def testEigWeight(self):
tol = 10**-3
n = 100
W = numpy.random.rand(n, n)
W = W.dot(W.T)
w, U = numpy.linalg.eig(W)
W = scipy.sparse.csr_matrix(W)
k = 4
m = 5
lmbda, V = EfficientNystrom.eigWeight(W, m, k)
MHat = V.dot(numpy.diag(lmbda)).dot(V.T)
I = scipy.sparse.eye(n, n)
L = GraphUtils.normalisedLaplacianSym(W)
M = I - L
#print(V)
numpy.linalg.norm(M.todense() - MHat)
#print(numpy.linalg.norm(M.todense()))
#self.assertTrue(numpy.linalg.norm(W - WHat) < tol)
#For fixed k, increasing m should improve approximation but not always
lastError = 10
for m in range(k+1, n+1, 10):
lmbda, V = EfficientNystrom.eigWeight(W, m, k)
#print(V)
MHat = V.dot(numpy.diag(lmbda)).dot(V.T)
error = numpy.linalg.norm(M.todense() - MHat)
self.assertTrue(error <= lastError)
lastError = error
def testEigWeight(self):
tol = 10**-3
n = 100
W = numpy.random.rand(n, n)
W = W.dot(W.T)
w, U = numpy.linalg.eig(W)
W = scipy.sparse.csr_matrix(W)
k = 4
m = 5
lmbda, V = EfficientNystrom.eigWeight(W, m, k)
MHat = V.dot(numpy.diag(lmbda)).dot(V.T)
I = scipy.sparse.eye(n, n)
L = GraphUtils.normalisedLaplacianSym(W)
M = I - L
#print(V)
numpy.linalg.norm(M.todense() - MHat)
#print(numpy.linalg.norm(M.todense()))
#self.assertTrue(numpy.linalg.norm(W - WHat) < tol)
#For fixed k, increasing m should improve approximation but not always
lastError = 10
for m in range(k + 1, n + 1, 10):
lmbda, V = EfficientNystrom.eigWeight(W, m, k)
#print(V)
MHat = V.dot(numpy.diag(lmbda)).dot(V.T)
error = numpy.linalg.norm(M.todense() - MHat)
self.assertTrue(error <= lastError)
lastError = error
if not os.path.exists(resultsDir):
logging.warn("Directory did not exist: " + resultsDir + ", created.")
os.makedirs(resultsDir)
iterator = getIterator()
subgraphIndicesList = []
for W in iterator:
logging.debug("Graph size " + str(W.shape[0]))
subgraphIndicesList.append(range(W.shape[0]))
#Try to find number of clusters at end of sequence by looking at eigengap
k = 2
if findEigs:
L = GraphUtils.normalisedLaplacianSym(W)
logging.debug("Computing eigenvalues")
omega, Q = scipy.sparse.linalg.eigsh(L, min(k, L.shape[0]-1), which="SM", ncv = min(20*k, L.shape[0]))
omegaDiff = numpy.diff(omega)
else:
omega = numpy.zeros(k)
omegaDiff = numpy.zeros(k-1)
#No obvious number of clusters and there are many edges
graph = SparseGraph(W.shape[0], W=W)
logging.debug("Computing graph statistics")
graphStats = GraphStatistics()
statsMatrix = graphStats.sequenceScalarStats(graph, subgraphIndicesList, slowStats=False)
import numpy
import scipy.sparse
from apgl.graph import GraphUtils
from sandbox.util.Util import Util
numpy.set_printoptions(suppress=True, precision=3)
n = 10
W1 = scipy.sparse.rand(n, n, 0.5).todense()
W1 = W1.T.dot(W1)
W2 = W1.copy()
W2[1, 2] = 1
W2[2, 1] = 1
print("W1=" + str(W1))
print("W2=" + str(W2))
L1 = GraphUtils.normalisedLaplacianSym(scipy.sparse.csr_matrix(W1))
L2 = GraphUtils.normalisedLaplacianSym(scipy.sparse.csr_matrix(W2))
deltaL = L2 - L1
print("L1=" + str(L1.todense()))
print("L2=" + str(L2.todense()))
print("deltaL=" + str(deltaL.todense()))
print("rank(deltaL)=" + str(Util.rank(deltaL.todense())))
import numpy
import scipy.sparse
from apgl.graph import GraphUtils
from sandbox.util.Util import Util
numpy.set_printoptions(suppress=True, precision=3)
n = 10
W1 = scipy.sparse.rand(n, n, 0.5).todense()
W1 = W1.T.dot(W1)
W2 = W1.copy()
W2[1, 2] = 1
W2[2, 1] = 1
print("W1="+str(W1))
print("W2="+str(W2))
L1 = GraphUtils.normalisedLaplacianSym(scipy.sparse.csr_matrix(W1))
L2 = GraphUtils.normalisedLaplacianSym(scipy.sparse.csr_matrix(W2))
deltaL = L2 - L1
print("L1="+str(L1.todense()))
print("L2="+str(L2.todense()))
print("deltaL="+str(deltaL.todense()))
print("rank(deltaL)=" + str(Util.rank(deltaL.todense())))
