture de AgglomerativeClustering.fit ( source ). La difficulté est que la méthode nécessite un certain nombre d'importations, donc elle finit par devenir un peu désagréable. Pour ajouter cette fonctionnalité:

  1. Insérez la ligne suivante après la ligne 748:

    kwargs ['return_distance'] = True

  2. Remplacer la ligne 752 par:

    self.children_, self.n_components_, self.n_leaves_, parents, self.distance = \

Cela vous donnera un nouvel attribut, distance, que vous pouvez facilement appeler.

Quelques points à noter:

  1. En faisant cela, je suis tombé sur ce problème à propos de la fonction check_array Sur la ligne 711. Cela peut être résolu en utilisant check_arrays (from sklearn.utils.validation import check_arrays). Vous pouvez modifier cette ligne pour devenir X = check_arrays(X)[0]. Cela semble être un bug (j'ai toujours ce problème sur la version la plus récente de scikit-learn).

  2. Selon la version de sklearn.cluster.hierarchical.linkage_tree Dont vous disposez, vous devrez peut-être également la modifier pour qu'elle soit celle fournie dans source .

Pour faciliter les choses pour tout le monde, voici le code complet que vous devrez utiliser:

from heapq import heapify, heappop, heappush, heappushpop
import warnings
import sys

import numpy as np
from scipy import sparse

from sklearn.base import BaseEstimator, ClusterMixin
from sklearn.externals.joblib import Memory
from sklearn.externals import six
from sklearn.utils.validation import check_arrays
from sklearn.utils.sparsetools import connected_components
from sklearn.cluster import _hierarchical
from sklearn.cluster.hierarchical import ward_tree
from sklearn.cluster._feature_agglomeration import AgglomerationTransform
from sklearn.utils.fast_dict import IntFloatDict

def _fix_connectivity(X, connectivity, n_components=None,
                      affinity="euclidean"):
    """
    Fixes the connectivity matrix
        - copies it
        - makes it symmetric
        - converts it to LIL if necessary
        - completes it if necessary
    """
    n_samples = X.shape[0]
    if (connectivity.shape[0] != n_samples or
        connectivity.shape[1] != n_samples):
        raise ValueError('Wrong shape for connectivity matrix: %s '
                         'when X is %s' % (connectivity.shape, X.shape))

    # Make the connectivity matrix symmetric:
    connectivity = connectivity + connectivity.T

    # Convert connectivity matrix to LIL
    if not sparse.isspmatrix_lil(connectivity):
        if not sparse.isspmatrix(connectivity):
            connectivity = sparse.lil_matrix(connectivity)
        else:
            connectivity = connectivity.tolil()

    # Compute the number of nodes
    n_components, labels = connected_components(connectivity)

    if n_components > 1:
        warnings.warn("the number of connected components of the "
                      "connectivity matrix is %d > 1. Completing it to avoid "
                      "stopping the tree early." % n_components,
                      stacklevel=2)
        # XXX: Can we do without completing the matrix?
        for i in xrange(n_components):
            idx_i = np.where(labels == i)[0]
            Xi = X[idx_i]
            for j in xrange(i):
                idx_j = np.where(labels == j)[0]
                Xj = X[idx_j]
                D = pairwise_distances(Xi, Xj, metric=affinity)
                ii, jj = np.where(D == np.min(D))
                ii = ii[0]
                jj = jj[0]
                connectivity[idx_i[ii], idx_j[jj]] = True
                connectivity[idx_j[jj], idx_i[ii]] = True

    return connectivity, n_components

# average and complete linkage
def linkage_tree(X, connectivity=None, n_components=None,
                 n_clusters=None, linkage='complete', affinity="euclidean",
                 return_distance=False):
    """Linkage agglomerative clustering based on a Feature matrix.
    The inertia matrix uses a Heapq-based representation.
    This is the structured version, that takes into account some topological
    structure between samples.
    Parameters
    ----------
    X : array, shape (n_samples, n_features)
        feature matrix representing n_samples samples to be clustered
    connectivity : sparse matrix (optional).
        connectivity matrix. Defines for each sample the neighboring samples
        following a given structure of the data. The matrix is assumed to
        be symmetric and only the upper triangular half is used.
        Default is None, i.e, the Ward algorithm is unstructured.
    n_components : int (optional)
        Number of connected components. If None the number of connected
        components is estimated from the connectivity matrix.
        NOTE: This parameter is now directly determined directly
        from the connectivity matrix and will be removed in 0.18
    n_clusters : int (optional)
        Stop early the construction of the tree at n_clusters. This is
        useful to decrease computation time if the number of clusters is
        not small compared to the number of samples. In this case, the
        complete tree is not computed, thus the 'children' output is of
        limited use, and the 'parents' output should rather be used.
        This option is valid only when specifying a connectivity matrix.
    linkage : {"average", "complete"}, optional, default: "complete"
        Which linkage critera to use. The linkage criterion determines which
        distance to use between sets of observation.
            - average uses the average of the distances of each observation of
              the two sets
            - complete or maximum linkage uses the maximum distances between
              all observations of the two sets.
    affinity : string or callable, optional, default: "euclidean".
        which metric to use. Can be "euclidean", "manhattan", or any
        distance know to paired distance (see metric.pairwise)
    return_distance : bool, default False
        whether or not to return the distances between the clusters.
    Returns
    -------
    children : 2D array, shape (n_nodes-1, 2)
        The children of each non-leaf node. Values less than `n_samples`
        correspond to leaves of the tree which are the original samples.
        A node `i` greater than or equal to `n_samples` is a non-leaf
        node and has children `children_[i - n_samples]`. Alternatively
        at the i-th iteration, children[i][0] and children[i][1]
        are merged to form node `n_samples + i`
    n_components : int
        The number of connected components in the graph.
    n_leaves : int
        The number of leaves in the tree.
    parents : 1D array, shape (n_nodes, ) or None
        The parent of each node. Only returned when a connectivity matrix
        is specified, elsewhere 'None' is returned.
    distances : ndarray, shape (n_nodes-1,)
        Returned when return_distance is set to True.
        distances[i] refers to the distance between children[i][0] and
        children[i][1] when they are merged.
    See also
    --------
    ward_tree : hierarchical clustering with ward linkage
    """
    X = np.asarray(X)
    if X.ndim == 1:
        X = np.reshape(X, (-1, 1))
    n_samples, n_features = X.shape

    linkage_choices = {'complete': _hierarchical.max_merge,
                       'average': _hierarchical.average_merge,
                      }
    try:
        join_func = linkage_choices[linkage]
    except KeyError:
        raise ValueError(
            'Unknown linkage option, linkage should be one '
            'of %s, but %s was given' % (linkage_choices.keys(), linkage))

    if connectivity is None:
        from scipy.cluster import hierarchy  # imports PIL

        if n_clusters is not None:
            warnings.warn('Partial build of the tree is implemented '
                          'only for structured clustering (i.e. with '
                          'explicit connectivity). The algorithm '
                          'will build the full tree and only '
                          'retain the lower branches required '
                          'for the specified number of clusters',
                          stacklevel=2)

        if affinity == 'precomputed':
            # for the linkage function of hierarchy to work on precomputed
            # data, provide as first argument an ndarray of the shape returned
            # by pdist: it is a flat array containing the upper triangular of
            # the distance matrix.
            i, j = np.triu_indices(X.shape[0], k=1)
            X = X[i, j]
        Elif affinity == 'l2':
            # Translate to something understood by scipy
            affinity = 'euclidean'
        Elif affinity in ('l1', 'manhattan'):
            affinity = 'cityblock'
        Elif callable(affinity):
            X = affinity(X)
            i, j = np.triu_indices(X.shape[0], k=1)
            X = X[i, j]
        out = hierarchy.linkage(X, method=linkage, metric=affinity)
        children_ = out[:, :2].astype(np.int)

        if return_distance:
            distances = out[:, 2]
            return children_, 1, n_samples, None, distances
        return children_, 1, n_samples, None

    if n_components is not None:
        warnings.warn(
            "n_components is now directly calculated from the connectivity "
            "matrix and will be removed in 0.18",
            DeprecationWarning)
    connectivity, n_components = _fix_connectivity(X, connectivity)

    connectivity = connectivity.tocoo()
    # Put the diagonal to zero
    diag_mask = (connectivity.row != connectivity.col)
    connectivity.row = connectivity.row[diag_mask]
    connectivity.col = connectivity.col[diag_mask]
    connectivity.data = connectivity.data[diag_mask]
    del diag_mask

    if affinity == 'precomputed':
        distances = X[connectivity.row, connectivity.col]
    else:
        # FIXME We compute all the distances, while we could have only computed
        # the "interesting" distances
        distances = paired_distances(X[connectivity.row],
                                     X[connectivity.col],
                                     metric=affinity)
    connectivity.data = distances

    if n_clusters is None:
        n_nodes = 2 * n_samples - 1
    else:
        assert n_clusters <= n_samples
        n_nodes = 2 * n_samples - n_clusters

    if return_distance:
        distances = np.empty(n_nodes - n_samples)
    # create inertia heap and connection matrix
    A = np.empty(n_nodes, dtype=object)
    inertia = list()

    # LIL seems to the best format to access the rows quickly,
    # without the numpy overhead of slicing CSR indices and data.
    connectivity = connectivity.tolil()
    # We are storing the graph in a list of IntFloatDict
    for ind, (data, row) in enumerate(Zip(connectivity.data,
                                          connectivity.rows)):
        A[ind] = IntFloatDict(np.asarray(row, dtype=np.intp),
                              np.asarray(data, dtype=np.float64))
        # We keep only the upper triangular for the heap
        # Generator expressions are faster than arrays on the following
        inertia.extend(_hierarchical.WeightedEdge(d, ind, r)
                       for r, d in Zip(row, data) if r < ind)
    del connectivity

    heapify(inertia)

    # prepare the main fields
    parent = np.arange(n_nodes, dtype=np.intp)
    used_node = np.ones(n_nodes, dtype=np.intp)
    children = []

    # recursive merge loop
    for k in xrange(n_samples, n_nodes):
        # identify the merge
        while True:
            Edge = heappop(inertia)
            if used_node[Edge.a] and used_node[Edge.b]:
                break
        i = Edge.a
        j = Edge.b

        if return_distance:
            # store distances
            distances[k - n_samples] = Edge.weight

        parent[i] = parent[j] = k
        children.append((i, j))
        # Keep track of the number of elements per cluster
        n_i = used_node[i]
        n_j = used_node[j]
        used_node[k] = n_i + n_j
        used_node[i] = used_node[j] = False

        # update the structure matrix A and the inertia matrix
        # a clever 'min', or 'max' operation between A[i] and A[j]
        coord_col = join_func(A[i], A[j], used_node, n_i, n_j)
        for l, d in coord_col:
            A[l].append(k, d)
            # Here we use the information from coord_col (containing the
            # distances) to update the heap
            heappush(inertia, _hierarchical.WeightedEdge(d, k, l))
        A[k] = coord_col
        # Clear A[i] and A[j] to save memory
        A[i] = A[j] = 0

    # Separate leaves in children (empty lists up to now)
    n_leaves = n_samples

    # # return numpy array for efficient caching
    children = np.array(children)[:, ::-1]

    if return_distance:
        return children, n_components, n_leaves, parent, distances
    return children, n_components, n_leaves, parent

# Matching names to tree-building strategies
def _complete_linkage(*args, **kwargs):
    kwargs['linkage'] = 'complete'  
    return linkage_tree(*args, **kwargs)

def _average_linkage(*args, **kwargs):
    kwargs['linkage'] = 'average'
    return linkage_tree(*args, **kwargs)

_TREE_BUILDERS = dict(
    ward=ward_tree,
    complete=_complete_linkage,
    average=_average_linkage,
    )

def _hc_cut(n_clusters, children, n_leaves):
    """Function cutting the ward tree for a given number of clusters.
    Parameters
    ----------
    n_clusters : int or ndarray
        The number of clusters to form.
    children : list of pairs. Length of n_nodes
        The children of each non-leaf node. Values less than `n_samples` refer
        to leaves of the tree. A greater value `i` indicates a node with
        children `children[i - n_samples]`.
    n_leaves : int
        Number of leaves of the tree.
    Returns
    -------
    labels : array [n_samples]
        cluster labels for each point
    """
    if n_clusters > n_leaves:
        raise ValueError('Cannot extract more clusters than samples: '
                         '%s clusters where given for a tree with %s leaves.'
                         % (n_clusters, n_leaves))
    # In this function, we store nodes as a heap to avoid recomputing
    # the max of the nodes: the first element is always the smallest
    # We use negated indices as heaps work on smallest elements, and we
    # are interested in largest elements
    # children[-1] is the root of the tree
    nodes = [-(max(children[-1]) + 1)]
    for i in xrange(n_clusters - 1):
        # As we have a heap, nodes[0] is the smallest element
        these_children = children[-nodes[0] - n_leaves]
        # Insert the 2 children and remove the largest node
        heappush(nodes, -these_children[0])
        heappushpop(nodes, -these_children[1])
    label = np.zeros(n_leaves, dtype=np.intp)
    for i, node in enumerate(nodes):
        label[_hierarchical._hc_get_descendent(-node, children, n_leaves)] = i
    return label

class AgglomerativeClustering(BaseEstimator, ClusterMixin):
    """
    Agglomerative Clustering
    Recursively merges the pair of clusters that minimally increases
    a given linkage distance.
    Parameters
    ----------
    n_clusters : int, default=2
        The number of clusters to find.
    connectivity : array-like or callable, optional
        Connectivity matrix. Defines for each sample the neighboring
        samples following a given structure of the data.
        This can be a connectivity matrix itself or a callable that transforms
        the data into a connectivity matrix, such as derived from
        kneighbors_graph. Default is None, i.e, the
        hierarchical clustering algorithm is unstructured.
    affinity : string or callable, default: "euclidean"
        Metric used to compute the linkage. Can be "euclidean", "l1", "l2",
        "manhattan", "cosine", or 'precomputed'.
        If linkage is "ward", only "euclidean" is accepted.
    memory : Instance of joblib.Memory or string (optional)
        Used to cache the output of the computation of the tree.
        By default, no caching is done. If a string is given, it is the
        path to the caching directory.
    n_components : int (optional)
        Number of connected components. If None the number of connected
        components is estimated from the connectivity matrix.
        NOTE: This parameter is now directly determined from the connectivity
        matrix and will be removed in 0.18
    compute_full_tree : bool or 'auto' (optional)
        Stop early the construction of the tree at n_clusters. This is
        useful to decrease computation time if the number of clusters is
        not small compared to the number of samples. This option is
        useful only when specifying a connectivity matrix. Note also that
        when varying the number of clusters and using caching, it may
        be advantageous to compute the full tree.
    linkage : {"ward", "complete", "average"}, optional, default: "ward"
        Which linkage criterion to use. The linkage criterion determines which
        distance to use between sets of observation. The algorithm will merge
        the pairs of cluster that minimize this criterion.
        - ward minimizes the variance of the clusters being merged.
        - average uses the average of the distances of each observation of
          the two sets.
        - complete or maximum linkage uses the maximum distances between
          all observations of the two sets.
    pooling_func : callable, default=np.mean
        This combines the values of agglomerated features into a single
        value, and should accept an array of shape [M, N] and the keyword
        argument ``axis=1``, and reduce it to an array of size [M].
    Attributes
    ----------
    labels_ : array [n_samples]
        cluster labels for each point
    n_leaves_ : int
        Number of leaves in the hierarchical tree.
    n_components_ : int
        The estimated number of connected components in the graph.
    children_ : array-like, shape (n_nodes-1, 2)
        The children of each non-leaf node. Values less than `n_samples`
        correspond to leaves of the tree which are the original samples.
        A node `i` greater than or equal to `n_samples` is a non-leaf
        node and has children `children_[i - n_samples]`. Alternatively
        at the i-th iteration, children[i][0] and children[i][1]
        are merged to form node `n_samples + i`
    """

    def __init__(self, n_clusters=2, affinity="euclidean",
                 memory=Memory(cachedir=None, verbose=0),
                 connectivity=None, n_components=None,
                 compute_full_tree='auto', linkage='ward',
                 pooling_func=np.mean):
        self.n_clusters = n_clusters
        self.memory = memory
        self.n_components = n_components
        self.connectivity = connectivity
        self.compute_full_tree = compute_full_tree
        self.linkage = linkage
        self.affinity = affinity
        self.pooling_func = pooling_func

    def fit(self, X, y=None):
        """Fit the hierarchical clustering on the data
        Parameters
        ----------
        X : array-like, shape = [n_samples, n_features]
            The samples a.k.a. observations.
        Returns
        -------
        self
        """
        X = check_arrays(X)[0]
        memory = self.memory
        if isinstance(memory, six.string_types):
            memory = Memory(cachedir=memory, verbose=0)

        if self.linkage == "ward" and self.affinity != "euclidean":
            raise ValueError("%s was provided as affinity. Ward can only "
                             "work with euclidean distances." %
                             (self.affinity, ))

        if self.linkage not in _TREE_BUILDERS:
            raise ValueError("Unknown linkage type %s."
                             "Valid options are %s" % (self.linkage,
                                                       _TREE_BUILDERS.keys()))
        tree_builder = _TREE_BUILDERS[self.linkage]

        connectivity = self.connectivity
        if self.connectivity is not None:
            if callable(self.connectivity):
                connectivity = self.connectivity(X)
            connectivity = check_arrays(
                connectivity, accept_sparse=['csr', 'coo', 'lil'])

        n_samples = len(X)
        compute_full_tree = self.compute_full_tree
        if self.connectivity is None:
            compute_full_tree = True
        if compute_full_tree == 'auto':
            # Early stopping is likely to give a speed up only for
            # a large number of clusters. The actual threshold
            # implemented here is heuristic
            compute_full_tree = self.n_clusters < max(100, .02 * n_samples)
        n_clusters = self.n_clusters
        if compute_full_tree:
            n_clusters = None

        # Construct the tree
        kwargs = {}
        kwargs['return_distance'] = True
        if self.linkage != 'ward':
            kwargs['linkage'] = self.linkage
            kwargs['affinity'] = self.affinity
        self.children_, self.n_components_, self.n_leaves_, parents, \
            self.distance = memory.cache(tree_builder)(X, connectivity,
                                       n_components=self.n_components,
                                       n_clusters=n_clusters,
                                       **kwargs)
        # Cut the tree
        if compute_full_tree:
            self.labels_ = _hc_cut(self.n_clusters, self.children_,
                                   self.n_leaves_)
        else:
            labels = _hierarchical.hc_get_heads(parents, copy=False)
            # copy to avoid holding a reference on the original array
            labels = np.copy(labels[:n_samples])
            # Reasign cluster numbers
            self.labels_ = np.searchsorted(np.unique(labels), labels)
        return self

Voici un exemple simple montrant comment utiliser la classe AgglomerativeClustering modifiée:

import numpy as np
import AgglomerativeClustering # Make sure to use the new one!!!
d = np.array(
    [
        [1, 2, 3],
        [4, 5, 6],
        [7, 8, 9]
    ]
)

clustering = AgglomerativeClustering(n_clusters=2, compute_full_tree=True,
    affinity='euclidean', linkage='complete')
clustering.fit(d)
print clustering.distance

Cet exemple a la sortie suivante:

[  5.19615242  10.39230485]

Cela peut alors être comparé à une implémentation scipy.cluster.hierarchy.linkage:

import numpy as np
from scipy.cluster.hierarchy import linkage

d = np.array(
        [
            [1, 2, 3],
            [4, 5, 6],
            [7, 8, 9]
        ]
)
print linkage(d, 'complete')

Production:

[[  1.           2.           5.19615242   2.        ]
 [  0.           3.          10.39230485   3.        ]]

Juste pour les coups de pied, j'ai décidé de donner suite à votre déclaration sur les performances:

import AgglomerativeClustering
from scipy.cluster.hierarchy import linkage
import numpy as np
import time

l = 1000; iters = 50
d = [np.random.random(100) for _ in xrange(1000)]

t = time.time()
for _ in xrange(iters):
    clustering = AgglomerativeClustering(n_clusters=l-1,
        affinity='euclidean', linkage='complete')
    clustering.fit(d)
scikit_time = (time.time() - t) / iters
print 'scikit-learn Time: {0}s'.format(scikit_time)

t = time.time()
for _ in xrange(iters):
    linkage(d, 'complete')
scipy_time = (time.time() - t) / iters
print 'SciPy Time: {0}s'.format(scipy_time)

print 'scikit-learn Speedup: {0}'.format(scipy_time / scikit_time)

Cela m'a donné les résultats suivants:

scikit-learn Time: 0.566560001373s
SciPy Time: 0.497740001678s
scikit-learn Speedup: 0.878530077083

Selon cela, l'implémentation de Scikit-Learn prend 0,88x le temps d'exécution de l'implémentation de SciPy, c'est-à-dire que l'implémentation de SciPy est 1,14x plus rapide. Il convient de noter que:

  1. J'ai modifié l'implémentation originale de scikit-learn

  2. Je n'ai fait qu'un petit nombre d'itérations

  3. Je n'ai testé qu'un petit nombre de cas de test (la taille du cluster ainsi que le nombre d'articles par dimension doivent être testés)

  4. J'ai exécuté SciPy en second, il a donc l'avantage d'obtenir plus de hits de cache sur les données source

  5. Les deux méthodes ne font pas exactement la même chose.

Avec tout cela à l'esprit, vous devez vraiment évaluer la méthode qui fonctionne le mieux pour votre application spécifique. Il y a aussi des raisons fonctionnelles d'aller avec une implémentation par rapport à l'autre.

15
TehTechGuy

Mise à jour: je recommande cette solution - https://stackoverflow.com/a/47769506/1333621 , si vous avez trouvé ma tentative utile, veuillez examiner la solution d'Arjun et réexaminer votre vote

Vous devrez générer une "matrice de liaison" à partir du tableau children_ où chaque ligne de la matrice de liaison a le format [idx1, idx2, distance, sample_count].

Ce n'est pas censé être une solution coller et exécuter, je ne garde pas la trace de ce que je devais importer - mais cela devrait être assez clair de toute façon.

Voici une façon de générer la structure requise Z et de visualiser le résultat

X est votre n_samples x n_features des données d'entrée

grappe

agg_cluster = sklearn.cluster.AgglomerativeClustering(n_clusters=n)
agg_labels = agg_cluster.fit_predict(X)

quelques structures de données vides

Z = []
# should really call this cluster dict
node_dict = {}
n_samples = len(X)

écrire une fonction récursive pour rassembler tous les nœuds feuilles associés à un cluster donné, calculer les distances et les positions des centroïdes

def get_all_children(k, verbose=False):
    i,j = agg_cluster.children_[k]

    if k in node_dict:
        return node_dict[k]['children']

    if i < leaf_count:
        left = [i]
    else:
        # read the AgglomerativeClustering doc. to see why I select i-n_samples
        left = get_all_children(i-n_samples)

    if j < leaf_count:
        right = [j]
    else:
        right = get_all_children(j-n_samples)

    if verbose:
        print k,i,j,left, right
    left_pos = np.mean(map(lambda ii: X[ii], left),axis=0)
    right_pos = np.mean(map(lambda ii: X[ii], right),axis=0)

    # this assumes that agg_cluster used euclidean distances
    dist = metrics.pairwise_distances([left_pos,right_pos],metric='euclidean')[0,1]

    all_children = [x for y in [left,right] for x in y]
    pos = np.mean(map(lambda ii: X[ii], all_children),axis=0)

    # store the results to speed up any additional or recursive evaluations
    node_dict[k] = {'top_child':[i,j],'children':all_children, 'pos':pos,'dist':dist, 'node_i':k + n_samples}
    return all_children
    #return node_di|ct

remplir node_dict et générer Z - avec distance et n_échantillons par nœud

for k,x in enumerate(agg_cluster.children_):   
    get_all_children(k,verbose=False)

# Every row in the linkage matrix has the format [idx1, idx2, distance, sample_count].
Z = [[v['top_child'][0],v['top_child'][1],v['dist'],len(v['children'])] for k,v in node_dict.iteritems()]
# create a version with log scaled distances for easier visualization
Z_log =[[v['top_child'][0],v['top_child'][1],np.log(1.0+v['dist']),len(v['children'])] for k,v in node_dict.iteritems()]

tracer en utilisant un dendrogramme scipy

   from scipy.cluster import hierarchy
   plt.figure()
   dn = hierarchy.dendrogram(Z_log,p=4,truncate_mode='level')
   plt.show()

dendrogram

être déçu par l'opacité de cette visualisation et souhaiter pouvoir explorer de manière interactive des clusters plus grands et examiner les distances directionnelles (non scalaires) entre les centroïdes :( - peut-être qu'une solution de bokeh existe?

les références

http://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.hierarchy.dendrogram.html

https://joernhees.de/blog/2015/08/26/scipy-hierarchical-clustering-and-dendrogram-tutorial/#Selecting-a-Distance-Cut-Off-aka-Determining-the-Number -of-Clusters

8
meyerson