def testIncrementEigenSystem(self):
print "< testIncrementEigenSystem >"
numVertices = 10
graph = SparseGraph(GeneralVertexList(numVertices))
p = 0.4
generator = ErdosRenyiGenerator(p)
graph = generator.generate(graph)
W = graph.getWeightMatrix()
L = graph.laplacianMatrix()
degrees = graph.outDegreeSequence()
D = numpy.diag(degrees)
lmbda1, Q1 = scipy.linalg.eig(L, D)
lmbda1 = lmbda1.real
Q1 = Q1.dot(numpy.diag(numpy.diag(Q1.T.dot(D).dot(Q1))**-0.5))
tol = 10**-6
k = 3
inds = numpy.argsort(lmbda1)[0:k]
lmbda1, Q1 = Util.indEig(lmbda1, Q1, inds)
#Similarity change vector
w = graph.getEdge(5, 7)
deltaW = 0.5
k = 3
clusterer = NingSpectralClustering(k)
lmbda2Approx, Q2Approx = clusterer.incrementEigenSystem(
lmbda1, Q1, scipy.sparse.csr_matrix(W), 5, 7, deltaW)
#Compute real eigenvectors then compare against these
Lhat = L.copy()
Lhat[5, 5] += deltaW
Lhat[7, 7] += deltaW
Lhat[5, 7] -= deltaW
Lhat[7, 5] -= deltaW
Dhat = numpy.diag(numpy.diag(Lhat))
lmbda2, Q2 = scipy.linalg.eig(Lhat, Dhat)
lmbda2, Q2 = Util.indEig(lmbda2, Q2, inds)
Q2Approx = Q2Approx.dot(
numpy.diag(numpy.diag(Q2Approx.T.dot(Q2Approx))**-0.5))
Q2 = Q2.dot(numpy.diag(numpy.sum(Q2**2, 0)**-0.5))
Q1 = Q1.dot(numpy.diag(numpy.sum(Q1**2, 0)**-0.5))
#Errors in the eigenvalues
logging.debug("Eigenvalue Errors")
logging.debug(numpy.linalg.norm(lmbda2 - lmbda2Approx))
logging.debug(numpy.linalg.norm(lmbda2 - lmbda1))
#Compute error according to the paper
error = numpy.sum(1 - numpy.diag(Q2.T.dot(Q2Approx))**2)
error2 = numpy.sum(1 - numpy.diag(Q2.T.dot(Q1))**2)
logging.debug("Eigenvector Errors")
logging.debug(error)
logging.debug(error2)
def testIncrementEigenSystem(self):
print "< testIncrementEigenSystem >"
numVertices = 10
graph = SparseGraph(GeneralVertexList(numVertices))
p = 0.4
generator = ErdosRenyiGenerator(p)
graph = generator.generate(graph)
W = graph.getWeightMatrix()
L = graph.laplacianMatrix()
degrees = graph.outDegreeSequence()
D = numpy.diag(degrees)
lmbda1, Q1 = scipy.linalg.eig(L, D)
lmbda1 = lmbda1.real
Q1 = Q1.dot(numpy.diag(numpy.diag(Q1.T.dot(D).dot(Q1))**-0.5))
tol = 10**-6
k = 3
inds = numpy.argsort(lmbda1)[0:k]
lmbda1, Q1 = Util.indEig(lmbda1, Q1, inds)
#Similarity change vector
w = graph.getEdge(5,7)
deltaW = 0.5
k = 3
clusterer = NingSpectralClustering(k)
lmbda2Approx, Q2Approx = clusterer.incrementEigenSystem(lmbda1, Q1, scipy.sparse.csr_matrix(W), 5, 7, deltaW)
#Compute real eigenvectors then compare against these
Lhat = L.copy();
Lhat[5,5] += deltaW; Lhat[7,7] += deltaW
Lhat[5,7] -= deltaW; Lhat[7,5] -= deltaW
Dhat = numpy.diag(numpy.diag(Lhat))
lmbda2, Q2 = scipy.linalg.eig(Lhat, Dhat)
lmbda2, Q2 = Util.indEig(lmbda2, Q2, inds)
Q2Approx = Q2Approx.dot(numpy.diag(numpy.diag(Q2Approx.T.dot(Q2Approx))**-0.5))
Q2 = Q2.dot(numpy.diag(numpy.sum(Q2**2, 0)**-0.5))
Q1 = Q1.dot(numpy.diag(numpy.sum(Q1**2, 0)**-0.5))
#Errors in the eigenvalues
logging.debug("Eigenvalue Errors")
logging.debug(numpy.linalg.norm(lmbda2 - lmbda2Approx))
logging.debug(numpy.linalg.norm(lmbda2 - lmbda1))
#Compute error according to the paper
error = numpy.sum(1 - numpy.diag(Q2.T.dot(Q2Approx))**2)
error2 = numpy.sum(1 - numpy.diag(Q2.T.dot(Q1))**2)
logging.debug("Eigenvector Errors")
logging.debug(error)
logging.debug(error2)
def testDebug(self):
if not os.path.isfile("lmbda.npy"):
print "blop"
return
print "< debugging Nings approach >"
lmbda = numpy.load("lmbda.npy")
Q = numpy.load("Q.npy")
W = numpy.load("W.npy")
i = numpy.load("i.npy")
j = numpy.load("j.npy")
deltaW = numpy.load("deltaW.npy")
clusterer = NingSpectralClustering(Q.shape[1])
clusterer.incrementEigenSystem(lmbda, Q, W, i, j, deltaW)
print "</ debugging Nings approach >"
def testDebug(self):
if not os.path.isfile("lmbda.npy"):
print "blop"
return
print "< debugging Nings approach >"
lmbda = numpy.load("lmbda.npy")
Q = numpy.load("Q.npy")
W = numpy.load("W.npy")
i = numpy.load("i.npy")
j = numpy.load("j.npy")
deltaW = numpy.load("deltaW.npy")
clusterer = NingSpectralClustering(Q.shape[1])
clusterer.incrementEigenSystem(lmbda, Q, W, i, j, deltaW)
print "</ debugging Nings approach >"
return (float(error)*2/(numVertices)/(numVertices-1))
#=========================================================================
#=========================================================================
# run
#=========================================================================
#=========================================================================
numIter = len(range(args.startingIteration, args.endingIteration))
logging.info("compute clusters")
exactClusterer = IterativeSpectralClustering(args.k1, alg="exact", computeSinTheta=True)
approxClusterer = IterativeSpectralClustering(args.k1, args.k2, T=args.exactFreq, alg="IASC", computeSinTheta=True)
nystromClusterer = IterativeSpectralClustering(args.k1, k3=args.k3, alg="nystrom", computeSinTheta=True)
RSvdClusterer = IterativeSpectralClustering(args.k1, k4=args.k4, alg="randomisedSvd", computeSinTheta=True)
ningsClusterer = NingSpectralClustering(args.k1, T=args.exactFreq, computeSinTheta=True)
exactClusterer.nb_iter_kmeans = 20
approxClusterer.nb_iter_kmeans = 20
nystromClusterer.nb_iter_kmeans = 20
RSvdClusterer.nb_iter_kmeans = 20
ningsClusterer.nb_iter_kmeans = 20
#exactClusterer.computeBound = args.computeBound # computeBound not implemented for exactClusterer
approxClusterer.computeBound = args.computeBound
#nystromClusterer.computeBound = args.computeBound # computeBound not implemented for nystromClusterer
#RSvdClusterer.computeBound = args.computeBound # computeBound not implemented for RSvdClusterer
#ningsClusterer.computeBound = args.computeBound # computeBound not implemented for ningsClusterer
def getGraphIterator():
def testIncrementEigenSystem2(self):
print "< testIncrementEigenSystem2 >"
"""
We use the example from the paper to see if the error in the eigenvalues
and eigenvectors decreases.
"""
numVertices = 10
graph = SparseGraph(GeneralVertexList(numVertices))
graph.addEdge(0, 1, 0.7)
graph.addEdge(1, 2, 0.4)
graph.addEdge(2, 3, 0.3)
graph.addEdge(1, 3, 0.1)
graph.addEdge(0, 4, 0.5)
graph.addEdge(3, 4, 0.4)
graph.addEdge(4, 5, 0.8)
graph.addEdge(3, 5, 0.3)
graph.addEdge(6, 5, 0.4)
graph.addEdge(5, 9, 0.5)
graph.addEdge(6, 9, 0.3)
graph.addEdge(6, 7, 0.1)
graph.addEdge(6, 8, 0.6)
graph.addEdge(7, 8, 0.7)
graph.addEdge(9, 8, 0.7)
W = graph.getWeightMatrix()
L = graph.laplacianWeightMatrix()
degrees = numpy.sum(W, 0)
D = numpy.diag(degrees)
k = 3
lmbda1, Q1 = scipy.linalg.eig(L, D)
inds = numpy.argsort(lmbda1)[0:k]
lmbda1, Q1 = Util.indEig(lmbda1, Q1, inds)
lmbda1 = lmbda1.real
#Remove edge 0, 4
r = numpy.zeros(numVertices, numpy.complex)
deltaW = -0.5
clusterer = NingSpectralClustering(k)
lmbda2Approx, Q2Approx = clusterer.incrementEigenSystem(lmbda1, Q1, scipy.sparse.csr_matrix(W), 0, 4, deltaW)
#Compute real eigenvectors then compare against these
Lhat = L + numpy.outer(r, r)
Dhat = numpy.diag(numpy.diag(Lhat))
lmbda2, Q2 = scipy.linalg.eig(Lhat, Dhat)
lmbda2, Q2 = Util.indEig(lmbda2, Q2, inds)
Q2Approx = Q2Approx.dot(numpy.diag(numpy.diag(Q2Approx.T.dot(Q2Approx))**-0.5))
Q2 = Q2.dot(numpy.diag(numpy.sum(Q2**2, 0)**-0.5))
Q1 = Q1.dot(numpy.diag(numpy.sum(Q1**2, 0)**-0.5))
#Compute error according to the paper
#2 iterations works best - 3 seems to be worse!!!
error2 = 1 - numpy.diag(Q2.T.dot(Q2Approx))**2
errors2 = 1 - numpy.diag(Q2.T.dot(Q1))**2
logging.debug("Eigenvector Errors")
logging.debug(error2)
logging.debug(errors2)
def testCluster(self):
print "< testCluster >"
numVertices = 8
graph = SparseGraph(GeneralVertexList(numVertices))
graph.addEdge(0, 1)
graph.addEdge(0, 2)
graph.addEdge(1, 2)
graph.addEdge(3, 4)
graph.addEdge(3, 5)
graph.addEdge(4, 5)
graph.addEdge(0, 3)
W = graph.getWeightMatrix()
graphIterator = []
graphIterator.append(W[0:6, 0:6].copy())
W[1, 6] += 1
W[6, 1] += 1
graphIterator.append(W[0:7, 0:7].copy())
W[4, 7] += 1
W[7, 4] += 1
graphIterator.append(W.copy())
graphIterator = iter(graphIterator)
k = 2
clusterer = NingSpectralClustering(k)
clustersList = clusterer.cluster(toSparseGraphListIterator(graphIterator))
#Why are the bottom rows of Q still zero?
#Try example in which only edges change
numVertices = 7
graph = SparseGraph(GeneralVertexList(numVertices))
graph.addEdge(0, 1)
graph.addEdge(0, 2)
graph.addEdge(1, 2)
graph.addEdge(3, 4)
WList = []
W = graph.getWeightMatrix()
WList.append(W[0:5, 0:5].copy())
graph.addEdge(3, 5)
graph.addEdge(4, 5)
W = graph.getWeightMatrix()
WList.append(W[0:6, 0:6].copy())
graph.addEdge(0, 6)
graph.addEdge(1, 6)
graph.addEdge(2, 6)
W = graph.getWeightMatrix()
WList.append(W[0:7, 0:7].copy())
iterator = iter(WList)
clustersList = clusterer.cluster(toSparseGraphListIterator(iterator))
#Seems to work, amazingly
#print(clustersList)
#Try removing rows/cols
W2 = W[0:5, 0:5]
W3 = W[0:4, 0:4]
WList = [W, W2, W3]
iterator = iter(WList)
clustersList = clusterer.cluster(toSparseGraphListIterator(iterator))
#nptst.assert_array_equal(clustersList[0][0:5], clustersList[1])
nptst.assert_array_equal(clustersList[1][0:4], clustersList[2])
#Make sure 1st clustering (without updates) is correct
L = GraphUtils.normalisedLaplacianRw(scipy.sparse.csr_matrix(W))
numpy.random.seed(21)
lmbda, Q = scipy.sparse.linalg.eigs(L, min(k, L.shape[0]-1), which="SM", ncv = min(20*k, L.shape[0]), v0=numpy.random.rand(L.shape[0]))
V = VqUtils.whiten(Q)
centroids, distortion = vq.kmeans(V, k, iter=20)
clusters, distortion = vq.vq(V, centroids)
#This should be equal but the eigenvector computation is unstable
#even with repeated runs (and no way to set the seed)
nptst.assert_array_equal(clusters, clustersList[0])
def testIncrementalEigenSystem3(self):
print "< testIncrementEigenSystem3 >"
"""
Test case where we add a vertex and need to increase size of eigenvectors.
"""
numVertices = 8
graph = SparseGraph(GeneralVertexList(numVertices))
graph.addEdge(0, 1)
graph.addEdge(0, 2)
graph.addEdge(1, 2)
graph.addEdge(3, 4)
graph.addEdge(3, 5)
graph.addEdge(4, 5)
graph.addEdge(0, 3)
graph.addEdge(1, 6)
graph.addEdge(4, 7)
subgraph = graph.subgraph(range(7))
W1 = subgraph.getWeightMatrix()
L1 = subgraph.laplacianWeightMatrix()
degrees1 = numpy.sum(W1, 0)
D1 = numpy.diag(degrees1)
W2 = graph.getWeightMatrix()
L2 = graph.laplacianWeightMatrix()
degrees1 = numpy.sum(W2, 0)
D2 = numpy.diag(degrees1)
k = 3
lmbda1, Q1 = scipy.linalg.eig(L1, D1)
inds = numpy.argsort(lmbda1)[0:k]
lmbda1, Q1 = Util.indEig(lmbda1, Q1, inds)
lmbda1 = lmbda1.real
L1hat = numpy.r_[numpy.c_[L1, numpy.zeros(numVertices-1)], numpy.zeros((1, numVertices))]
W1hat = numpy.r_[numpy.c_[W1, numpy.zeros(numVertices-1)], numpy.zeros((1, numVertices))]
D1hat = numpy.r_[numpy.c_[D1, numpy.zeros(numVertices-1)], numpy.zeros((1, numVertices))]
lmbda1, Q2 = scipy.linalg.eig(L2, D2)
inds = numpy.argsort(lmbda1)[0:k]
lmbda1, Q2 = Util.indEig(lmbda1, Q2, inds)
lmbda1 = lmbda1.real
Q1 = numpy.r_[Q1, numpy.ones((1, Q1.shape[1]))]
#Increase size of eigenvector - not clear how to do this
clusterer = NingSpectralClustering(k)
lmbda2Approx, Q2Approx = clusterer.incrementEigenSystem(lmbda1, Q1, scipy.sparse.csr_matrix(W1hat), 4, 7, 1)
Q2Approx = Q2Approx.dot(numpy.diag(numpy.diag(Q2Approx.T.dot(Q2Approx))**-0.5))
Q2 = Q2.dot(numpy.diag(numpy.sum(Q2**2, 0)**-0.5))
Q1 = Q1.dot(numpy.diag(numpy.sum(Q1**2, 0)**-0.5))
#Setting the last value of the eigenvectors to zero seems to improve
#over setting them to 1, but the last eigenvector has a huge error.
errors1 = 1 - numpy.diag(Q2.T.dot(Q2Approx))**2
errors2 = 1 - numpy.diag(Q2.T.dot(Q1))**2
logging.debug("Eigenvector Errors for added vertex")
logging.debug(errors1)
logging.debug(errors2)
def testIncrementEigenSystem2(self):
print "< testIncrementEigenSystem2 >"
"""
We use the example from the paper to see if the error in the eigenvalues
and eigenvectors decreases.
"""
numVertices = 10
graph = SparseGraph(GeneralVertexList(numVertices))
graph.addEdge(0, 1, 0.7)
graph.addEdge(1, 2, 0.4)
graph.addEdge(2, 3, 0.3)
graph.addEdge(1, 3, 0.1)
graph.addEdge(0, 4, 0.5)
graph.addEdge(3, 4, 0.4)
graph.addEdge(4, 5, 0.8)
graph.addEdge(3, 5, 0.3)
graph.addEdge(6, 5, 0.4)
graph.addEdge(5, 9, 0.5)
graph.addEdge(6, 9, 0.3)
graph.addEdge(6, 7, 0.1)
graph.addEdge(6, 8, 0.6)
graph.addEdge(7, 8, 0.7)
graph.addEdge(9, 8, 0.7)
W = graph.getWeightMatrix()
L = graph.laplacianWeightMatrix()
degrees = numpy.sum(W, 0)
D = numpy.diag(degrees)
k = 3
lmbda1, Q1 = scipy.linalg.eig(L, D)
inds = numpy.argsort(lmbda1)[0:k]
lmbda1, Q1 = Util.indEig(lmbda1, Q1, inds)
lmbda1 = lmbda1.real
#Remove edge 0, 4
r = numpy.zeros(numVertices, numpy.complex)
deltaW = -0.5
clusterer = NingSpectralClustering(k)
lmbda2Approx, Q2Approx = clusterer.incrementEigenSystem(
lmbda1, Q1, scipy.sparse.csr_matrix(W), 0, 4, deltaW)
#Compute real eigenvectors then compare against these
Lhat = L + numpy.outer(r, r)
Dhat = numpy.diag(numpy.diag(Lhat))
lmbda2, Q2 = scipy.linalg.eig(Lhat, Dhat)
lmbda2, Q2 = Util.indEig(lmbda2, Q2, inds)
Q2Approx = Q2Approx.dot(
numpy.diag(numpy.diag(Q2Approx.T.dot(Q2Approx))**-0.5))
Q2 = Q2.dot(numpy.diag(numpy.sum(Q2**2, 0)**-0.5))
Q1 = Q1.dot(numpy.diag(numpy.sum(Q1**2, 0)**-0.5))
#Compute error according to the paper
#2 iterations works best - 3 seems to be worse!!!
error2 = 1 - numpy.diag(Q2.T.dot(Q2Approx))**2
errors2 = 1 - numpy.diag(Q2.T.dot(Q1))**2
logging.debug("Eigenvector Errors")
logging.debug(error2)
logging.debug(errors2)
def testCluster(self):
print "< testCluster >"
numVertices = 8
graph = SparseGraph(GeneralVertexList(numVertices))
graph.addEdge(0, 1)
graph.addEdge(0, 2)
graph.addEdge(1, 2)
graph.addEdge(3, 4)
graph.addEdge(3, 5)
graph.addEdge(4, 5)
graph.addEdge(0, 3)
W = graph.getWeightMatrix()
graphIterator = []
graphIterator.append(W[0:6, 0:6].copy())
W[1, 6] += 1
W[6, 1] += 1
graphIterator.append(W[0:7, 0:7].copy())
W[4, 7] += 1
W[7, 4] += 1
graphIterator.append(W.copy())
graphIterator = iter(graphIterator)
k = 2
clusterer = NingSpectralClustering(k)
clustersList = clusterer.cluster(
toSparseGraphListIterator(graphIterator))
#Why are the bottom rows of Q still zero?
#Try example in which only edges change
numVertices = 7
graph = SparseGraph(GeneralVertexList(numVertices))
graph.addEdge(0, 1)
graph.addEdge(0, 2)
graph.addEdge(1, 2)
graph.addEdge(3, 4)
WList = []
W = graph.getWeightMatrix()
WList.append(W[0:5, 0:5].copy())
graph.addEdge(3, 5)
graph.addEdge(4, 5)
W = graph.getWeightMatrix()
WList.append(W[0:6, 0:6].copy())
graph.addEdge(0, 6)
graph.addEdge(1, 6)
graph.addEdge(2, 6)
W = graph.getWeightMatrix()
WList.append(W[0:7, 0:7].copy())
iterator = iter(WList)
clustersList = clusterer.cluster(toSparseGraphListIterator(iterator))
#Seems to work, amazingly
#print(clustersList)
#Try removing rows/cols
W2 = W[0:5, 0:5]
W3 = W[0:4, 0:4]
WList = [W, W2, W3]
iterator = iter(WList)
clustersList = clusterer.cluster(toSparseGraphListIterator(iterator))
#nptst.assert_array_equal(clustersList[0][0:5], clustersList[1])
nptst.assert_array_equal(clustersList[1][0:4], clustersList[2])
#Make sure 1st clustering (without updates) is correct
L = GraphUtils.normalisedLaplacianRw(scipy.sparse.csr_matrix(W))
numpy.random.seed(21)
lmbda, Q = scipy.sparse.linalg.eigs(L,
min(k, L.shape[0] - 1),
which="SM",
ncv=min(20 * k, L.shape[0]),
v0=numpy.random.rand(L.shape[0]))
V = VqUtils.whiten(Q)
centroids, distortion = vq.kmeans(V, k, iter=20)
clusters, distortion = vq.vq(V, centroids)
#This should be equal but the eigenvector computation is unstable
#even with repeated runs (and no way to set the seed)
nptst.assert_array_equal(clusters, clustersList[0])
def testIncrementalEigenSystem3(self):
print "< testIncrementEigenSystem3 >"
"""
Test case where we add a vertex and need to increase size of eigenvectors.
"""
numVertices = 8
graph = SparseGraph(GeneralVertexList(numVertices))
graph.addEdge(0, 1)
graph.addEdge(0, 2)
graph.addEdge(1, 2)
graph.addEdge(3, 4)
graph.addEdge(3, 5)
graph.addEdge(4, 5)
graph.addEdge(0, 3)
graph.addEdge(1, 6)
graph.addEdge(4, 7)
subgraph = graph.subgraph(range(7))
W1 = subgraph.getWeightMatrix()
L1 = subgraph.laplacianWeightMatrix()
degrees1 = numpy.sum(W1, 0)
D1 = numpy.diag(degrees1)
W2 = graph.getWeightMatrix()
L2 = graph.laplacianWeightMatrix()
degrees1 = numpy.sum(W2, 0)
D2 = numpy.diag(degrees1)
k = 3
lmbda1, Q1 = scipy.linalg.eig(L1, D1)
inds = numpy.argsort(lmbda1)[0:k]
lmbda1, Q1 = Util.indEig(lmbda1, Q1, inds)
lmbda1 = lmbda1.real
L1hat = numpy.r_[numpy.c_[L1, numpy.zeros(numVertices - 1)],
numpy.zeros((1, numVertices))]
W1hat = numpy.r_[numpy.c_[W1, numpy.zeros(numVertices - 1)],
numpy.zeros((1, numVertices))]
D1hat = numpy.r_[numpy.c_[D1, numpy.zeros(numVertices - 1)],
numpy.zeros((1, numVertices))]
lmbda1, Q2 = scipy.linalg.eig(L2, D2)
inds = numpy.argsort(lmbda1)[0:k]
lmbda1, Q2 = Util.indEig(lmbda1, Q2, inds)
lmbda1 = lmbda1.real
Q1 = numpy.r_[Q1, numpy.ones((1, Q1.shape[1]))]
#Increase size of eigenvector - not clear how to do this
clusterer = NingSpectralClustering(k)
lmbda2Approx, Q2Approx = clusterer.incrementEigenSystem(
lmbda1, Q1, scipy.sparse.csr_matrix(W1hat), 4, 7, 1)
Q2Approx = Q2Approx.dot(
numpy.diag(numpy.diag(Q2Approx.T.dot(Q2Approx))**-0.5))
Q2 = Q2.dot(numpy.diag(numpy.sum(Q2**2, 0)**-0.5))
Q1 = Q1.dot(numpy.diag(numpy.sum(Q1**2, 0)**-0.5))
#Setting the last value of the eigenvectors to zero seems to improve
#over setting them to 1, but the last eigenvector has a huge error.
errors1 = 1 - numpy.diag(Q2.T.dot(Q2Approx))**2
errors2 = 1 - numpy.diag(Q2.T.dot(Q1))**2
logging.debug("Eigenvector Errors for added vertex")
logging.debug(errors1)
logging.debug(errors2)
#k3s = [3]
#k4s = [3]
if saveResults:
numClusters = 3
k1 = numClusters
T = 8 # index of iteration where exact decomposition is computed
exactClusterer = IterativeSpectralClustering(k1, alg="exact", computeSinTheta=True)
iascClusterers = []
for k2 in k2s:
iascClusterers.append(IterativeSpectralClustering(k1, k2, alg="IASC", computeSinTheta=True, T=T))
nystromClusterers = []
for k3 in k3s:
nystromClusterers.append(IterativeSpectralClustering(k1, k3=k3, alg="nystrom", computeSinTheta=True))
ningsClusterer = NingSpectralClustering(k1, T=T, computeSinTheta=True)
randSvdClusterers = []
for k4 in k4s:
randSvdClusterers.append(IterativeSpectralClustering(k1, k4=k4, alg="randomisedSvd", computeSinTheta=True))
numRepetitions = 50
# numRepetitions = 2
do_Nings = True
clustErrApprox = numpy.zeros((ps.shape[0], numGraphs, numRepetitions, len(k2s)))
clustErrExact = numpy.zeros((ps.shape[0], numGraphs, numRepetitions))
clustErrNings = numpy.zeros((ps.shape[0], numGraphs, numRepetitions))
clustErrNystrom = numpy.zeros((ps.shape[0], numGraphs, numRepetitions, len(k3s)))
clustErrRandSvd = numpy.zeros((ps.shape[0], numGraphs, numRepetitions, len(k4s)))
sinThetaApprox = numpy.zeros((ps.shape[0], numGraphs, numRepetitions, len(k2s)))
sinThetaExact = numpy.zeros((ps.shape[0], numGraphs, numRepetitions))