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)
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)
