def testNormaliseArray(self):
numExamples = 10
numFeatures = 3
preprocessor = Standardiser()
# Test an everyday matrix
X = numpy.random.rand(numExamples, numFeatures)
Xn = preprocessor.normaliseArray(X)
normV = preprocessor.getNormVector()
self.assertAlmostEquals(numpy.sum(Xn * Xn), numFeatures, places=3)
norms = numpy.sum(Xn * Xn, 0)
for i in range(0, norms.shape[0]):
self.assertAlmostEquals(norms[i], 1, places=3)
self.assertTrue((X / normV == Xn).all())
# Zero one column
preprocessor = Standardiser()
X[:, 1] = 0
Xn = preprocessor.normaliseArray(X)
normV = preprocessor.getNormVector()
self.assertAlmostEquals(numpy.sum(Xn * Xn), numFeatures - 1, places=3)
self.assertTrue((X / normV == Xn).all())
# Now take out 3 rows of X, normalise and compare to normalised X
Xs = X[0:3, :]
Xsn = preprocessor.normaliseArray(Xs)
self.assertTrue((Xsn == Xn[0:3, :]).all())
def cluster(self, graph):
"""
Take a graph and cluster using the method in "On spectral clusering: analysis
and algorithm" by Ng et al., 2001.
:param graph: the graph to cluster
:type graph: :class:`apgl.graph.AbstractMatrixGraph`
:returns: An array of size graph.getNumVertices() of cluster membership
"""
L = graph.normalisedLaplacianSym()
omega, Q = numpy.linalg.eig(L)
inds = numpy.argsort(omega)
#First normalise rows, then columns
standardiser = Standardiser()
V = standardiser.normaliseArray(Q[:, inds[0:self.k]].T).T
V = vq.whiten(V)
#Using kmeans2 here seems to result in a high variance
#in the quality of clustering. Therefore stick to kmeans
centroids, clusters = vq.kmeans(V, self.k, iter=self.numIterKmeans)
clusters, distortion = vq.vq(V, centroids)
return clusters
def matrixSimilarity(self, V1, V2):
"""
Compute a vertex similarity matrix C, such that the ijth entry is the matching
score between V1_i and V2_j, where larger is a better match.
"""
X = numpy.r_[V1, V2]
standardiser = Standardiser()
X = standardiser.normaliseArray(X)
V1 = X[0 : V1.shape[0], :]
V2 = X[V1.shape[0] :, :]
# print(X)
# Extend arrays with zeros to make them the same size
# if V1.shape[0] < V2.shape[0]:
# V1 = Util.extendArray(V1, V2.shape, numpy.min(V1))
# elif V2.shape[0] < V1.shape[0]:
# V2 = Util.extendArray(V2, V1.shape, numpy.min(V2))
# Let's compute C as the distance between vertices
# Distance is bounded by 1
D = Util.distanceMatrix(V1, V2)
maxD = numpy.max(D)
minD = numpy.min(D)
if (maxD - minD) != 0:
C = (maxD - D) / (maxD - minD)
else:
C = numpy.ones((V1.shape[0], V2.shape[0]))
return C
def cluster(self, graph):
"""
Take a graph and cluster using the method in "On spectral clusering: analysis
and algorithm" by Ng et al., 2001.
:param graph: the graph to cluster
:type graph: :class:`apgl.graph.AbstractMatrixGraph`
:returns: An array of size graph.getNumVertices() of cluster membership
"""
L = graph.normalisedLaplacianSym()
omega, Q = numpy.linalg.eig(L)
inds = numpy.argsort(omega)
#First normalise rows, then columns
standardiser = Standardiser()
V = standardiser.normaliseArray(Q[:, inds[0:self.k]].T).T
V = vq.whiten(V)
#Using kmeans2 here seems to result in a high variance
#in the quality of clustering. Therefore stick to kmeans
centroids, clusters = vq.kmeans(V, self.k, iter=self.numIterKmeans)
clusters, distortion = vq.vq(V, centroids)
return clusters
def matrixSimilarity(self, V1, V2):
"""
Compute a vertex similarity matrix C, such that the ijth entry is the matching
score between V1_i and V2_j, where larger is a better match.
"""
X = numpy.r_[V1, V2]
standardiser = Standardiser()
X = standardiser.normaliseArray(X)
V1 = X[0:V1.shape[0], :]
V2 = X[V1.shape[0]:, :]
#print(X)
#Extend arrays with zeros to make them the same size
#if V1.shape[0] < V2.shape[0]:
# V1 = Util.extendArray(V1, V2.shape, numpy.min(V1))
#elif V2.shape[0] < V1.shape[0]:
# V2 = Util.extendArray(V2, V1.shape, numpy.min(V2))
#Let's compute C as the distance between vertices
#Distance is bounded by 1
D = Util.distanceMatrix(V1, V2)
maxD = numpy.max(D)
minD = numpy.min(D)
if (maxD - minD) != 0:
C = (maxD - D) / (maxD - minD)
else:
C = numpy.ones((V1.shape[0], V2.shape[0]))
return C
def clusterFromIterator(self, graphListIterator, verbose=False):
"""
Find a set of clusters for the graphs given by the iterator. If verbose
is true the each iteration is timed and bounded the results are returned
as lists.
The difference between a weight matrix and the previous one should be
positive.
"""
clustersList = []
decompositionTimeList = []
kMeansTimeList = []
boundList = []
sinThetaList = []
i = 0
for subW in graphListIterator:
if __debug__:
Parameter.checkSymmetric(subW)
if self.logStep and i % self.logStep == 0:
logging.debug("Graph index: " + str(i))
logging.debug("Clustering graph of size " + str(subW.shape))
if self.alg != "efficientNystrom":
ABBA = GraphUtils.shiftLaplacian(subW)
# --- Eigen value decomposition ---
startTime = time.time()
if self.alg == "IASC":
if i % self.T != 0:
omega, Q = self.approxUpdateEig(subW, ABBA, omega, Q)
if self.computeBound:
inds = numpy.flipud(numpy.argsort(omega))
Q = Q[:, inds]
omega = omega[inds]
bounds = self.pertBound(omega, Q, omegaKbot, AKbot,
self.k2)
#boundList.append([i, bounds[0], bounds[1]])
#Now use accurate values of norm of R and delta
rank = Util.rank(ABBA.todense())
gamma, U = scipy.sparse.linalg.eigsh(ABBA,
rank - 1,
which="LM",
ncv=ABBA.shape[0])
#logging.debug("gamma=" + str(gamma))
bounds2 = self.realBound(omega, Q, gamma, AKbot,
self.k2)
boundList.append(
[bounds[0], bounds[1], bounds2[0], bounds2[1]])
else:
logging.debug("Computing exact eigenvectors")
self.storeInformation(subW, ABBA)
if self.computeBound:
#omega, Q = scipy.sparse.linalg.eigsh(ABBA, min(self.k2*2, ABBA.shape[0]-1), which="LM", ncv = min(10*self.k2, ABBA.shape[0]))
rank = Util.rank(ABBA.todense())
omega, Q = scipy.sparse.linalg.eigsh(ABBA,
rank - 1,
which="LM",
ncv=ABBA.shape[0])
inds = numpy.flipud(numpy.argsort(omega))
omegaKbot = omega[inds[self.k2:]]
QKbot = Q[:, inds[self.k2:]]
AKbot = (QKbot * omegaKbot).dot(QKbot.T)
omegaSort = numpy.flipud(numpy.sort(omega))
boundList.append([0] * 4)
else:
omega, Q = scipy.sparse.linalg.eigsh(
ABBA,
min(self.k2, ABBA.shape[0] - 1),
which="LM",
ncv=min(10 * self.k2, ABBA.shape[0]))
elif self.alg == "nystrom":
omega, Q = Nystrom.eigpsd(ABBA, self.k3)
elif self.alg == "exact":
omega, Q = scipy.sparse.linalg.eigsh(
ABBA,
min(self.k1, ABBA.shape[0] - 1),
which="LM",
ncv=min(15 * self.k1, ABBA.shape[0]))
elif self.alg == "efficientNystrom":
omega, Q = EfficientNystrom.eigWeight(subW, self.k2, self.k1)
elif self.alg == "randomisedSvd":
Q, omega, R = RandomisedSVD.svd(ABBA, self.k4)
else:
raise ValueError("Invalid Algorithm: " + str(self.alg))
if self.computeSinTheta:
omegaExact, QExact = scipy.linalg.eigh(ABBA.todense())
inds = numpy.flipud(numpy.argsort(omegaExact))
QExactKbot = QExact[:, inds[self.k1:]]
inds = numpy.flipud(numpy.argsort(omega))
QApproxK = Q[:, inds[:self.k1]]
sinThetaList.append(
scipy.linalg.norm(QExactKbot.T.dot(QApproxK)))
decompositionTimeList.append(time.time() - startTime)
if self.alg == "IASC":
self.storeInformation(subW, ABBA)
# --- Kmeans ---
startTime = time.time()
inds = numpy.flipud(numpy.argsort(omega))
standardiser = Standardiser()
#For some very strange reason we get an overflow when computing the
#norm of the rows of Q even though its elements are bounded by 1.
#We'll ignore it for now
try:
V = standardiser.normaliseArray(Q[:, inds[0:self.k1]].real.T).T
except FloatingPointError as e:
logging.warn("FloatingPointError: " + str(e))
V = VqUtils.whiten(V)
if i == 0:
centroids, distortion = vq.kmeans(V,
self.k1,
iter=self.nb_iter_kmeans)
else:
centroids = self.findCentroids(V, clusters[:subW.shape[0]])
if centroids.shape[0] < self.k1:
nb_missing_centroids = self.k1 - centroids.shape[0]
random_centroids = V[numpy.random.randint(
0, V.shape[0], nb_missing_centroids), :]
centroids = numpy.vstack((centroids, random_centroids))
centroids, distortion = vq.kmeans(
V, centroids) #iter can only be 1
clusters, distortion = vq.vq(V, centroids)
kMeansTimeList.append(time.time() - startTime)
clustersList.append(clusters)
#logging.debug("subW.shape: " + str(subW.shape))
#logging.debug("len(clusters): " + str(len(clusters)))
#from sandbox.util.ProfileUtils import ProfileUtils
#logging.debug("Total memory usage: " + str(ProfileUtils.memory()/10**6) + "MB")
if ProfileUtils.memory() > 10**9:
ProfileUtils.memDisplay(locals())
i += 1
if verbose:
eigenQuality = {
"boundList": boundList,
"sinThetaList": sinThetaList
}
return clustersList, numpy.array(
(decompositionTimeList, kMeansTimeList)).T, eigenQuality
else:
return clustersList
def clusterFromIterator(self, graphListIterator, verbose=False):
"""
Find a set of clusters for the graphs given by the iterator. If verbose
is true the each iteration is timed and bounded the results are returned
as lists.
The difference between a weight matrix and the previous one should be
positive.
"""
clustersList = []
decompositionTimeList = []
kMeansTimeList = []
boundList = []
sinThetaList = []
i = 0
for subW in graphListIterator:
if __debug__:
Parameter.checkSymmetric(subW)
if self.logStep and i % self.logStep == 0:
logging.debug("Graph index: " + str(i))
logging.debug("Clustering graph of size " + str(subW.shape))
if self.alg!="efficientNystrom":
ABBA = GraphUtils.shiftLaplacian(subW)
# --- Eigen value decomposition ---
startTime = time.time()
if self.alg=="IASC":
if i % self.T != 0:
omega, Q = self.approxUpdateEig(subW, ABBA, omega, Q)
if self.computeBound:
inds = numpy.flipud(numpy.argsort(omega))
Q = Q[:, inds]
omega = omega[inds]
bounds = self.pertBound(omega, Q, omegaKbot, AKbot, self.k2)
#boundList.append([i, bounds[0], bounds[1]])
#Now use accurate values of norm of R and delta
rank = Util.rank(ABBA.todense())
gamma, U = scipy.sparse.linalg.eigsh(ABBA, rank-1, which="LM", ncv = ABBA.shape[0])
#logging.debug("gamma=" + str(gamma))
bounds2 = self.realBound(omega, Q, gamma, AKbot, self.k2)
boundList.append([bounds[0], bounds[1], bounds2[0], bounds2[1]])
else:
logging.debug("Computing exact eigenvectors")
self.storeInformation(subW, ABBA)
if self.computeBound:
#omega, Q = scipy.sparse.linalg.eigsh(ABBA, min(self.k2*2, ABBA.shape[0]-1), which="LM", ncv = min(10*self.k2, ABBA.shape[0]))
rank = Util.rank(ABBA.todense())
omega, Q = scipy.sparse.linalg.eigsh(ABBA, rank-1, which="LM", ncv = ABBA.shape[0])
inds = numpy.flipud(numpy.argsort(omega))
omegaKbot = omega[inds[self.k2:]]
QKbot = Q[:, inds[self.k2:]]
AKbot = (QKbot*omegaKbot).dot(QKbot.T)
omegaSort = numpy.flipud(numpy.sort(omega))
boundList.append([0]*4)
else:
omega, Q = scipy.sparse.linalg.eigsh(ABBA, min(self.k2, ABBA.shape[0]-1), which="LM", ncv = min(10*self.k2, ABBA.shape[0]))
elif self.alg == "nystrom":
omega, Q = Nystrom.eigpsd(ABBA, self.k3)
elif self.alg == "exact":
omega, Q = scipy.sparse.linalg.eigsh(ABBA, min(self.k1, ABBA.shape[0]-1), which="LM", ncv = min(15*self.k1, ABBA.shape[0]))
elif self.alg == "efficientNystrom":
omega, Q = EfficientNystrom.eigWeight(subW, self.k2, self.k1)
elif self.alg == "randomisedSvd":
Q, omega, R = RandomisedSVD.svd(ABBA, self.k4)
else:
raise ValueError("Invalid Algorithm: " + str(self.alg))
if self.computeSinTheta:
omegaExact, QExact = scipy.linalg.eigh(ABBA.todense())
inds = numpy.flipud(numpy.argsort(omegaExact))
QExactKbot = QExact[:, inds[self.k1:]]
inds = numpy.flipud(numpy.argsort(omega))
QApproxK = Q[:,inds[:self.k1]]
sinThetaList.append(scipy.linalg.norm(QExactKbot.T.dot(QApproxK)))
decompositionTimeList.append(time.time()-startTime)
if self.alg=="IASC":
self.storeInformation(subW, ABBA)
# --- Kmeans ---
startTime = time.time()
inds = numpy.flipud(numpy.argsort(omega))
standardiser = Standardiser()
#For some very strange reason we get an overflow when computing the
#norm of the rows of Q even though its elements are bounded by 1.
#We'll ignore it for now
try:
V = standardiser.normaliseArray(Q[:, inds[0:self.k1]].real.T).T
except FloatingPointError as e:
logging.warn("FloatingPointError: " + str(e))
V = VqUtils.whiten(V)
if i == 0:
centroids, distortion = vq.kmeans(V, self.k1, iter=self.nb_iter_kmeans)
else:
centroids = self.findCentroids(V, clusters[:subW.shape[0]])
if centroids.shape[0] < self.k1:
nb_missing_centroids = self.k1 - centroids.shape[0]
random_centroids = V[numpy.random.randint(0, V.shape[0], nb_missing_centroids),:]
centroids = numpy.vstack((centroids, random_centroids))
centroids, distortion = vq.kmeans(V, centroids) #iter can only be 1
clusters, distortion = vq.vq(V, centroids)
kMeansTimeList.append(time.time()-startTime)
clustersList.append(clusters)
#logging.debug("subW.shape: " + str(subW.shape))
#logging.debug("len(clusters): " + str(len(clusters)))
#from sandbox.util.ProfileUtils import ProfileUtils
#logging.debug("Total memory usage: " + str(ProfileUtils.memory()/10**6) + "MB")
if ProfileUtils.memory() > 10**9:
ProfileUtils.memDisplay(locals())
i += 1
if verbose:
eigenQuality = {"boundList" : boundList, "sinThetaList" : sinThetaList}
return clustersList, numpy.array((decompositionTimeList, kMeansTimeList)).T, eigenQuality
else:
return clustersList
