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 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 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 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)
