def testVertexSimilarities(self): matcher = GraphMatch(alpha=0.0) C = matcher.vertexSimilarities(self.graph1, self.graph1) Cdiag = numpy.diag(C) nptst.assert_array_almost_equal(Cdiag, numpy.ones(Cdiag.shape[0])) #Now compute trace(C)/||C|| #print(numpy.trace(C)/numpy.linalg.norm(C)) #Test use of feature inds matcher = GraphMatch(alpha=0.0, featureInds=numpy.array([0])) C = matcher.vertexSimilarities(self.graph1, self.graph2) #Now, let's vary the non-used feature self.graph1.vlist[:, 1] = 0 C2 = matcher.vertexSimilarities(self.graph1, self.graph2) nptst.assert_array_equal(C, C2) self.graph2.vlist[:, 1] = 0 C2 = matcher.vertexSimilarities(self.graph1, self.graph2) nptst.assert_array_equal(C, C2) #Vary used feature self.graph1.vlist[:, 0] = 0 C2 = matcher.vertexSimilarities(self.graph1, self.graph2) self.assertTrue((C != C2).any())
def testMatrixSimilarity(self): numExamples = 5 numFeatures = 3 V1 = numpy.random.rand(numExamples, numFeatures) matcher = GraphMatch(alpha=0.0) C = matcher.matrixSimilarity(V1, V1) Cdiag = numpy.diag(C) nptst.assert_array_almost_equal(Cdiag, numpy.ones(Cdiag.shape[0])) V1[:, 2] *= 10 C2 = matcher.matrixSimilarity(V1, V1) Cdiag = numpy.diag(C2) nptst.assert_array_almost_equal(Cdiag, numpy.ones(Cdiag.shape[0])) nptst.assert_array_almost_equal(C, C2) #print("Running match") J = numpy.ones((numExamples, numFeatures)) Z = numpy.zeros((numExamples, numFeatures)) C2 = matcher.matrixSimilarity(J, Z) #This should be 1 ideally nptst.assert_array_almost_equal(C2, numpy.ones(C2.shape)) C2 = matcher.matrixSimilarity(J, J) nptst.assert_array_almost_equal(C2, numpy.ones(C2.shape))
def testMatch(self): matcher = GraphMatch(algorithm="U", alpha=0.3) permutation, distance, time = matcher.match(self.graph1, self.graph2) #Checked output file - seems correct distance2 = GraphMatch(alpha=0.0).distance(self.graph1, self.graph2, permutation) self.assertAlmostEquals(distance[0], distance2) #Now test case in which alpha is different matcher = GraphMatch(algorithm="U", alpha=0.5) permutation, distance, time = matcher.match(self.graph1, self.graph2) distance2 = GraphMatch(alpha=0.0).distance(self.graph1, self.graph2, permutation) self.assertAlmostEquals(distance[0], distance2) #Test normalised distance alpha = 0.0 permutation, distance, time = GraphMatch(algorithm="U", alpha=alpha).match( self.graph1, self.graph2) distance2 = GraphMatch(alpha=alpha).distance(self.graph1, self.graph2, permutation, True) self.assertAlmostEquals(distance[1], distance2) alpha = 1.0 permutation, distance, time = GraphMatch(algorithm="U", alpha=alpha).match( self.graph1, self.graph2) distance2 = GraphMatch(alpha=alpha).distance(self.graph1, self.graph2, permutation, True) self.assertAlmostEquals(distance[1], distance2, 5) #Test empty graph alpha = 0.0 graph1 = SparseGraph(VertexList(0, 0)) graph2 = SparseGraph(VertexList(0, 0)) permutation, distance, time = GraphMatch(algorithm="U", alpha=alpha).match( graph1, graph2) nptst.assert_array_equal(permutation, numpy.array([], numpy.int)) self.assertEquals(distance, [0, 0, 0]) #Test where 1 graph is empty permutation, distance, time = GraphMatch(algorithm="U", alpha=alpha).match( graph1, self.graph1) self.assertEquals( numpy.linalg.norm(self.graph1.getWeightMatrix())**2, distance[0]) self.assertEquals(distance[1], 1) self.assertEquals(distance[2], 1) permutation, distance, time = GraphMatch(algorithm="U", alpha=alpha).match( self.graph1, graph1) self.assertEquals( numpy.linalg.norm(self.graph1.getWeightMatrix())**2, distance[0]) self.assertEquals(distance[1], 1) self.assertEquals(distance[2], 1) alpha = 1.0 permutation, distance, time = GraphMatch(algorithm="U", alpha=alpha).match( graph1, self.graph1) self.assertEquals( numpy.linalg.norm(self.graph1.getWeightMatrix())**2, distance[0]) V2 = self.graph1.vlist.getVertices() V1 = numpy.zeros(V2.shape) C = GraphMatch(algorithm="U", alpha=alpha).matrixSimilarity(V1, V2) dist = numpy.trace(C) / numpy.linalg.norm(C) self.assertAlmostEquals(distance[1], -dist, 4) self.assertAlmostEquals(distance[2], -dist, 4) permutation, distance, time = GraphMatch(algorithm="U", alpha=alpha).match( self.graph1, graph1) self.assertEquals( numpy.linalg.norm(self.graph1.getWeightMatrix())**2, distance[0]) self.assertAlmostEquals(distance[1], -dist, 4) self.assertAlmostEquals(distance[2], -dist, 4) #Test one graph which is a subgraph of another p = 0.2 k = 10 numVertices = 20 generator = SmallWorldGenerator(p, k) graph = SparseGraph(VertexList(numVertices, 2)) graph = generator.generate(graph) subgraphInds = numpy.random.permutation(numVertices)[0:10] subgraph = graph.subgraph(subgraphInds) matcher = GraphMatch(algorithm="U", alpha=0.0) permutation, distance, time = matcher.match(graph, subgraph) distance = matcher.distance(graph, subgraph, permutation, True, True) self.assertTrue(distance < 1)
def testDistance2(self): permutation = numpy.arange(self.numVertices) dist = GraphMatch(alpha=0.0).distance2(self.graph1, self.graph1, permutation) self.assertEquals(dist, 0.0) dist = GraphMatch(alpha=0.0).distance2(self.graph1, self.graph2, permutation) dist2 = GraphMatch(alpha=0.0).distance(self.graph1, self.graph2, permutation, True) self.assertAlmostEquals(dist, dist2) permutation = numpy.arange(self.numVertices) permutation[8] = 9 permutation[9] = 8 dist = GraphMatch(alpha=0.0).distance2(self.graph1, self.graph2, permutation) dist2 = GraphMatch(alpha=0.0).distance(self.graph1, self.graph2, permutation, True) self.assertAlmostEquals(dist, dist2) #Try graphs of unequal size graph3 = self.graph1.subgraph(range(8)) permutation = numpy.arange(self.numVertices) dist1 = GraphMatch(alpha=0.0).distance2(self.graph1, graph3, permutation) dist1a = GraphMatch(alpha=0.0).distance2(graph3, self.graph1, permutation) self.assertEquals(dist1, dist1a) graph3 = self.graph1.subgraph(range(5)) dist2 = GraphMatch(alpha=0.0).distance2(self.graph1, graph3, permutation) dist2a = GraphMatch(alpha=0.0).distance2(graph3, self.graph1, permutation) self.assertEquals(dist2, dist2a) self.assertTrue(dist1 < dist2) #Test case where alpha!=0 alpha = 1.0 permutation = numpy.arange(self.numVertices) distance = GraphMatch(alpha=alpha).distance2(self.graph1, self.graph1, permutation) self.assertEquals(distance, 0.0) #Check distances are between 0 and 1 for i in range(100): alpha = numpy.random.rand() permutation = numpy.random.permutation(self.numVertices) distance = GraphMatch(alpha=alpha).distance2( self.graph1, self.graph1, permutation) self.assertTrue(0 <= distance <= 1)
def testDistance(self): permutation = numpy.arange(self.numVertices) dist = GraphMatch(alpha=0.0).distance(self.graph1, self.graph1, permutation) self.assertEquals(dist, 0.0) dist = GraphMatch(alpha=0.0).distance(self.graph1, self.graph2, permutation) self.assertAlmostEquals(dist, 50.0) permutation = numpy.arange(self.numVertices) permutation[8] = 9 permutation[9] = 8 dist = GraphMatch(alpha=0.0).distance(self.graph1, self.graph2, permutation) self.assertAlmostEquals(dist, 54.0) #Try graphs of unequal size graph3 = self.graph1.subgraph(range(8)) permutation = numpy.arange(self.numVertices) dist1 = GraphMatch(alpha=0.0).distance(self.graph1, graph3, permutation) dist1a = GraphMatch(alpha=0.0).distance(graph3, self.graph1, permutation) self.assertEquals(dist1, dist1a) graph3 = self.graph1.subgraph(range(5)) dist2 = GraphMatch(alpha=0.0).distance(self.graph1, graph3, permutation) dist2a = GraphMatch(alpha=0.0).distance(graph3, self.graph1, permutation) self.assertEquals(dist2, dist2a) self.assertTrue(dist1 < dist2) #Test case where alpha!=0 alpha = 1.0 permutation = numpy.arange(self.numVertices) distance = GraphMatch(alpha=alpha).distance(self.graph1, self.graph2, permutation, False) C = GraphMatch(alpha=alpha).vertexSimilarities(self.graph1, self.graph2) distance2 = -numpy.trace(C) self.assertEquals(distance, distance2) #Check case where we want non negativve distance even when alpha!=0 distance = GraphMatch(alpha=alpha).distance(self.graph1, self.graph2, permutation, True, True) self.assertTrue(distance >= 0) permutation = numpy.arange(self.numVertices) distance = GraphMatch(alpha=alpha).distance(self.graph1, self.graph1, permutation, True, True) self.assertEquals(distance, 0) #Check case where both graphs are empty graph1 = SparseGraph(VertexList(0, 0)) graph2 = SparseGraph(VertexList(0, 0)) permutation = numpy.array([], numpy.int) distance = GraphMatch(alpha=alpha).distance(graph1, graph1, permutation, True, True) self.assertEquals(distance, 0) #Now, just one graph is empty #Distance is always 1 due to normalisations alpha = 0.0 permutation = numpy.arange(10, dtype=numpy.int) distance = GraphMatch(alpha=alpha).distance(self.graph1, graph1, permutation, True, True) self.assertEquals(distance, 1.0) permutation = numpy.arange(10, dtype=numpy.int) distance = GraphMatch(alpha=alpha).distance(self.graph2, graph1, permutation, True, True) self.assertEquals(distance, 1.0) #distance = GraphMatch(alpha=alpha).distance(self.graph1, graph1, permutation, False, False) #self.assertEquals(distance, numpy.linalg.norm(self.graph1.getWeightMatrix())**2) alpha = 0.9 matcher = GraphMatch("U", alpha=alpha) permutation, distanceVector, time = matcher.match(self.graph2, graph1) distance = matcher.distance(self.graph2, graph1, permutation, True, True) self.assertEquals(distance, 1.0) alpha = 1.0 permutation = numpy.arange(10, dtype=numpy.int) distance = GraphMatch(alpha=alpha).distance(self.graph1, graph1, permutation, True, True) self.assertEquals(distance, 1.0) permutation = numpy.arange(10, dtype=numpy.int) distance = GraphMatch(alpha=alpha).distance(self.graph2, graph1, permutation, True, True) self.assertEquals(distance, 1.0) alpha = 0.5 permutation = numpy.arange(10, dtype=numpy.int) distance = GraphMatch(alpha=alpha).distance(self.graph2, graph1, permutation, True, True) self.assertEquals(distance, 1.0) #Test on unequal graphs and compare against distance from graphm alpha = 0.5 matcher = GraphMatch(alpha=alpha) permutation, distanceVector, time = matcher.match( self.graph1, self.graph2) distance = matcher.distance(self.graph1, self.graph2, permutation, True, False) self.assertAlmostEquals(distanceVector[1], distance, 3)