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/ cluster / _hierarchical.py
"""Hierarchical Agglomerative Clustering
These routines perform some hierarchical agglomerative clustering of some
input data.
Authors : Vincent Michel, Bertrand Thirion, Alexandre Gramfort,
Gael Varoquaux
License: BSD 3 clause
"""
from heapq import heapify, heappop, heappush, heappushpop
import warnings
import numpy as np
from scipy import sparse
from scipy.sparse.csgraph import connected_components
from ..base import BaseEstimator, ClusterMixin
from ..metrics.pairwise import paired_distances, pairwise_distances
from ..utils import check_array
from ..utils.validation import check_memory
from . import _hierarchical_fast as _hierarchical
from ._feature_agglomeration import AgglomerationTransform
from ..utils._fast_dict import IntFloatDict
from ..utils.fixes import _astype_copy_false
from ..utils import deprecated
###############################################################################
# For non fully-connected graphs
def _fix_connectivity(X, connectivity, affinity):
"""
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_connected_components, labels = connected_components(connectivity)
if n_connected_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_connected_components,
stacklevel=2)
# XXX: Can we do without completing the matrix?
for i in range(n_connected_components):
idx_i = np.where(labels == i)[0]
Xi = X[idx_i]
for j in range(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_connected_components
def _single_linkage_tree(connectivity, n_samples, n_nodes, n_clusters,
n_connected_components, return_distance):
"""
Perform single linkage clustering on sparse data via the minimum
spanning tree from scipy.sparse.csgraph, then using union-find to label.
The parent array is then generated by walking through the tree.
"""
from scipy.sparse.csgraph import minimum_spanning_tree
# explicitly cast connectivity to ensure safety
connectivity = connectivity.astype('float64',
**_astype_copy_false(connectivity))
# Ensure zero distances aren't ignored by setting them to "epsilon"
epsilon_value = np.finfo(dtype=connectivity.data.dtype).eps
connectivity.data[connectivity.data == 0] = epsilon_value
# Use scipy.sparse.csgraph to generate a minimum spanning tree
mst = minimum_spanning_tree(connectivity.tocsr())
# Convert the graph to scipy.cluster.hierarchy array format
mst = mst.tocoo()
# Undo the epsilon values
mst.data[mst.data == epsilon_value] = 0
mst_array = np.vstack([mst.row, mst.col, mst.data]).T
# Sort edges of the min_spanning_tree by weight
mst_array = mst_array[np.argsort(mst_array.T[2]), :]
# Convert edge list into standard hierarchical clustering format
single_linkage_tree = _hierarchical._single_linkage_label(mst_array)
children_ = single_linkage_tree[:, :2].astype(np.int)
# Compute parents
parent = np.arange(n_nodes, dtype=np.intp)
for i, (left, right) in enumerate(children_, n_samples):
if n_clusters is not None and i >= n_nodes:
break
if left < n_nodes:
parent[left] = i
if right < n_nodes:
parent[right] = i
if return_distance:
distances = single_linkage_tree[:, 2]
return children_, n_connected_components, n_samples, parent, distances
return children_, n_connected_components, n_samples, parent
###############################################################################
# Hierarchical tree building functions
def ward_tree(X, connectivity=None, n_clusters=None, return_distance=False):
"""Ward clustering based on a Feature matrix.
Recursively merges the pair of clusters that minimally increases
within-cluster variance.
The inertia matrix uses a Heapq-based representation.
This is the structured version, that takes into account some topological
structure between samples.
Read more in the :ref:`User Guide <hierarchical_clustering>`.
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_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.
return_distance : bool (optional)
If True, return the distance 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_connected_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 : 1D array, shape (n_nodes-1, )
Only returned if return_distance is set to True (for compatibility).
The distances between the centers of the nodes. `distances[i]`
corresponds to a weighted euclidean distance between
the nodes `children[i, 1]` and `children[i, 2]`. If the nodes refer to
leaves of the tree, then `distances[i]` is their unweighted euclidean
distance. Distances are updated in the following way
(from scipy.hierarchy.linkage):
The new entry :math:`d(u,v)` is computed as follows,
.. math::
d(u,v) = \\sqrt{\\frac{|v|+|s|}
{T}d(v,s)^2
+ \\frac{|v|+|t|}
{T}d(v,t)^2
- \\frac{|v|}
{T}d(s,t)^2}
where :math:`u` is the newly joined cluster consisting of
clusters :math:`s` and :math:`t`, :math:`v` is an unused
cluster in the forest, :math:`T=|v|+|s|+|t|`, and
:math:`|*|` is the cardinality of its argument. This is also
known as the incremental algorithm.
"""
X = np.asarray(X)
if X.ndim == 1:
X = np.reshape(X, (-1, 1))
n_samples, n_features = X.shape
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)
X = np.require(X, requirements="W")
out = hierarchy.ward(X)
children_ = out[:, :2].astype(np.intp)
if return_distance:
distances = out[:, 2]
return children_, 1, n_samples, None, distances
else:
return children_, 1, n_samples, None
connectivity, n_connected_components = _fix_connectivity(
X, connectivity,
affinity='euclidean')
if n_clusters is None:
n_nodes = 2 * n_samples - 1
else:
if n_clusters > n_samples:
raise ValueError('Cannot provide more clusters than samples. '
'%i n_clusters was asked, and there are %i samples.'
% (n_clusters, n_samples))
n_nodes = 2 * n_samples - n_clusters
# create inertia matrix
coord_row = []
coord_col = []
A = []
for ind, row in enumerate(connectivity.rows):
A.append(row)
# We keep only the upper triangular for the moments
# Generator expressions are faster than arrays on the following
row = [i for i in row if i < ind]
coord_row.extend(len(row) * [ind, ])
coord_col.extend(row)
coord_row = np.array(coord_row, dtype=np.intp, order='C')
coord_col = np.array(coord_col, dtype=np.intp, order='C')
# build moments as a list
moments_1 = np.zeros(n_nodes, order='C')
moments_1[:n_samples] = 1
moments_2 = np.zeros((n_nodes, n_features), order='C')
moments_2[:n_samples] = X
inertia = np.empty(len(coord_row), dtype=np.float64, order='C')
_hierarchical.compute_ward_dist(moments_1, moments_2, coord_row, coord_col,
inertia)
inertia = list(zip(inertia, coord_row, coord_col))
heapify(inertia)
# prepare the main fields
parent = np.arange(n_nodes, dtype=np.intp)
used_node = np.ones(n_nodes, dtype=bool)
children = []
if return_distance:
distances = np.empty(n_nodes - n_samples)
not_visited = np.empty(n_nodes, dtype=np.int8, order='C')
# recursive merge loop
for k in range(n_samples, n_nodes):
# identify the merge
while True:
inert, i, j = heappop(inertia)
if used_node[i] and used_node[j]:
break
parent[i], parent[j] = k, k
children.append((i, j))
used_node[i] = used_node[j] = False
if return_distance: # store inertia value
distances[k - n_samples] = inert
# update the moments
moments_1[k] = moments_1[i] + moments_1[j]
moments_2[k] = moments_2[i] + moments_2[j]
# update the structure matrix A and the inertia matrix
coord_col = []
not_visited.fill(1)
not_visited[k] = 0
_hierarchical._get_parents(A[i], coord_col, parent, not_visited)
_hierarchical._get_parents(A[j], coord_col, parent, not_visited)
# List comprehension is faster than a for loop
[A[l].append(k) for l in coord_col]
A.append(coord_col)
coord_col = np.array(coord_col, dtype=np.intp, order='C')
coord_row = np.empty(coord_col.shape, dtype=np.intp, order='C')
coord_row.fill(k)
n_additions = len(coord_row)
ini = np.empty(n_additions, dtype=np.float64, order='C')
_hierarchical.compute_ward_dist(moments_1, moments_2,
coord_row, coord_col, ini)
# List comprehension is faster than a for loop
[heappush(inertia, (ini[idx], k, coord_col[idx]))
for idx in range(n_additions)]
# Separate leaves in children (empty lists up to now)
n_leaves = n_samples
# sort children to get consistent output with unstructured version
children = [c[::-1] for c in children]
children = np.array(children) # return numpy array for efficient caching
if return_distance:
# 2 is scaling factor to compare w/ unstructured version
distances = np.sqrt(2. * distances)
return children, n_connected_components, n_leaves, parent, distances
else:
return children, n_connected_components, n_leaves, parent
# single average and complete linkage
def linkage_tree(X, connectivity=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.
Read more in the :ref:`User Guide <hierarchical_clustering>`.
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_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", "single"}, optional, default: "complete"
Which linkage criteria 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.
- single uses the minimum of the 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_connected_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,
'single': None} # Single linkage is handled differently
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 affinity == 'cosine' and np.any(~np.any(X, axis=1)):
raise ValueError(
'Cosine affinity cannot be used when X contains zero vectors')
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, copy=False)
if return_distance:
distances = out[:, 2]
return children_, 1, n_samples, None, distances
return children_, 1, n_samples, None
connectivity, n_connected_components = _fix_connectivity(
X, connectivity,
affinity=affinity)
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].astype(
'float64', **_astype_copy_false(X))
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 linkage == 'single':
return _single_linkage_tree(connectivity, n_samples, n_nodes,
n_clusters, n_connected_components,
return_distance)
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 range(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_connected_components, n_leaves, parent, distances
return children, n_connected_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)
def _single_linkage(*args, **kwargs):
kwargs['linkage'] = 'single'
return linkage_tree(*args, **kwargs)
_TREE_BUILDERS = dict(
ward=ward_tree,
complete=_complete_linkage,
average=_average_linkage,
single=_single_linkage)
###############################################################################
# Functions for cutting hierarchical clustering tree
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 : 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_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 _ in range(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(ClusterMixin, BaseEstimator):
"""
Agglomerative Clustering
Recursively merges the pair of clusters that minimally increases
a given linkage distance.
Read more in the :ref:`User Guide <hierarchical_clustering>`.
Parameters
----------
n_clusters : int or None, optional (default=2)
The number of clusters to find. It must be ``None`` if
``distance_threshold`` is not ``None``.
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.
If "precomputed", a distance matrix (instead of a similarity matrix)
is needed as input for the fit method.
memory : None, str or object with the joblib.Memory interface, 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.
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.
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. It must be ``True`` if
``distance_threshold`` is not ``None``.
linkage : {"ward", "complete", "average", "single"}, 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.
- single uses the minimum of the distances between all observations
of the two sets.
distance_threshold : float, optional (default=None)
The linkage distance threshold above which, clusters will not be
merged. If not ``None``, ``n_clusters`` must be ``None`` and
``compute_full_tree`` must be ``True``.
.. versionadded:: 0.21
Attributes
----------
n_clusters_ : int
The number of clusters found by the algorithm. If
``distance_threshold=None``, it will be equal to the given
``n_clusters``.
labels_ : array [n_samples]
cluster labels for each point
n_leaves_ : int
Number of leaves in the hierarchical tree.
n_connected_components_ : int
The estimated number of connected components in the graph.
children_ : array-like, shape (n_samples-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`
Examples
--------
>>> from sklearn.cluster import AgglomerativeClustering
>>> import numpy as np
>>> X = np.array([[1, 2], [1, 4], [1, 0],
... [4, 2], [4, 4], [4, 0]])
>>> clustering = AgglomerativeClustering().fit(X)
>>> clustering
AgglomerativeClustering()
>>> clustering.labels_
array([1, 1, 1, 0, 0, 0])
"""
def __init__(self, n_clusters=2, affinity="euclidean",
memory=None,
connectivity=None, compute_full_tree='auto',
linkage='ward', distance_threshold=None):
self.n_clusters = n_clusters
self.distance_threshold = distance_threshold
self.memory = memory
self.connectivity = connectivity
self.compute_full_tree = compute_full_tree
self.linkage = linkage
self.affinity = affinity
@deprecated("The ``n_components_`` attribute was deprecated "
"in favor of ``n_connected_components_`` in 0.21 "
"and will be removed in 0.23.")
@property
def n_components_(self):
return self.n_connected_components_
def fit(self, X, y=None):
"""Fit the hierarchical clustering from features, or distance matrix.
Parameters
----------
X : array-like, shape (n_samples, n_features) or (n_samples, n_samples)
Training instances to cluster, or distances between instances if
``affinity='precomputed'``.
y : Ignored
Not used, present here for API consistency by convention.
Returns
-------
self
"""
X = check_array(X, ensure_min_samples=2, estimator=self)
memory = check_memory(self.memory)
if self.n_clusters is not None and self.n_clusters <= 0:
raise ValueError("n_clusters should be an integer greater than 0."
" %s was provided." % str(self.n_clusters))
if not ((self.n_clusters is None) ^ (self.distance_threshold is None)):
raise ValueError("Exactly one of n_clusters and "
"distance_threshold has to be set, and the other "
"needs to be None.")
if (self.distance_threshold is not None
and not self.compute_full_tree):
raise ValueError("compute_full_tree must be True if "
"distance_threshold is set.")
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_array(
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':
if self.distance_threshold is not None:
compute_full_tree = True
else:
# 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 = {}
if self.linkage != 'ward':
kwargs['linkage'] = self.linkage
kwargs['affinity'] = self.affinity
distance_threshold = self.distance_threshold
return_distance = distance_threshold is not None
out = memory.cache(tree_builder)(X, connectivity,
n_clusters=n_clusters,
return_distance=return_distance,
**kwargs)
(self.children_,
self.n_connected_components_,
self.n_leaves_,
parents) = out[:4]
if return_distance:
self.distances_ = out[-1]
self.n_clusters_ = np.count_nonzero(
self.distances_ >= distance_threshold) + 1
else:
self.n_clusters_ = self.n_clusters
# 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])
# Reassign cluster numbers
self.labels_ = np.searchsorted(np.unique(labels), labels)
return self
def fit_predict(self, X, y=None):
"""Fit the hierarchical clustering from features or distance matrix,
and return cluster labels.
Parameters
----------
X : array-like, shape (n_samples, n_features) or (n_samples, n_samples)
Training instances to cluster, or distances between instances if
``affinity='precomputed'``.
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)
class FeatureAgglomeration(AgglomerativeClustering, AgglomerationTransform):
"""Agglomerate features.
Similar to AgglomerativeClustering, but recursively merges features
instead of samples.
Read more in the :ref:`User Guide <hierarchical_clustering>`.
Parameters
----------
n_clusters : int or None, optional (default=2)
The number of clusters to find. It must be ``None`` if
``distance_threshold`` is not ``None``.
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 : None, str or object with the joblib.Memory interface, 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.
connectivity : array-like or callable, optional
Connectivity matrix. Defines for each feature the neighboring
features 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.
compute_full_tree : bool or 'auto', optional, default "auto"
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 features. 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. It must be ``True`` if
``distance_threshold`` is not ``None``.
linkage : {"ward", "complete", "average", "single"}, optional\
(default="ward")
Which linkage criterion to use. The linkage criterion determines which
distance to use between sets of features. 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 feature of
the two sets.
- complete or maximum linkage uses the maximum distances between
all features of the two sets.
- single uses the minimum of the 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].
distance_threshold : float, optional (default=None)
The linkage distance threshold above which, clusters will not be
merged. If not ``None``, ``n_clusters`` must be ``None`` and
``compute_full_tree`` must be ``True``.
.. versionadded:: 0.21
Attributes
----------
n_clusters_ : int
The number of clusters found by the algorithm. If
``distance_threshold=None``, it will be equal to the given
``n_clusters``.
labels_ : array-like, (n_features,)
cluster labels for each feature.
n_leaves_ : int
Number of leaves in the hierarchical tree.
n_connected_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_features`
correspond to leaves of the tree which are the original samples.
A node `i` greater than or equal to `n_features` is a non-leaf
node and has children `children_[i - n_features]`. Alternatively
at the i-th iteration, children[i][0] and children[i][1]
are merged to form node `n_features + i`
distances_ : array-like, shape (n_nodes-1,)
Distances between nodes in the corresponding place in `children_`.
Only computed if distance_threshold is not None.
Examples
--------
>>> import numpy as np
>>> from sklearn import datasets, cluster
>>> digits = datasets.load_digits()
>>> images = digits.images
>>> X = np.reshape(images, (len(images), -1))
>>> agglo = cluster.FeatureAgglomeration(n_clusters=32)
>>> agglo.fit(X)
FeatureAgglomeration(n_clusters=32)
>>> X_reduced = agglo.transform(X)
>>> X_reduced.shape
(1797, 32)
"""
def __init__(self, n_clusters=2, affinity="euclidean",
memory=None,
connectivity=None, compute_full_tree='auto',
linkage='ward', pooling_func=np.mean,
distance_threshold=None):
super().__init__(
n_clusters=n_clusters, memory=memory, connectivity=connectivity,
compute_full_tree=compute_full_tree, linkage=linkage,
affinity=affinity, distance_threshold=distance_threshold)
self.pooling_func = pooling_func
def fit(self, X, y=None, **params):
"""Fit the hierarchical clustering on the data
Parameters
----------
X : array-like of shape (n_samples, n_features)
The data
y : Ignored
Returns
-------
self
"""
X = check_array(X, accept_sparse=['csr', 'csc', 'coo'],
ensure_min_features=2, estimator=self)
return AgglomerativeClustering.fit(self, X.T, **params)
@property
def fit_predict(self):
raise AttributeError