sklearn凝集凝集連鎖マトリックス
完全なリンクを描画しようとしています scipy.cluster.hierarchy.dendrogram 、および scipy.cluster.hierarchy.linkage は sklearn.AgglomerativeClustering よりも遅いことがわかりました。
ただし、 sklearn.AgglomerativeClustering は、クラスター間の距離と元の観測値の数を返しません。これはscipy.cluster.hierarchy.dendrogramに必要です。それらを取る方法はありますか？
私は、sklearnを変更せずに、再帰関数を使用せずにそれを実行するためのsciptを作成しました。使用する前に次のことに注意してください。
- マージの距離は、子のマージの距離に対して減少する場合があります。これらのケースを処理するための3つの方法を追加しました。最大値を取る、何もしない、またはl2ノルムで増やす。 l2ノルムロジックはまだ検証されていません。自分に合ったものを自分で確認してください。
パッケージをインポートします：
from sklearn.cluster import AgglomerativeClustering
import numpy as np
import matplotlib.pyplot as plt
from scipy.cluster.hierarchy import dendrogram
重みと距離を計算する関数：
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
2つのクラスターと2つのサブクラスターのサンプルデータを作成します：
# 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)
サンプルデータ：
クラスタリングモデルに適合
model = AgglomerativeClustering(n_clusters=2,linkage="ward")
model.fit(X)
関数を呼び出して距離を見つけ、それを系統樹に渡します
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()
出力系統図：
それは可能ですが、それはきれいではありません。 （少なくとも）_AgglomerativeClustering.fit_（ source ）の小さな書き換えが必要です。困難なのは、このメソッドが多くのインポートを必要とするため、最終的に少し見た目が悪くなることです。この機能を追加するには：
行748の後に次の行を挿入します。
kwargs ['return_distance'] = True
752行目を次のように置き換えます。
self.children_、self.n_components_、self.n_leaves_、親、self.distance = \
これにより、新しい属性distanceが得られ、簡単に呼び出すことができます。
注意点がいくつかあります：
これを行うと、711行目の_
check_array_関数に関する this の問題に遭遇しました。これは_check_arrays_（_from sklearn.utils.validation import check_arrays_）を使用して修正できます。その行を変更してX = check_arrays(X)[0]にできます。これはバグのようです（scikit-learnの最新バージョンではこの問題がまだあります）。使用している_
sklearn.cluster.hierarchical.linkage_tree_のバージョンによっては、 source で提供されているものに変更する必要があります。
すべての人にとって物事を簡単にするために、使用する必要がある完全なコードを以下に示します。
_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
_以下は、変更されたAgglomerativeClusteringクラスの使用方法を示す簡単な例です。
_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
_この例の出力は次のとおりです。
_[ 5.19615242 10.39230485]
_次に、これを_scipy.cluster.hierarchy.linkage_実装と比較できます。
_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')
_出力：
_[[ 1. 2. 5.19615242 2. ]
[ 0. 3. 10.39230485 3. ]]
_キックのために、パフォーマンスに関するあなたの声明をフォローアップすることにしました。
_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)
_これにより、次の結果が得られました。
_scikit-learn Time: 0.566560001373s
SciPy Time: 0.497740001678s
scikit-learn Speedup: 0.878530077083
_これによると、Scikit-Learnの実装はSciPy実装の実行時間の0.88倍かかります。つまり、SciPyの実装は1.14倍高速です。注意すべきこと：
元のscikit-learn実装を変更しました
私は少数の反復しかしませんでした
少数のテストケースのみをテストしました（クラスターサイズとディメンションごとのアイテム数の両方をテストする必要があります）
2番目にSciPyを実行したため、ソースデータでより多くのキャッシュヒットを取得できるという利点がありました。
2つの方法は、まったく同じことを行いません。
これらすべてを念頭に置いて、特定のアプリケーションに対してどのメソッドがよりよく機能するかを実際に評価する必要があります。また、ある実装を他の実装よりも機能的にする理由もあります。
更新：このソリューションをお勧めします- https://stackoverflow.com/a/47769506/1333621 、私の試みが有用であることがわかった場合は、Arjunのソリューションを調べて、投票
children_配列から "linkage matrix"を生成する必要があります。ここで、linkage matrixのすべての行の形式は[idx1、idx2、distance、sample_count]です。
これは貼り付けて実行するソリューションを意図したものではなく、インポートする必要があるものを追跡していませんが、とにかくはっきりしているはずです。
必要な構造Zを生成し、結果を視覚化する1つの方法を次に示します
Xはあなたのn_samples x n_features入力データ
集まる
agg_cluster = sklearn.cluster.AgglomerativeClustering(n_clusters=n)
agg_labels = agg_cluster.fit_predict(X)
いくつかの空のデータ構造
Z = []
# should really call this cluster dict
node_dict = {}
n_samples = len(X)
特定のクラスターに関連付けられたすべての葉ノードを収集し、距離と重心位置を計算する再帰関数を作成します
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
node_dictおよびZを生成-ノードごとの距離とn_samples
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()]
scipy樹形図を使用してプロットする
from scipy.cluster import hierarchy
plt.figure()
dn = hierarchy.dendrogram(Z_log,p=4,truncate_mode='level')
plt.show()
この視覚化がどれほど不透明であるかに失望し、インタラクティブに大きなクラスターにドリルダウンし、重心間の方向（スカラーではない）の距離を調べることができることを望んでいます:(ボケソリューションが存在する可能性がありますか？
参照
http://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.hierarchy.dendrogram.html