def readFromFile(self, fileName):
X = numpy.loadtxt(fileName, skiprows=1, converters=self.converters)
vertexIds = numpy.zeros(X.shape[0] * 2)
#First, we will map the vertex Ids to a set of numbers
for i in range(0, X.shape[0]):
vertexIds[2 * i] = X[i, self.vertex1IdIndex]
vertexIds[2 * i + 1] = X[i, self.vertex2IdIndex]
vertexIds = numpy.unique(vertexIds)
numVertices = vertexIds.shape[0]
numFeatures = len(self.vertex1Indices)
vList = VertexList(numVertices, numFeatures)
sGraph = SparseGraph(vList, self.undirected)
for i in range(0, X.shape[0]):
vertex1Id = X[i, self.vertex1IdIndex]
vertex2Id = X[i, self.vertex2IdIndex]
vertex1 = X[i, self.vertex1Indices]
vertex2 = X[i, self.vertex2Indices]
vertex1VListId = numpy.nonzero(vertexIds == vertex1Id)[0]
vertex2VListId = numpy.nonzero(vertexIds == vertex2Id)[0]
vertex1VListId = int(vertex1VListId)
vertex2VListId = int(vertex2VListId)
vList.setVertex(vertex1VListId, vertex1)
vList.setVertex(vertex2VListId, vertex2)
sGraph.addEdge(vertex1VListId, vertex2VListId, self.edgeWeight)
logging.info("Read " + fileName + " with " +
str(sGraph.getNumVertices()) + " vertices and " +
str(sGraph.getNumEdges()) + " edges")
return sGraph
def readFromFile(self, fileName):
X = numpy.loadtxt(fileName, skiprows=1, converters=self.converters)
vertexIds = numpy.zeros(X.shape[0]*2)
#First, we will map the vertex Ids to a set of numbers
for i in range(0, X.shape[0]):
vertexIds[2*i] = X[i, self.vertex1IdIndex]
vertexIds[2*i+1] = X[i, self.vertex2IdIndex]
vertexIds = numpy.unique(vertexIds)
numVertices = vertexIds.shape[0]
numFeatures = len(self.vertex1Indices)
vList = VertexList(numVertices, numFeatures)
sGraph = SparseGraph(vList, self.undirected)
for i in range(0, X.shape[0]):
vertex1Id = X[i, self.vertex1IdIndex]
vertex2Id = X[i, self.vertex2IdIndex]
vertex1 = X[i, self.vertex1Indices]
vertex2 = X[i, self.vertex2Indices]
vertex1VListId = numpy.nonzero(vertexIds==vertex1Id)[0]
vertex2VListId = numpy.nonzero(vertexIds==vertex2Id)[0]
vertex1VListId = int(vertex1VListId)
vertex2VListId = int(vertex2VListId)
vList.setVertex(vertex1VListId, vertex1)
vList.setVertex(vertex2VListId, vertex2)
sGraph.addEdge(vertex1VListId, vertex2VListId, self.edgeWeight)
logging.info("Read " + fileName + " with " + str(sGraph.getNumVertices()) + " vertices and " + str(sGraph.getNumEdges()) + " edges")
return sGraph
def testClusterOnIncreasingGraphs(self):
#Create a large graph and try the clustering.
numClusters = 3
ClusterSize = 30
numFeatures = 0
pNoise = 0
pClust = 1
numVertices = numClusters*ClusterSize
vList = GeneralVertexList(numVertices)
vList = VertexList(numVertices, numFeatures)
graph = SparseGraph(vList)
# ell = 2
# m = 2
# generator = BarabasiAlbertGenerator(ell, m)
# graph = generator.generate(graph)
#Generate matrix of probabilities
W = numpy.ones((numVertices, numVertices))*pNoise
for i in range(numClusters):
W[ClusterSize*i:ClusterSize*(i+1), ClusterSize*i:ClusterSize*(i+1)] = pClust
P = numpy.random.rand(numVertices, numVertices)
W = numpy.array(P < W, numpy.float)
upTriInds = numpy.triu_indices(numVertices)
W[upTriInds] = 0
W = W + W.T
graph = SparseGraph(vList)
graph.setWeightMatrix(W)
indices = numpy.random.permutation(numVertices)
subgraphIndicesList = [indices[0:numVertices/2], indices]
k1 = numClusters
k2 = 10
clusterer = IterativeSpectralClustering(k1, k2)
#Test full computation of eigenvectors
graphIterator = IncreasingSubgraphListIterator(graph, subgraphIndicesList)
clustersList = clusterer.clusterFromIterator(graphIterator, False)
self.assertEquals(len(clustersList), len(subgraphIndicesList))
for i in range(len(clustersList)):
clusters = clustersList[i]
self.assertEquals(len(subgraphIndicesList[i]), len(clusters))
#print(clusters)
#Test full computation of eigenvectors with iterator
graphIterator = IncreasingSubgraphListIterator(graph, subgraphIndicesList)
clustersList = clusterer.clusterFromIterator(graphIterator, False)
self.assertEquals(len(clustersList), len(subgraphIndicesList))
for i in range(len(clustersList)):
clusters = clustersList[i]
self.assertEquals(len(subgraphIndicesList[i]), len(clusters))
#print(clusters)
#Now test approximation of eigenvectors with iterator
graphIterator = IncreasingSubgraphListIterator(graph, subgraphIndicesList)
clustersList2 = clusterer.clusterFromIterator(graphIterator)
for i in range(len(clustersList2)):
clusters = clustersList2[i]
self.assertEquals(len(subgraphIndicesList[i]), len(clusters))
#print(clusters)
#Test case where 2 graphs are identical
subgraphIndicesList = []
subgraphIndicesList.append(range(graph.getNumVertices()))
subgraphIndicesList.append(range(graph.getNumVertices()))
graphIterator = IncreasingSubgraphListIterator(graph, subgraphIndicesList)
clustersList = clusterer.clusterFromIterator(graphIterator, True)
class PermutationGraphKernelTest(unittest.TestCase):
def setUp(self):
self.tol = 10**-4
self.numVertices = 5
self.numFeatures = 2
vertexList1 = VertexList(self.numVertices, self.numFeatures)
vertexList1.setVertex(0, numpy.array([1, 1]))
vertexList1.setVertex(1, numpy.array([1, 2]))
vertexList1.setVertex(2, numpy.array([3, 2]))
vertexList1.setVertex(3, numpy.array([4, 2]))
vertexList1.setVertex(4, numpy.array([2, 6]))
vertexList2 = VertexList(self.numVertices, self.numFeatures)
vertexList2.setVertex(0, numpy.array([1, 3]))
vertexList2.setVertex(1, numpy.array([7, 2]))
vertexList2.setVertex(2, numpy.array([3, 22]))
vertexList2.setVertex(3, numpy.array([54, 2]))
vertexList2.setVertex(4, numpy.array([2, 34]))
self.sGraph1 = SparseGraph(vertexList1)
self.sGraph1.addEdge(0, 1)
self.sGraph1.addEdge(0, 2)
self.sGraph1.addEdge(1, 2)
self.sGraph1.addEdge(2, 3)
self.sGraph2 = SparseGraph(vertexList2)
self.sGraph2.addEdge(0, 1)
self.sGraph2.addEdge(0, 2)
self.sGraph2.addEdge(1, 2)
self.sGraph2.addEdge(2, 3)
self.sGraph2.addEdge(3, 4)
self.sGraph3 = SparseGraph(vertexList2)
self.sGraph3.addEdge(4, 1)
self.sGraph3.addEdge(4, 2)
self.sGraph3.addEdge(1, 2)
self.sGraph3.addEdge(1, 0)
def testEvaluate(self):
tau = 1.0
linearKernel = LinearKernel()
graphKernel = PermutationGraphKernel(tau, linearKernel)
"""
First tests - if the graphs have identical edges then permutation is identity matrix
provided that tau = 1.
"""
(evaluation, f, P, SW1, SW2, SK1,
SK2) = graphKernel.evaluate(self.sGraph1, self.sGraph1, True)
self.assertTrue(
numpy.linalg.norm(P - numpy.eye(self.numVertices)) <= self.tol)
S1, U = numpy.linalg.eigh(self.sGraph1.getWeightMatrix())
S2, U = numpy.linalg.eigh(self.sGraph2.getWeightMatrix())
evaluation2 = numpy.dot(S1, S1)
self.assertTrue(numpy.linalg.norm(SW1 - S1) <= self.tol)
self.assertTrue(numpy.linalg.norm(SW2 - S1) <= self.tol)
self.assertTrue(abs(evaluation - evaluation2) <= self.tol)
(evaluation, f, P, SW1, SW2, SK1,
SK2) = graphKernel.evaluate(self.sGraph2, self.sGraph2, True)
self.assertTrue(
numpy.linalg.norm(P - numpy.eye(self.numVertices)) <= self.tol)
evaluation2 = numpy.dot(S2, S2)
self.assertTrue(numpy.linalg.norm(SW1 - S2) <= self.tol)
self.assertTrue(numpy.linalg.norm(SW2 - S2) <= self.tol)
self.assertTrue(abs(evaluation - evaluation2) <= self.tol)
#Test symmetry
self.assertEquals(graphKernel.evaluate(self.sGraph1, self.sGraph2),
graphKernel.evaluate(self.sGraph2, self.sGraph1))
#Now we choose tau != 1
tau = 0.5
graphKernel = PermutationGraphKernel(tau, linearKernel)
(evaluation, f, P, SW1, SW2, SK1,
SK2) = graphKernel.evaluate(self.sGraph1, self.sGraph1, True)
self.assertTrue(
numpy.linalg.norm(P - numpy.eye(self.numVertices)) <= self.tol)
self.assertTrue(graphKernel.evaluate(self.sGraph1, self.sGraph1) >= 0)
self.assertTrue(graphKernel.evaluate(self.sGraph2, self.sGraph2) >= 0)
self.assertTrue(
(graphKernel.evaluate(self.sGraph1, self.sGraph2) -
graphKernel.evaluate(self.sGraph2, self.sGraph1)) <= self.tol)
(evaluation, f, P, SW1, SW2, SK1,
SK2) = graphKernel.evaluate(self.sGraph1, self.sGraph2, True)
self.assertTrue(
numpy.linalg.norm(numpy.dot(P.T, P) -
numpy.eye(self.numVertices)) <= self.tol)
#Choose tau=0
tau = 0.0
graphKernel = PermutationGraphKernel(tau, linearKernel)
(evaluation, f, P, SW1, SW2, SK1,
SK2) = graphKernel.evaluate(self.sGraph1, self.sGraph1, True)
self.assertTrue(
numpy.linalg.norm(P - numpy.eye(self.numVertices)) <= self.tol)
self.assertTrue(
numpy.linalg.norm(numpy.dot(P.T, P) -
numpy.eye(self.numVertices)) <= self.tol)
X1 = self.sGraph1.getVertexList().getVertices(
list(range(0, (self.sGraph1.getNumVertices()))))
X2 = self.sGraph2.getVertexList().getVertices(
list(range(0, (self.sGraph2.getNumVertices()))))
S1, U = numpy.linalg.eigh(numpy.dot(X1, X1.T))
S2, V = numpy.linalg.eigh(numpy.dot(X2, X2.T))
evaluation2 = numpy.dot(S1, S1)
self.assertTrue(numpy.linalg.norm(SK1 - S1) <= self.tol)
self.assertTrue(numpy.linalg.norm(SK2 - S1) <= self.tol)
self.assertTrue(abs(evaluation - evaluation2) <= self.tol)
self.assertTrue(
(graphKernel.evaluate(self.sGraph1, self.sGraph2) -
graphKernel.evaluate(self.sGraph2, self.sGraph1)) <= self.tol)
#Test value is zero when we have a graph which is a permutation of the next
def testEvaluate2(self):
tau = 1.0
linearKernel = LinearKernel()
graphKernel = PermutationGraphKernel(tau, linearKernel)
(evaluation, f, P, SW1, SW2, SK1,
SK2) = graphKernel.evaluate(self.sGraph1, self.sGraph3, True)
W1 = self.sGraph1.getWeightMatrix()
W2 = self.sGraph3.getWeightMatrix()
self.assertTrue(
numpy.linalg.norm(Util.mdot(P, W1, P.T) - W2) <= self.tol)
self.assertAlmostEquals(f, 0, 7)
from scipy.sparse import csr_matrix
from pyamg import smoothed_aggregation_solver
from apgl.generator.ErdosRenyiGenerator import ErdosRenyiGenerator
from apgl.graph.SparseGraph import SparseGraph
from apgl.graph.GeneralVertexList import GeneralVertexList
numpy.set_printoptions(suppress=True, precision=4, linewidth=100)
numpy.random.seed(21)
p = 0.001
numVertices = 10000
generator = ErdosRenyiGenerator(p)
graph = SparseGraph(GeneralVertexList(numVertices))
graph = generator.generate(graph)
print("Num vertices = " + str(graph.getNumVertices()))
print("Num edges = " + str(graph.getNumEdges()))
L = graph.normalisedLaplacianSym(sparse=True)
# L = csr_matrix(L)
print("Created Laplacian")
# ml = smoothed_aggregation_solver(L)
# M = ml.aspreconditioner()
start = time.clock()
w, V = scipy.sparse.linalg.eigsh(L, k=20)
totalTime = time.clock() - start
print(totalTime)
class PermutationGraphKernelTest(unittest.TestCase):
def setUp(self):
self.tol = 10**-4
self.numVertices = 5
self.numFeatures = 2
vertexList1 = VertexList(self.numVertices, self.numFeatures)
vertexList1.setVertex(0, numpy.array([1, 1]))
vertexList1.setVertex(1, numpy.array([1, 2]))
vertexList1.setVertex(2, numpy.array([3, 2]))
vertexList1.setVertex(3, numpy.array([4, 2]))
vertexList1.setVertex(4, numpy.array([2, 6]))
vertexList2 = VertexList(self.numVertices, self.numFeatures)
vertexList2.setVertex(0, numpy.array([1, 3]))
vertexList2.setVertex(1, numpy.array([7, 2]))
vertexList2.setVertex(2, numpy.array([3, 22]))
vertexList2.setVertex(3, numpy.array([54, 2]))
vertexList2.setVertex(4, numpy.array([2, 34]))
self.sGraph1 = SparseGraph(vertexList1)
self.sGraph1.addEdge(0, 1)
self.sGraph1.addEdge(0, 2)
self.sGraph1.addEdge(1, 2)
self.sGraph1.addEdge(2, 3)
self.sGraph2 = SparseGraph(vertexList2)
self.sGraph2.addEdge(0, 1)
self.sGraph2.addEdge(0, 2)
self.sGraph2.addEdge(1, 2)
self.sGraph2.addEdge(2, 3)
self.sGraph2.addEdge(3, 4)
self.sGraph3 = SparseGraph(vertexList2)
self.sGraph3.addEdge(4, 1)
self.sGraph3.addEdge(4, 2)
self.sGraph3.addEdge(1, 2)
self.sGraph3.addEdge(1, 0)
def testEvaluate(self):
tau = 1.0
linearKernel = LinearKernel()
graphKernel = PermutationGraphKernel(tau, linearKernel)
"""
First tests - if the graphs have identical edges then permutation is identity matrix
provided that tau = 1.
"""
(evaluation, f, P, SW1, SW2, SK1, SK2) = graphKernel.evaluate(self.sGraph1, self.sGraph1, True)
self.assertTrue(numpy.linalg.norm(P - numpy.eye(self.numVertices)) <= self.tol)
S1, U = numpy.linalg.eigh(self.sGraph1.getWeightMatrix())
S2, U = numpy.linalg.eigh(self.sGraph2.getWeightMatrix())
evaluation2 = numpy.dot(S1, S1)
self.assertTrue(numpy.linalg.norm(SW1 - S1) <= self.tol)
self.assertTrue(numpy.linalg.norm(SW2 - S1) <= self.tol)
self.assertTrue(abs(evaluation - evaluation2) <= self.tol)
(evaluation, f, P, SW1, SW2, SK1, SK2) = graphKernel.evaluate(self.sGraph2, self.sGraph2, True)
self.assertTrue(numpy.linalg.norm(P - numpy.eye(self.numVertices)) <= self.tol)
evaluation2 = numpy.dot(S2, S2)
self.assertTrue(numpy.linalg.norm(SW1 - S2) <= self.tol)
self.assertTrue(numpy.linalg.norm(SW2 - S2) <= self.tol)
self.assertTrue(abs(evaluation - evaluation2) <= self.tol)
#Test symmetry
self.assertEquals(graphKernel.evaluate(self.sGraph1, self.sGraph2), graphKernel.evaluate(self.sGraph2, self.sGraph1))
#Now we choose tau != 1
tau = 0.5
graphKernel = PermutationGraphKernel(tau, linearKernel)
(evaluation, f, P, SW1, SW2, SK1, SK2) = graphKernel.evaluate(self.sGraph1, self.sGraph1, True)
self.assertTrue(numpy.linalg.norm(P - numpy.eye(self.numVertices)) <= self.tol)
self.assertTrue(graphKernel.evaluate(self.sGraph1, self.sGraph1) >= 0)
self.assertTrue(graphKernel.evaluate(self.sGraph2, self.sGraph2) >= 0)
self.assertTrue((graphKernel.evaluate(self.sGraph1, self.sGraph2)- graphKernel.evaluate(self.sGraph2, self.sGraph1)) <= self.tol)
(evaluation, f, P, SW1, SW2, SK1, SK2) = graphKernel.evaluate(self.sGraph1, self.sGraph2, True)
self.assertTrue(numpy.linalg.norm(numpy.dot(P.T, P) - numpy.eye(self.numVertices)) <= self.tol)
#Choose tau=0
tau = 0.0
graphKernel = PermutationGraphKernel(tau, linearKernel)
(evaluation, f, P, SW1, SW2, SK1, SK2) = graphKernel.evaluate(self.sGraph1, self.sGraph1, True)
self.assertTrue(numpy.linalg.norm(P - numpy.eye(self.numVertices)) <= self.tol)
self.assertTrue(numpy.linalg.norm(numpy.dot(P.T, P) - numpy.eye(self.numVertices)) <= self.tol)
X1 = self.sGraph1.getVertexList().getVertices(list(range(0, (self.sGraph1.getNumVertices()))))
X2 = self.sGraph2.getVertexList().getVertices(list(range(0, (self.sGraph2.getNumVertices()))))
S1, U = numpy.linalg.eigh(numpy.dot(X1, X1.T))
S2, V = numpy.linalg.eigh(numpy.dot(X2, X2.T))
evaluation2 = numpy.dot(S1, S1)
self.assertTrue(numpy.linalg.norm(SK1 - S1) <= self.tol)
self.assertTrue(numpy.linalg.norm(SK2 - S1) <= self.tol)
self.assertTrue(abs(evaluation - evaluation2) <= self.tol)
self.assertTrue((graphKernel.evaluate(self.sGraph1, self.sGraph2)- graphKernel.evaluate(self.sGraph2, self.sGraph1)) <= self.tol)
#Test value is zero when we have a graph which is a permutation of the next
def testEvaluate2(self):
tau = 1.0
linearKernel = LinearKernel()
graphKernel = PermutationGraphKernel(tau, linearKernel)
(evaluation, f, P, SW1, SW2, SK1, SK2) = graphKernel.evaluate(self.sGraph1, self.sGraph3, True)
W1 = self.sGraph1.getWeightMatrix()
W2 = self.sGraph3.getWeightMatrix()
self.assertTrue(numpy.linalg.norm(Util.mdot(P, W1, P.T)-W2) <= self.tol)
self.assertAlmostEquals(f, 0, 7)
from scipy.sparse import csr_matrix
from pyamg import smoothed_aggregation_solver
from apgl.generator.ErdosRenyiGenerator import ErdosRenyiGenerator
from apgl.graph.SparseGraph import SparseGraph
from apgl.graph.GeneralVertexList import GeneralVertexList
numpy.set_printoptions(suppress=True, precision=4, linewidth=100)
numpy.random.seed(21)
p = 0.001
numVertices = 10000
generator = ErdosRenyiGenerator(p)
graph = SparseGraph(GeneralVertexList(numVertices))
graph = generator.generate(graph)
print("Num vertices = " + str(graph.getNumVertices()))
print("Num edges = " + str(graph.getNumEdges()))
L = graph.normalisedLaplacianSym(sparse=True)
#L = csr_matrix(L)
print("Created Laplacian")
#ml = smoothed_aggregation_solver(L)
#M = ml.aspreconditioner()
start = time.clock()
w, V = scipy.sparse.linalg.eigsh(L, k=20)
totalTime = time.clock() - start
print(totalTime)
#print(w)
