def __hieclu(self):
#use Hierarchical clustering
print 'using hierarchical clustering......'
ac = Ward(n_clusters=self.k)
ac.fit(self.data_matrix)
result = ac.fit_predict(self.data_matrix)
return result
def hieclu(data_matrix, k):
#use Hierarchical clustering
print 'using hierarchical clustering......'
ac = Ward(n_clusters=k)
ac.fit(data_matrix)
result = ac.fit_predict(data_matrix)
return result
def test_connectivity_popagation():
"""
Check that connectivity in the ward tree is propagated correctly during
merging.
"""
from sklearn.neighbors import NearestNeighbors
X = np.array(
[
(0.014, 0.120),
(0.014, 0.099),
(0.014, 0.097),
(0.017, 0.153),
(0.017, 0.153),
(0.018, 0.153),
(0.018, 0.153),
(0.018, 0.153),
(0.018, 0.153),
(0.018, 0.153),
(0.018, 0.153),
(0.018, 0.153),
(0.018, 0.152),
(0.018, 0.149),
(0.018, 0.144),
]
)
nn = NearestNeighbors(n_neighbors=10).fit(X)
connectivity = nn.kneighbors_graph(X)
ward = Ward(n_clusters=4, connectivity=connectivity)
# If changes are not propagated correctly, fit crashes with an
# IndexError
ward.fit(X)
def compute_clusters(dataset, features_vector):
"""
Apply clustering method
"""
labels = dataset.target
true_k = np.unique(labels).shape[0]
# Run clustering method
print "Performing clustering with method ", cmd_options.clust_method.upper(
)
print
if (cmd_options.clust_method == "hclust"):
result = features_vector.toarray()
ward = Ward(n_clusters=true_k)
ward.fit(result)
return ward
if (cmd_options.clust_method == "kmeans"):
km = KMeans(n_clusters=true_k,
init='k-means++',
max_iter=1000,
verbose=1)
km.fit(features_vector)
return km
def test_connectivity_popagation():
"""
Check that connectivity in the ward tree is propagated correctly during
merging.
"""
from sklearn.neighbors import kneighbors_graph
X = np.array([
(.014, .120),
(.014, .099),
(.014, .097),
(.017, .153),
(.017, .153),
(.018, .153),
(.018, .153),
(.018, .153),
(.018, .153),
(.018, .153),
(.018, .153),
(.018, .153),
(.018, .152),
(.018, .149),
(.018, .144),
])
connectivity = kneighbors_graph(X, 10)
ward = Ward(n_clusters=4, connectivity=connectivity)
# If changes are not propagated correctly, fit crashes with an
# IndexError
ward.fit(X)
def __hieclu(self): #use Hierarchical clustering print 'using hierarchical clustering......' ac = Ward(n_clusters = self.k) ac.fit(self.data_matrix) result = ac.fit_predict(self.data_matrix) return result
def hieclu(data_matrix, k): #use Hierarchical clustering print 'using hierarchical clustering......' ac = Ward(n_clusters=k) ac.fit(data_matrix) result = ac.fit_predict(data_matrix) return result
def test_connectivity_popagation():
"""
Check that connectivity in the ward tree is propagated correctly during
merging.
"""
from sklearn.neighbors import NearestNeighbors
X = np.array([
(.014, .120),
(.014, .099),
(.014, .097),
(.017, .153),
(.017, .153),
(.018, .153),
(.018, .153),
(.018, .153),
(.018, .153),
(.018, .153),
(.018, .153),
(.018, .153),
(.018, .152),
(.018, .149),
(.018, .144),
])
nn = NearestNeighbors(n_neighbors=10, warn_on_equidistant=False).fit(X)
connectivity = nn.kneighbors_graph(X)
ward = Ward(n_clusters=4, connectivity=connectivity)
# If changes are not propagated correctly, fit crashes with an
# IndexError
ward.fit(X)
def test_ward_clustering():
"""
Check that we obtain the correct number of clusters with Ward clustering.
"""
rnd = np.random.RandomState(0)
mask = np.ones([10, 10], dtype=np.bool)
X = rnd.randn(100, 50)
connectivity = grid_to_graph(*mask.shape)
clustering = Ward(n_clusters=10, connectivity=connectivity)
clustering.fit(X)
assert_true(np.size(np.unique(clustering.labels_)) == 10)
def test_ward_clustering():
"""
Check that we obtain the correct number of clusters with Ward clustering.
"""
np.random.seed(0)
mask = np.ones([10, 10], dtype=np.bool)
X = np.random.randn(100, 50)
connectivity = grid_to_graph(*mask.shape)
clustering = Ward(n_clusters=10, connectivity=connectivity)
clustering.fit(X)
assert_true(np.size(np.unique(clustering.labels_)) == 10)
def test_connectivity_fixing_non_lil():
"""
Check non regression of a bug if a non item assignable connectivity is
provided with more than one component.
"""
# create dummy data
x = np.array([[0, 0], [1, 1]])
# create a mask with several components to force connectivity fixing
m = np.array([[True, False], [False, True]])
c = grid_to_graph(n_x=2, n_y=2, mask=m)
w = Ward(connectivity=c)
w.fit(x)
def test_connectivity_fixing_non_lil():
"""
Check non regression of a bug if a non item assignable connectivity is
provided with more than one component.
"""
# create dummy data
x = np.array([[0, 0], [1, 1]])
# create a mask with several components to force connectivity fixing
m = np.array([[True, False], [False, True]])
c = grid_to_graph(n_x=2, n_y=2, mask=m)
w = Ward(connectivity=c)
w.fit(x)
def test_ward_clustering():
"""
Check that we obtain the correct number of clusters with Ward clustering.
"""
rnd = np.random.RandomState(0)
mask = np.ones([10, 10], dtype=np.bool)
X = rnd.randn(100, 50)
connectivity = grid_to_graph(*mask.shape)
clustering = Ward(n_clusters=10, connectivity=connectivity)
clustering.fit(X)
# test caching
clustering = Ward(n_clusters=10, connectivity=connectivity,
memory=mkdtemp())
clustering.fit(X)
labels = clustering.labels_
assert_true(np.size(np.unique(labels)) == 10)
# Turn caching off now
clustering = Ward(n_clusters=10, connectivity=connectivity)
# Check that we obtain the same solution with early-stopping of the
# tree building
clustering.compute_full_tree = False
clustering.fit(X)
np.testing.assert_array_equal(clustering.labels_, labels)
clustering.connectivity = None
clustering.fit(X)
assert_true(np.size(np.unique(clustering.labels_)) == 10)
# Check that we raise a TypeError on dense matrices
clustering = Ward(n_clusters=10,
connectivity=connectivity.todense())
assert_raises(TypeError, clustering.fit, X)
clustering = Ward(n_clusters=10,
connectivity=sparse.lil_matrix(
connectivity.todense()[:10, :10]))
assert_raises(ValueError, clustering.fit, X)
def spectral_cluster(data, n_clusters, method='sl'):
# 获取拉普拉斯矩阵
if method == 'NJW':
lap_matrix = get_lap_matrix_njw(data, 0.1)
eigenvalues, eigenvectors = np.linalg.eig(lap_matrix)
idx = eigenvalues.argsort()[::-1]
eigenvalues = eigenvalues[idx]
eigenvectors = eigenvectors[:, idx]
elif method == 'self-tuning':
lap_matrix = get_lap_matrix_self_tuning(data)
eigenvalues, eigenvectors = np.linalg.eig(lap_matrix)
idx = eigenvalues.argsort()[::-1]
eigenvalues = eigenvalues[idx]
eigenvectors = eigenvectors[:, idx]
else:
lap_matrix = get_lap_matrix_sl(data, 0.1)
eigenvalues, eigenvectors = np.linalg.eig(lap_matrix)
idx = eigenvalues.argsort()
eigenvalues = eigenvalues[idx]
eigenvectors = eigenvectors[:, idx]
#print(eigenvalues)
# 获取前n_clusters个特征向量
x_matrix = eigenvectors[:, 0:n_clusters]
# 归一化特征向量矩阵
y_matrix = normal_eigen(x_matrix)
# 调用自己写的k_means函数
"""
k_dist_dic, k_centers_dic, cluster_group = kmeans.k_means(y_matrix, n_clusters)
mat_plot_cluster_sample(data, cluster_group, method)
"""
# 调用自己写的bi_k_means函数
"""center_list, cluster_assign = bikmeans.exe_bi_k_means(y_matrix, n_clusters)
labels = cluster_assign[:, 0]
mat_plot_cluster_sample(data, labels. method)
# 调用sklearn中的KMeans函数，效果比自己写的强了好多
k_means = KMeans(n_clusters)
k_means.fit(y_matrix)
#k_centers = k_means.cluster_centers_
#mat_plot_cluster_sample(data, k_means.labels_, method)
"""
# 调用sklearn中的hierarchical 聚类方法进行聚类
hie_cluster = Ward(n_clusters)
hie_cluster.fit(y_matrix)
mat_plot_cluster_sample(data, hie_cluster.labels_, method)
def ward(self, X, n_clusters, plot=True):
k_means = Ward(n_clusters=n_clusters, copy=False, compute_full_tree=True, memory="cache")
k_means.fit(X)
labels = k_means.labels_
pl.close('all')
pl.figure(1)
pl.clf()
if plot:
colors = "rbgcmybgrcmybgrcmybgrcm" * 10
X2d = RandomizedPCA(n_components=2).fit_transform(X)
for i in xrange(len(X2d)):
x = X2d[i]
pl.plot(x[0], x[1], "o", markerfacecolor=colors[labels[i]], markeredgecolor=colors[labels[i]], alpha=0.035)
pl.show()
return k_means.labels_
def cluster_ward(self, calpha=True):
'''
cluster the positively predicted residues using the Ward method.
Returns a list of cluster labels the same length as the number of positively predicted residues.
'''
if calpha:
data_atoms = self.positive_surface_residues.ca
#else:
# data_atoms = self.positive_surface_residues.select('ca or sidechain').copy()
if data_atoms.getCoords().shape[0] < 4:
print self.pdbid, data_atoms.getCoords().shape
return {}
connectivity = kneighbors_graph(data_atoms.getCoords(), 5)
ward = Ward(n_clusters=self.WARD_N_CLUSTERS, connectivity=connectivity)
ward.fit(data_atoms.getCoords())
resnums = data_atoms.getResnums()
reslabels = ward.labels_
clusters = sorted([resnums[reslabels==i] for i in set(reslabels)], key=len, reverse=True)
return dict(enumerate(clusters))
def compute_clusters(dataset,features_vector):
"""
Apply clustering method
"""
labels = dataset.target
true_k = np.unique(labels).shape[0]
# Run clustering method
print "Performing clustering with method ", cmd_options.clust_method.upper()
print
if(cmd_options.clust_method == "hclust"):
result = features_vector.toarray()
ward = Ward(n_clusters=true_k)
ward.fit(result)
return ward
if(cmd_options.clust_method == "kmeans"):
km = KMeans(n_clusters=true_k, init='k-means++', max_iter=1000, verbose=1)
km.fit(features_vector)
return km
print("Homogeneity k-means: %0.3f" % metrics.homogeneity_score(labels, km.labels_))
print("Completeness k-means: %0.3f" % metrics.completeness_score(labels, km.labels_))
print("V-measure k-means: %0.3f" % metrics.v_measure_score(labels, km.labels_))
print("Silhouette Coefficient k-means: %0.3f" % metrics.silhouette_score(clustering, km.labels_, sample_size = 8000))
# DBSCAN
# Structured hierarchical clustering
db = DBSCAN()
db.fit(clustering)
print 'DBSCAN clusters created..'
print("Homogeneity DBSCAN: %0.3f" % metrics.homogeneity_score(labels, db.labels_))
print("Completeness DBSCAN: %0.3f" % metrics.completeness_score(labels, db.labels_))
print("V-measure DBSCAN: %0.3f" % metrics.v_measure_score(labels, db.labels_))
print("Silhouette Coefficient DBSCAN: %0.3f" % metrics.silhouette_score(clustering, db.labels_, sample_size = 5000))
# Structured hierarchical clustering
ward = Ward(n_clusters = 9)
ward.fit(clustering)
print 'Hierarchical clusters created..'
print("Homogeneity hierarchical: %0.3f" % metrics.homogeneity_score(labels, ward.labels_))
print("Completeness hierarchical: %0.3f" % metrics.completeness_score(labels, ward.labels_))
print("V-measure hierarchical: %0.3f" % metrics.v_measure_score(labels, ward.labels_))
print("Silhouette Coefficient hierarchical: %0.3f" % metrics.silhouette_score(clustering, ward.labels_, sample_size = 5000))
print i
train = pd.concat([train, pd.get_dummies(raw_train[i])], axis=1)
freq = train.groupby('Report ID').sum()
freq = freq.drop('Has Combined Queries', 1)
# Train Model #############################
num_cluster = 12
kmean = KMeans(n_clusters=num_cluster, max_iter=400, verbose = 0, n_jobs = 2, n_init=20, tol=1e-6)
model_kmean = kmean.fit(freq)
ward = Ward(n_clusters=num_cluster)
model_ward = ward.fit(freq)
from sklearn.neighbors import kneighbors_graph
connectivity = kneighbors_graph(freq, n_neighbors=4)
#ward = Ward(n_clusters=num_cluster, connectivity = connectivity)
#model_ward = ward.fit(freq)
# Visualization #####################################################
import mpl_toolkits.mplot3d.axes3d as p3
import pylab as pl
from sklearn.datasets.samples_generator import make_friedman3
def plot(model, data, name):
def encode(self, interm_rep, neighborhood_size = 26,
clust_ratio=10,
encoding='geometrical',
similarity_measure='pearson',
threshold=0.3, n_jobs=1, **kwds):
"""
Parameters
----------
interm_rep: IntermRep
IntermRep object containing the arr_xyz and arr_voxel matrixes.
neighborhood_size: int
Number of neighbors each voxel will be connected to.
clust_ratio: int
The number of clusters will be equal to n/clust_ratio, where n is
the number of voxels.
encoding: string
Type of encoding. 'geometrical' and 'functional' are allowed.
similarity_measure: string
Similarity measure used to compare the representative value of each
parcel (cluster). 'pearson' or the measures available in scikit-learn
are allowed.
threshold: float
Threshold applied to the similarity values in order to define the
edges in the graph.
Returns
-------
g: Graph
Networkx graph representing the graph encoding of the data.
"""
#computing the connectivity matrix, each voxel is connected to
#"neighborhood_size" neighbors.
#
conn = kneighbors_graph(interm_rep.arr_xyz, n_neighbors=neighborhood_size)
# conn_n = kneighbors_graph(interm_rep.arr_xyz, n_neighbors=neighborhood_size)
# conn_r = radius_neighbors_graph(interm_rep.arr_xyz, radius=10)
# conn = conn_n * conn_r
#Hierarchical clustering algorithm. The number of clusters is defined
#accoring to the parameter "clust_ratio".
ward = Ward(n_clusters=len(interm_rep.arr_xyz)/clust_ratio, connectivity=conn)
#ward = Ward(n_clusters=60, connectivity=conn)
#Type of encoding: geometrical (only xyz data is used) or
# functional (voxel time series is used).
if encoding=='geometrical':
ward.fit(interm_rep.arr_xyz)
elif encoding=='functional':
ward.fit(interm_rep.arr_voxels)
labels = ward.labels_
#Plotting the voxels with the cluster labels.
#pp.plot_clustering_intermediate_representation(interm_rep, labels*10)
#Computing the unique cluster indentifiers
l_unique = np.unique(labels)
mean_voxels = np.zeros((len(l_unique), interm_rep.arr_voxels.shape[1]))
mean_xyz = np.zeros((len(l_unique), interm_rep.arr_xyz.shape[1]))
cont = 0
for i in l_unique:
#Taking the possitions corresponding to the same cluster.
pos = np.where(labels == i)[0]
#Taking data from these possitions and computing the mean time serie
m_voxel = interm_rep.arr_voxels[pos].mean(0)
#Taking the xyz from these positions and computing the mean value
m_xyz = interm_rep.arr_xyz[pos].mean(0)
mean_voxels[cont] = m_voxel
mean_xyz[cont] = m_xyz
cont += 1
#plotting the voxels time series for each cluster
#pp.plot_interm_representation_time_series(ir.IntermRep(mean_voxels, mean_xyz))
#The new intermediate representation is given by mean_voxels and
# mean_xyz.
#Computing similarity matrix and applying the threshold
adj_mat = np.zeros((len(mean_voxels), len(mean_voxels)),
dtype = np.byte)
for j in range(len(mean_voxels) - 1):
for k in range(j + 1, len(mean_voxels)):
if similarity_measure == 'pearson':
aux = st.pearsonr(mean_voxels[j], mean_voxels[k])[0]
else:
aux = skpw.pairwise_kernel(mean_voxels[j], mean_voxels[k],
metric = similarity_measure,
n_jobs = n_jobs)
if aux >= threshold:
adj_mat[j,k] = 1
adj_mat[k,j] = 1
# #Weighted encoding (for graph kernels that work with weighted graphs)
# #------------------------------------
# adj_mat = np.zeros((len(mean_voxels), len(mean_voxels)),
# dtype = np.float)
# for j in range(len(mean_voxels) - 1):
# for k in range(j + 1, len(mean_voxels)):
# if similarity_measure == 'pearson':
# aux = st.pearsonr(mean_voxels[j], mean_voxels[k])[0]
# else:
# aux = skpw.pairwise_kernel(mean_voxels[j], mean_voxels[k],
# metric = similarity_measure,
# n_jobs = n_jobs)
## if aux >= threshold:
## adj_mat[j,k] = aux
## adj_mat[k,j] = aux
# adj_mat[j,k] = adj_mat[k,j] = aux
# adj_mat = (adj_mat - np.mean(adj_mat))/np.std(adj_mat)
# adj_mat = (adj_mat - np.min(adj_mat))/(np.max(adj_mat) - np.min(adj_mat))
# adj_mat = np.where(adj_mat>=threshold, 1, 0)
# #------------------------------------
#Building the graph from the adjacency matrix
g = nx.from_numpy_matrix(adj_mat)
#Spliting the node degrees into some categories and using them as node labels.
# num_lab = 5
deg = g.degree()
# for k in deg:
# deg[k]/= num_lab
nx.set_node_attributes(g, 'node_label', deg)
############
#Storing the mean time-series of each parcell as a node attribute
ts_att = {}
mv = mean_voxels.tolist()
for pos in range(len(mv)):
ts_att[pos] = mv[pos]
nx.set_node_attributes(g, 'time_series', ts_att)
#Saving the graphs for CLFR subject (the one for which I have the structural data)
# if interm_rep.subj_name == 'CLFR':
# nx.write_gexf(g, 'graph_gephi_format.gexf')
# np.savetxt('CLFR_clusters_xyz.txt', mean_xyz, fmt='%1d', delimiter=' ')
# edges = np.array(np.where(adj_mat==1)).T
# np.savetxt('CLFR_clusters_timeseries_cond%s.txt' %(interm_rep.cls), edges, fmt='%1d', delimiter=' ')
#Plot Graphs
#pp.plot_graph(mean_xyz, g)
return g
def ward(X, n_clust):
"H"
ward = Ward(n_clusters=n_clust)
ward.fit(X)
return ward
def HierachicalClustering(X, Expect_ext):
from sklearn.cluster import Ward
HC = Ward(n_clusters=Expect_ext)
HC.fit(X)
return HC.labels_
def ward(X, n_clust):
"H"
ward = Ward(n_clusters=n_clust)
ward.fit(X)
return ward
class VisualVocabulary:
""" Creates a visual vocabulary and quantises visual features """
def __init__(self, pathFile=None, flagVerbose=False):
self.mbk = None
self.ward = None
# If a path file is provided...
if pathFile != None:
# ...read from disk
self.loadFromDisk(pathFile)
if flagVerbose == True:
self.flagVerbose = 1
else:
self.flagVerbose = 0
def readImageIdsFromTxtFile(self, pathTxtFile):
""" Read the image IDs contained in a text file """
print pathTxtFile
if not os.path.exists(pathTxtFile):
print 'File not found ' + pathTxtFile
return []
# Read the file containing the image IDs
fileDataset = open(pathTxtFile, 'r')
# Read lines from the text file, stripping the end of line character
imageIds = [line.strip() for line in fileDataset]
# Close file
fileDataset.close()
return imageIds
def buildFromImageCollection(self,
pathTxtFile,
pathDirImages,
fileImageExtension,
vocabularySize=4096,
maxNumImages=sys.maxint):
# Read the image IDs
imageIds = self.readImageIdsFromTxtFile(pathTxtFile)
# If there are more images than the considered ones...
if (len(imageIds) > maxNumImages):
imageIds = random.sample(imageIds, maxNumImages)
# Extract the SURF descriptors from a collection of images and save in dictionary
surfExtractor = SurfExtractor(True, True)
surfExtractor.processCollectionFilesImage(imageIds, pathDirImages,
fileImageExtension)
# Create a numpy array from the descriptors
descriptors = surfExtractor.getDescriptors()
arr_descriptor = np.vstack(tuple(descriptors))
# if( self.flagRunOnServer == True):
# # K-means: The amount of clusters is specified with 'k' in the sci-kit version
# # in the GPI computation service
# self.mbk = MiniBatchKMeans(init='k-means++',
# k=vocabularySize,
# init_size=3*vocabularySize,
# max_no_improvement=10,
# verbose=1)
# else:
# K-means: The amount of clusters is specified in 'n_clusters' in latest scikit-learn version
self.mbk = MiniBatchKMeans(init='k-means++',
n_clusters=vocabularySize,
init_size=3 * vocabularySize,
max_no_improvement=10,
verbose=self.flagVerbose)
self.mbk.fit(arr_descriptor)
def buildFromImageCollectionWard(self,
pathTxtFile,
pathDirImages,
fileImageExtension,
vocabularySize,
maxNumImages=sys.maxint):
# vocabularySize could be 4096
# Read the image IDs
imageIds = self.readImageIdsFromTxtFile(pathTxtFile)
# If there are more images than the considered ones...
if (len(imageIds) > maxNumImages):
imageIds = random.sample(imageIds, maxNumImages)
# Extract the SURF descriptors from a collection of images and save in dictionary
surfExtractor = SurfExtractor(True)
surfExtractor.processCollectionFilesImage(imageIds, pathDirImages,
fileImageExtension)
# Create a numpy array from the descriptors
descriptors = surfExtractor.getDescriptors()
arr_descriptor = np.vstack(tuple(descriptors))
#self.mbk = MiniBatchKMeans(init='k-means++',
# k=vocabularySize,
# n_init=10,
# max_no_improvement=10,
# verbose=0)
self.ward = Ward(n_clusters=vocabularySize)
self.ward.fit(arr_descriptor)
def loadFromDisk(self, pathFile):
if not os.path.exists(pathFile):
print "File not found " + pathFile
return
self.mbk = pickle.load(open(pathFile, "rb"))
def saveToDisk(self, pathFile):
# Save mini batch K-Means to disk using Pickle
pickle.dump(self.mbk, open(pathFile, "wb"))
def quantizeVector(self, descriptors):
# if len(descriptors)<128:
# descriptors
# Vector quantization with the visual vocabulary
quant = self.mbk.predict(descriptors)
# Build Histogram
histogram = np.histogram(quant, bins=self.mbk.n_clusters)
# histogram = np.histogram(quant, bins=self.mbk.k)
return histogram
from sklearn.cluster import Ward
ward = Ward(n_clusters=15)
n_samples = np.logspace(.5, 3, 9)
n_features = np.logspace(1, 3.5, 7)
N_samples, N_features = np.meshgrid(n_samples,
n_features)
scikits_time = np.zeros(N_samples.shape)
scipy_time = np.zeros(N_samples.shape)
for i, n in enumerate(n_samples):
for j, p in enumerate(n_features):
X = np.random.normal(size=(n, p))
t0 = time.time()
ward.fit(X)
scikits_time[j, i] = time.time() - t0
t0 = time.time()
hierarchy.ward(X)
scipy_time[j, i] = time.time() - t0
ratio = scikits_time/scipy_time
pl.clf()
pl.imshow(np.log(ratio), aspect='auto', origin="lower")
pl.colorbar()
pl.contour(ratio, levels=[1, ], colors='k')
pl.yticks(range(len(n_features)), n_features.astype(np.int))
pl.ylabel('N features')
pl.xticks(range(len(n_samples)), n_samples.astype(np.int))
pl.xlabel('N samples')
from sklearn.cluster import Ward
ward = Ward(n_clusters=3)
n_samples = np.logspace(.5, 3, 9)
n_features = np.logspace(1, 3.5, 7)
N_samples, N_features = np.meshgrid(n_samples,
n_features)
scikits_time = np.zeros(N_samples.shape)
scipy_time = np.zeros(N_samples.shape)
for i, n in enumerate(n_samples):
for j, p in enumerate(n_features):
X = np.random.normal(size=(n, p))
t0 = time.time()
ward.fit(X)
scikits_time[j, i] = time.time() - t0
t0 = time.time()
hierarchy.ward(X)
scipy_time[j, i] = time.time() - t0
ratio = scikits_time / scipy_time
pl.figure("scikit-learn Ward's method benchmark results")
pl.imshow(np.log(ratio), aspect='auto', origin="lower")
pl.colorbar()
pl.contour(ratio, levels=[1, ], colors='k')
pl.yticks(range(len(n_features)), n_features.astype(np.int))
pl.ylabel('N features')
pl.xticks(range(len(n_samples)), n_samples.astype(np.int))
pl.xlabel('N samples')
