def cluster(self, graph):
"""
Take a graph and cluster using the method in "On spectral clusering: analysis
and algorithm" by Ng et al., 2001.
:param graph: the graph to cluster
:type graph: :class:`apgl.graph.AbstractMatrixGraph`
:returns: An array of size graph.getNumVertices() of cluster membership
"""
L = graph.normalisedLaplacianSym()
omega, Q = numpy.linalg.eig(L)
inds = numpy.argsort(omega)
#First normalise rows, then columns
standardiser = Standardiser()
V = standardiser.normaliseArray(Q[:, inds[0:self.k]].T).T
V = vq.whiten(V)
#Using kmeans2 here seems to result in a high variance
#in the quality of clustering. Therefore stick to kmeans
centroids, clusters = vq.kmeans(V, self.k, iter=self.numIterKmeans)
clusters, distortion = vq.vq(V, centroids)
return clusters
def matrixSimilarity(self, V1, V2):
"""
Compute a vertex similarity matrix C, such that the ijth entry is the matching
score between V1_i and V2_j, where larger is a better match.
"""
X = numpy.r_[V1, V2]
standardiser = Standardiser()
X = standardiser.normaliseArray(X)
V1 = X[0 : V1.shape[0], :]
V2 = X[V1.shape[0] :, :]
# print(X)
# Extend arrays with zeros to make them the same size
# if V1.shape[0] < V2.shape[0]:
# V1 = Util.extendArray(V1, V2.shape, numpy.min(V1))
# elif V2.shape[0] < V1.shape[0]:
# V2 = Util.extendArray(V2, V1.shape, numpy.min(V2))
# Let's compute C as the distance between vertices
# Distance is bounded by 1
D = Util.distanceMatrix(V1, V2)
maxD = numpy.max(D)
minD = numpy.min(D)
if (maxD - minD) != 0:
C = (maxD - D) / (maxD - minD)
else:
C = numpy.ones((V1.shape[0], V2.shape[0]))
return C
def matrixSimilarity(self, V1, V2):
"""
Compute a vertex similarity matrix C, such that the ijth entry is the matching
score between V1_i and V2_j, where larger is a better match.
"""
X = numpy.r_[V1, V2]
standardiser = Standardiser()
X = standardiser.normaliseArray(X)
V1 = X[0:V1.shape[0], :]
V2 = X[V1.shape[0]:, :]
#print(X)
#Extend arrays with zeros to make them the same size
#if V1.shape[0] < V2.shape[0]:
# V1 = Util.extendArray(V1, V2.shape, numpy.min(V1))
#elif V2.shape[0] < V1.shape[0]:
# V2 = Util.extendArray(V2, V1.shape, numpy.min(V2))
#Let's compute C as the distance between vertices
#Distance is bounded by 1
D = Util.distanceMatrix(V1, V2)
maxD = numpy.max(D)
minD = numpy.min(D)
if (maxD - minD) != 0:
C = (maxD - D) / (maxD - minD)
else:
C = numpy.ones((V1.shape[0], V2.shape[0]))
return C
def cluster(self, graph):
"""
Take a graph and cluster using the method in "On spectral clusering: analysis
and algorithm" by Ng et al., 2001.
:param graph: the graph to cluster
:type graph: :class:`apgl.graph.AbstractMatrixGraph`
:returns: An array of size graph.getNumVertices() of cluster membership
"""
L = graph.normalisedLaplacianSym()
omega, Q = numpy.linalg.eig(L)
inds = numpy.argsort(omega)
#First normalise rows, then columns
standardiser = Standardiser()
V = standardiser.normaliseArray(Q[:, inds[0:self.k]].T).T
V = vq.whiten(V)
#Using kmeans2 here seems to result in a high variance
#in the quality of clustering. Therefore stick to kmeans
centroids, clusters = vq.kmeans(V, self.k, iter=self.numIterKmeans)
clusters, distortion = vq.vq(V, centroids)
return clusters
def testScaleArray(self):
numExamples = 10
numFeatures = 3
X = numpy.random.rand(numExamples, numFeatures)
preprocessor = Standardiser()
Xs = preprocessor.scaleArray(X)
minVals = numpy.amin(Xs, 0)
maxVals = numpy.amax(Xs, 0)
tol = 10 ** -6
self.assertTrue(numpy.linalg.norm(minVals + numpy.ones(X.shape[1])) <= tol)
self.assertTrue(numpy.linalg.norm(maxVals - numpy.ones(X.shape[1])) <= tol)
# Now test stanrdisation on other matrix
X = numpy.array([[2, 1], [-1, -2], [0.6, 0.3]])
preprocessor = Standardiser()
Xs = preprocessor.scaleArray(X)
X2 = numpy.array([[2, 1], [-1, -2], [0.6, 0.3], [4, 2]])
Xs2 = preprocessor.scaleArray(X2)
self.assertTrue(numpy.linalg.norm(Xs2[0:3, :] - Xs) < tol)
def testUnstandardiseArray(self):
numExamples = 10
numFeatures = 3
tol = 10 ** -6
preprocessor = Standardiser()
# Test an everyday matrix
X = numpy.random.rand(numExamples, numFeatures)
Xs = preprocessor.standardiseArray(X)
X2 = preprocessor.unstandardiseArray(Xs)
self.assertTrue(numpy.linalg.norm(X2 - X) < tol)
def testLearningRate(self):
numExamples = 100
trainX, trainY = data.make_regression(numExamples)
trainX = Standardiser().normaliseArray(trainX)
trainY = Standardiser().normaliseArray(trainY)
learner = DecisionTreeLearner(pruneType="CART", maxDepth=20, minSplit=1)
foldsSet = numpy.arange(2, 7, 2)
gammas = numpy.array(numpy.round(2**numpy.arange(1, 8, 1)-1), dtype=numpy.int)
paramDict = {}
paramDict["setGamma"] = gammas
betaGrid = learner.learningRate(trainX, trainY, foldsSet, paramDict)
#Compute beta more directly
numParams = gammas.shape[0]
sampleSize = trainX.shape[0]
sampleMethod = Sampling.crossValidation
Cvs = numpy.array([1])
penalties = numpy.zeros((foldsSet.shape[0], numParams))
betas = numpy.zeros(gammas.shape[0])
for k in range(foldsSet.shape[0]):
folds = foldsSet[k]
logging.debug("Folds " + str(folds))
idx = sampleMethod(folds, trainX.shape[0])
#Now try penalisation
resultsList = learner.parallelPen(trainX, trainY, idx, paramDict, Cvs)
bestLearner, trainErrors, currentPenalties = resultsList[0]
penalties[k, :] = currentPenalties
for i in range(gammas.shape[0]):
inds = numpy.logical_and(numpy.isfinite(penalties[:, i]), penalties[:, i]>0)
tempPenalties = penalties[:, i][inds]
tempfoldsSet = numpy.array(foldsSet, numpy.float)[inds]
if tempPenalties.shape[0] > 1:
x = numpy.log((tempfoldsSet-1)/tempfoldsSet*sampleSize)
y = numpy.log(tempPenalties)+numpy.log(tempfoldsSet)
clf = linear_model.LinearRegression()
clf.fit(numpy.array([x]).T, y)
betas[i] = clf.coef_[0]
betas = -betas
nptst.assert_array_equal(betaGrid, betas)
def testLearnModel(self):
numExamples = 50
numFeatures = 200
preprocessor = Standardiser()
X = numpy.random.randn(numExamples, numFeatures)
X = preprocessor.standardiseArray(X)
c = numpy.random.rand(numFeatures)
y = numpy.dot(X, c)
tol = 0.05
kernel = LinearKernel()
lmbda = 0.0001
predictor = KernelShiftRegression(kernel, lmbda)
alpha, b = predictor.learnModel(X, y)
predY = predictor.predict(X)
self.assertTrue(Evaluator.rootMeanSqError(y, predY) < tol)
#Try increasing y
y = y + 5
lmbda = 0.2
predictor = KernelShiftRegression(kernel, lmbda)
alpha, b = predictor.learnModel(X, y)
predY = predictor.predict(X)
self.assertTrue(numpy.abs(b - 5) < 0.1)
self.assertTrue(Evaluator.rootMeanSqError(y, predY) < 0.1)
#Try making prediction for multilabel Y
C = numpy.random.rand(numFeatures, numFeatures)
Y = numpy.dot(X, C)
predictor = KernelShiftRegression(kernel, lmbda)
alpha, b = predictor.learnModel(X, Y)
predY = predictor.predict(X)
self.assertTrue(Evaluator.rootMeanSqError(Y, predY) < 0.1)
#Now, shift the data
s = numpy.random.rand(numFeatures)
Y = Y + s
predictor = KernelShiftRegression(kernel, lmbda)
alpha, b = predictor.learnModel(X, Y)
predY = predictor.predict(X)
self.assertTrue(numpy.linalg.norm(b - s) < 0.1)
self.assertTrue(Evaluator.rootMeanSqError(Y, predY) < 0.1)
def testLearnModel(self):
numExamples = 50
numFeatures = 200
preprocessor = Standardiser()
X = numpy.random.randn(numExamples, numFeatures)
X = preprocessor.standardiseArray(X)
c = numpy.random.rand(numFeatures)
y = numpy.dot(X, c)
tol = 0.05
kernel = LinearKernel()
lmbda = 0.0001
predictor = KernelShiftRegression(kernel, lmbda)
alpha, b = predictor.learnModel(X, y)
predY = predictor.predict(X)
self.assertTrue(Evaluator.rootMeanSqError(y, predY) < tol)
#Try increasing y
y = y + 5
lmbda = 0.2
predictor = KernelShiftRegression(kernel, lmbda)
alpha, b = predictor.learnModel(X, y)
predY = predictor.predict(X)
self.assertTrue(numpy.abs(b - 5) < 0.1)
self.assertTrue(Evaluator.rootMeanSqError(y, predY) < 0.1)
#Try making prediction for multilabel Y
C = numpy.random.rand(numFeatures, numFeatures)
Y = numpy.dot(X, C)
predictor = KernelShiftRegression(kernel, lmbda)
alpha, b = predictor.learnModel(X, Y)
predY = predictor.predict(X)
self.assertTrue(Evaluator.rootMeanSqError(Y, predY) < 0.1)
#Now, shift the data
s = numpy.random.rand(numFeatures)
Y = Y + s
predictor = KernelShiftRegression(kernel, lmbda)
alpha, b = predictor.learnModel(X, Y)
predY = predictor.predict(X)
self.assertTrue(numpy.linalg.norm(b - s) < 0.1)
self.assertTrue(Evaluator.rootMeanSqError(Y, predY) < 0.1)
def testRecursiveSetPrune(self):
numExamples = 1000
X, y = data.make_regression(numExamples)
y = Standardiser().normaliseArray(y)
numTrain = numpy.round(numExamples * 0.66)
trainX = X[0:numTrain, :]
trainY = y[0:numTrain]
testX = X[numTrain:, :]
testY = y[numTrain:]
learner = DecisionTreeLearner()
learner.learnModel(trainX, trainY)
rootId = (0,)
learner.tree.getVertex(rootId).setTestInds(numpy.arange(testX.shape[0]))
learner.recursiveSetPrune(testX, testY, rootId)
for vertexId in learner.tree.getAllVertexIds():
tempY = testY[learner.tree.getVertex(vertexId).getTestInds()]
predY = numpy.ones(tempY.shape[0])*learner.tree.getVertex(vertexId).getValue()
error = numpy.sum((tempY-predY)**2)
self.assertAlmostEquals(error, learner.tree.getVertex(vertexId).getTestError())
#Check leaf indices form all indices
inds = numpy.array([])
for vertexId in learner.tree.leaves():
inds = numpy.union1d(inds, learner.tree.getVertex(vertexId).getTestInds())
nptst.assert_array_equal(inds, numpy.arange(testY.shape[0]))
def testStandardiseArray(self):
numExamples = 10
numFeatures = 3
preprocessor = Standardiser()
# Test an everyday matrix
X = numpy.random.rand(numExamples, numFeatures)
Xs = preprocessor.standardiseArray(X)
self.assertAlmostEquals(numpy.sum(Xs), 0, places=3)
self.assertAlmostEquals(numpy.sum(Xs * Xs), numFeatures, places=3)
# Now, test on a portion of a matrix
Xss = preprocessor.standardiseArray(X[1:5, :])
self.assertTrue((Xss == Xs[1:5, :]).all())
def testPredict2(self):
#Test on Gauss2D dataset
dataDir = PathDefaults.getDataDir()
fileName = dataDir + "Gauss2D_learn.csv"
XY = numpy.loadtxt(fileName,
skiprows=1,
usecols=(1, 2, 3),
delimiter=",")
X = XY[:, 0:2]
y = XY[:, 2]
fileName = dataDir + "Gauss2D_test.csv"
testXY = numpy.loadtxt(fileName,
skiprows=1,
usecols=(1, 2, 3),
delimiter=",")
testX = testXY[:, 0:2]
testY = testXY[:, 2]
X = Standardiser().standardiseArray(X)
testX = Standardiser().standardiseArray(testX)
maxDepths = range(3, 10)
trainAucs = numpy.array([
0.7194734, 0.7284824, 0.7332185, 0.7348198, 0.7366152, 0.7367508,
0.7367508, 0.7367508
])
testAucs = numpy.array([
0.6789078, 0.6844632, 0.6867918, 0.6873420, 0.6874820, 0.6874400,
0.6874400, 0.6874400
])
i = 0
#The results are approximately the same, but not exactly
for maxDepth in maxDepths:
treeRank = TreeRank(self.leafRanklearner)
treeRank.setMaxDepth(maxDepth)
treeRank.learnModel(X, y)
trainScores = treeRank.predict(X)
testScores = treeRank.predict(testX)
self.assertAlmostEquals(Evaluator.auc(trainScores, y),
trainAucs[i], 2)
self.assertAlmostEquals(Evaluator.auc(testScores, testY),
testAucs[i], 1)
i += 1
def testCentreArray(self):
numExamples = 10
numFeatures = 3
preprocessor = Standardiser()
# Test an everyday matrix
X = numpy.random.rand(numExamples, numFeatures)
Xc = preprocessor.centreArray(X)
centreV = preprocessor.getCentreVector()
self.assertAlmostEquals(numpy.sum(Xc), 0, places=3)
self.assertTrue((X - centreV == Xc).all())
# Now take out 3 rows of X, normalise and compare to normalised X
Xs = X[0:3, :]
Xsc = preprocessor.centreArray(Xs)
self.assertTrue((Xsc == Xc[0:3, :]).all())
def testNormaliseArray(self):
numExamples = 10
numFeatures = 3
preprocessor = Standardiser()
# Test an everyday matrix
X = numpy.random.rand(numExamples, numFeatures)
Xn = preprocessor.normaliseArray(X)
normV = preprocessor.getNormVector()
self.assertAlmostEquals(numpy.sum(Xn * Xn), numFeatures, places=3)
norms = numpy.sum(Xn * Xn, 0)
for i in range(0, norms.shape[0]):
self.assertAlmostEquals(norms[i], 1, places=3)
self.assertTrue((X / normV == Xn).all())
# Zero one column
preprocessor = Standardiser()
X[:, 1] = 0
Xn = preprocessor.normaliseArray(X)
normV = preprocessor.getNormVector()
self.assertAlmostEquals(numpy.sum(Xn * Xn), numFeatures - 1, places=3)
self.assertTrue((X / normV == Xn).all())
# Now take out 3 rows of X, normalise and compare to normalised X
Xs = X[0:3, :]
Xsn = preprocessor.normaliseArray(Xs)
self.assertTrue((Xsn == Xn[0:3, :]).all())
def testPredict2(self):
#Test on Gauss2D dataset
dataDir = PathDefaults.getDataDir()
fileName = dataDir + "Gauss2D_learn.csv"
XY = numpy.loadtxt(fileName, skiprows=1, usecols=(1,2,3), delimiter=",")
X = XY[:, 0:2]
y = XY[:, 2]
y = y*2 - 1
fileName = dataDir + "Gauss2D_test.csv"
testXY = numpy.loadtxt(fileName, skiprows=1, usecols=(1,2,3), delimiter=",")
testX = testXY[:, 0:2]
testY = testXY[:, 2]
testY = testY*2-1
X = Standardiser().standardiseArray(X)
testX = Standardiser().standardiseArray(testX)
numTrees = 5
minSplit = 50
maxDepths = range(3, 10)
trainAucs = numpy.array([0.7252582, 0.7323278, 0.7350289, 0.7372529, 0.7399985, 0.7382176, 0.7395104, 0.7386347])
testAucs = numpy.array([0.6806122, 0.6851614, 0.6886183, 0.6904147, 0.6897266, 0.6874600, 0.6875980, 0.6878801])
i = 0
#The results are approximately the same, but not exactly
for maxDepth in maxDepths:
treeRankForest = TreeRankForest(self.leafRanklearner)
treeRankForest.setMaxDepth(maxDepth)
treeRankForest.setMinSplit(minSplit)
treeRankForest.setNumTrees(numTrees)
treeRankForest.learnModel(X, y)
trainScores = treeRankForest.predict(X)
testScores = treeRankForest.predict(testX)
print(Evaluator.auc(trainScores, y), Evaluator.auc(testScores, testY))
self.assertAlmostEquals(Evaluator.auc(trainScores, y), trainAucs[i], 1)
self.assertAlmostEquals(Evaluator.auc(testScores, testY), testAucs[i], 1)
i+=1
def testClassify(self):
numExamples = 10
numFeatures = 20
X = numpy.random.randn(numExamples, numFeatures)
y = numpy.sign(numpy.random.randn(numExamples))
logging.debug(y)
preprocessor = Standardiser()
X = preprocessor.standardiseArray(X)
tol = 10**-5
lmbda = 1.0
kernel = LinearKernel()
predictor = KernelRidgeRegression(kernel, lmbda)
predictor.learnModel(X, y)
classY, predY = predictor.classify(X)
self.assertTrue(numpy.logical_or(classY == 1, classY == -1).all())
def testLearnModel2(self):
numExamples = 200
numFeatures = 100
X = numpy.random.randn(numExamples, numFeatures)
y = numpy.random.randn(numExamples)
preprocessor = Standardiser()
X = preprocessor.standardiseArray(X)
tol = 10**-3
kernel = LinearKernel()
#Try using a low-rank matrix
lmbda = 0.001
predictor = KernelShiftRegression(kernel, lmbda)
alpha, b = predictor.learnModel(X, y)
predY = predictor.predict(X)
logging.debug((numpy.linalg.norm(y)))
logging.debug((numpy.linalg.norm(predY - y)))
def testLearnModel2(self):
numExamples = 200
numFeatures = 100
X = numpy.random.randn(numExamples, numFeatures)
y = numpy.random.randn(numExamples)
preprocessor = Standardiser()
X = preprocessor.standardiseArray(X)
tol = 10**-3
kernel = LinearKernel()
#Try using a low-rank matrix
lmbda = 0.001
predictor = KernelShiftRegression(kernel, lmbda)
alpha, b = predictor.learnModel(X, y)
predY = predictor.predict(X)
logging.debug((numpy.linalg.norm(y)))
logging.debug((numpy.linalg.norm(predY - y)))
def setUp(self):
numpy.random.seed(21)
numpy.seterr(all="raise")
numExamples = 100
numFeatures = 10
self.X = numpy.random.rand(numExamples, numFeatures)
c = numpy.random.rand(numFeatures)
self.y = numpy.array(
numpy.sign(self.X.dot(c) - numpy.mean(self.X.dot(c))), numpy.int)
logging.basicConfig(stream=sys.stdout, level=logging.DEBUG)
self.X = Standardiser().standardiseArray(self.X)
def testSetSvmType(self):
try:
import sklearn
except ImportError as error:
return
numExamples = 100
numFeatures = 10
X = numpy.random.randn(numExamples, numFeatures)
X = Standardiser().standardiseArray(X)
c = numpy.random.randn(numFeatures)
y = numpy.dot(X, numpy.array([c]).T).ravel() + 1
y2 = numpy.array(y > 0, numpy.int32) * 2 - 1
svm = LibSVM()
svm.setSvmType("Epsilon_SVR")
self.assertEquals(svm.getType(), "Epsilon_SVR")
#Try to get a good error
Cs = 2**numpy.arange(-6, 4, dtype=numpy.float)
epsilons = 2**numpy.arange(-6, 4, dtype=numpy.float)
bestError = 10
for C in Cs:
for epsilon in epsilons:
svm.setEpsilon(epsilon)
svm.setC(C)
svm.learnModel(X, y)
yp = svm.predict(X)
if Evaluator.rootMeanSqError(y, yp) < bestError:
bestError = Evaluator.rootMeanSqError(y, yp)
self.assertTrue(
bestError < Evaluator.rootMeanSqError(y, numpy.zeros(y.shape[0])))
svm.setSvmType("C_SVC")
svm.learnModel(X, y2)
yp2 = svm.predict(X)
self.assertTrue(0 <= Evaluator.binaryError(y2, yp2) <= 1)
def testCARTPrune(self):
numExamples = 500
X, y = data.make_regression(numExamples)
y = Standardiser().standardiseArray(y)
numTrain = numpy.round(numExamples * 0.33)
numValid = numpy.round(numExamples * 0.33)
trainX = X[0:numTrain, :]
trainY = y[0:numTrain]
validX = X[numTrain:numTrain+numValid, :]
validY = y[numTrain:numTrain+numValid]
testX = X[numTrain+numValid:, :]
testY = y[numTrain+numValid:]
learner = DecisionTreeLearner(pruneType="none", maxDepth=10, minSplit=2)
learner.learnModel(trainX, trainY)
learner = DecisionTreeLearner(pruneType="CART", maxDepth=10, minSplit=2, gamma=1000)
learner.learnModel(trainX, trainY)
self.assertTrue(learner.tree.getNumVertices() <= 1000)
predY = learner.predict(trainX)
learner.setGamma(200)
learner.learnModel(trainX, trainY)
self.assertTrue(learner.tree.getNumVertices() <= 200)
learner.setGamma(100)
learner.learnModel(trainX, trainY)
self.assertTrue(learner.tree.getNumVertices() <= 100)
learner = DecisionTreeLearner(pruneType="none", maxDepth=10, minSplit=2)
learner.learnModel(trainX, trainY)
predY2 = learner.predict(trainX)
#Gamma = 0 implies no pruning
nptst.assert_array_equal(predY, predY2)
#Full pruning
learner = DecisionTreeLearner(pruneType="CART", maxDepth=3, gamma=1)
learner.learnModel(trainX, trainY)
self.assertEquals(learner.tree.getNumVertices(), 1)
def testCvPrune(self):
numExamples = 500
X, y = data.make_regression(numExamples)
y = Standardiser().standardiseArray(y)
numTrain = numpy.round(numExamples * 0.33)
numValid = numpy.round(numExamples * 0.33)
trainX = X[0:numTrain, :]
trainY = y[0:numTrain]
validX = X[numTrain:numTrain+numValid, :]
validY = y[numTrain:numTrain+numValid]
testX = X[numTrain+numValid:, :]
testY = y[numTrain+numValid:]
learner = DecisionTreeLearner()
learner.learnModel(trainX, trainY)
error1 = Evaluator.rootMeanSqError(learner.predict(testX), testY)
#print(learner.getTree())
unprunedTree = learner.tree.copy()
learner.setGamma(1000)
learner.cvPrune(trainX, trainY)
self.assertEquals(unprunedTree.getNumVertices(), learner.tree.getNumVertices())
learner.setGamma(100)
learner.cvPrune(trainX, trainY)
#Test if pruned tree is subtree of current:
for vertexId in learner.tree.getAllVertexIds():
self.assertTrue(vertexId in unprunedTree.getAllVertexIds())
#The error should be better after pruning
learner.learnModel(trainX, trainY)
#learner.cvPrune(validX, validY, 0.0, 5)
learner.repPrune(validX, validY)
error2 = Evaluator.rootMeanSqError(learner.predict(testX), testY)
self.assertTrue(error1 >= error2)
def testModelSelect(self):
"""
We test the results on some data and compare to SVR.
"""
numExamples = 200
X, y = data.make_regression(numExamples, noise=0.5)
X = Standardiser().standardiseArray(X)
y = Standardiser().standardiseArray(y)
trainX = X[0:100, :]
trainY = y[0:100]
testX = X[100:, :]
testY = y[100:]
learner = DecisionTreeLearner(maxDepth=20, minSplit=10, pruneType="REP-CV")
learner.setPruneCV(8)
paramDict = {}
paramDict["setGamma"] = numpy.linspace(0.0, 1.0, 10)
paramDict["setPruneCV"] = numpy.arange(6, 11, 2, numpy.int)
folds = 5
idx = Sampling.crossValidation(folds, trainX.shape[0])
bestTree, cvGrid = learner.parallelModelSelect(trainX, trainY, idx, paramDict)
predY = bestTree.predict(testX)
error = Evaluator.rootMeanSqError(testY, predY)
print(error)
learner = DecisionTreeLearner(maxDepth=20, minSplit=5, pruneType="CART")
paramDict = {}
paramDict["setGamma"] = numpy.linspace(0.0, 1.0, 50)
folds = 5
idx = Sampling.crossValidation(folds, trainX.shape[0])
bestTree, cvGrid = learner.parallelModelSelect(trainX, trainY, idx, paramDict)
predY = bestTree.predict(testX)
error = Evaluator.rootMeanSqError(testY, predY)
print(error)
return
#Let's compare to the SVM
learner2 = LibSVM(kernel='gaussian', type="Epsilon_SVR")
paramDict = {}
paramDict["setC"] = 2.0**numpy.arange(-10, 14, 2, dtype=numpy.float)
paramDict["setGamma"] = 2.0**numpy.arange(-10, 4, 2, dtype=numpy.float)
paramDict["setEpsilon"] = learner2.getEpsilons()
idx = Sampling.crossValidation(folds, trainX.shape[0])
bestSVM, cvGrid = learner2.parallelModelSelect(trainX, trainY, idx, paramDict)
predY = bestSVM.predict(testX)
error = Evaluator.rootMeanSqError(testY, predY)
print(error)
def testLearnModel(self):
numExamples = 50
numFeatures = 200
X = numpy.random.randn(numExamples, numFeatures)
y = numpy.random.randn(numExamples)
preprocessor = Standardiser()
X = preprocessor.standardiseArray(X)
tol = 10**-3
kernel = LinearKernel()
#Compare Linear kernel with linear ridge regression
lmbda = 0.1
predictor = KernelRidgeRegression(kernel, lmbda)
alpha = predictor.learnModel(X, y)
predY = predictor.predict(X)
K = numpy.dot(X, X.T)
alpha2 = numpy.dot(
numpy.linalg.inv(K + lmbda * numpy.eye(numExamples)), y)
predY2 = X.dot(
numpy.linalg.inv(
numpy.dot(X.T, X) + lmbda * numpy.eye(numFeatures))).dot(
X.T).dot(y)
#logging.debug(numpy.linalg.norm(alpha - alpha2))
self.assertTrue(numpy.linalg.norm(alpha - alpha2) < tol)
self.assertTrue(numpy.linalg.norm(predY - predY2) < tol)
lmbda = 0.5
predictor = KernelRidgeRegression(kernel, lmbda)
alpha = predictor.learnModel(X, y)
predY = predictor.predict(X)
K = numpy.dot(X, X.T)
alpha2 = numpy.dot(
numpy.linalg.inv(K + lmbda * numpy.eye(numExamples)), y)
predY2 = X.dot(
numpy.linalg.inv(
numpy.dot(X.T, X) + lmbda * numpy.eye(numFeatures))).dot(
X.T).dot(y)
self.assertTrue(numpy.linalg.norm(alpha - alpha2) < tol)
self.assertTrue(numpy.linalg.norm(predY - predY2) < tol)
#Now test on an alternative test set
numTestExamples = 50
testX = numpy.random.randn(numTestExamples, numFeatures)
predictor = KernelRidgeRegression(kernel, lmbda)
alpha = predictor.learnModel(X, y)
predY = predictor.predict(testX)
K = numpy.dot(X, X.T)
alpha2 = numpy.dot(
numpy.linalg.inv(K + lmbda * numpy.eye(numExamples)), y)
predY2 = testX.dot(
numpy.linalg.inv(
numpy.dot(X.T, X) + lmbda * numpy.eye(numFeatures))).dot(
X.T).dot(y)
self.assertTrue(numpy.linalg.norm(alpha - alpha2) < tol)
self.assertTrue(numpy.linalg.norm(predY - predY2) < tol)
#Use the method against a multi-label example
Y = numpy.random.randn(numExamples, numFeatures)
alpha = predictor.learnModel(X, Y)
self.assertTrue(alpha.shape == (numExamples, numFeatures))
def clusterFromIterator(self, graphListIterator, verbose=False):
"""
Find a set of clusters for the graphs given by the iterator. If verbose
is true the each iteration is timed and bounded the results are returned
as lists.
The difference between a weight matrix and the previous one should be
positive.
"""
clustersList = []
decompositionTimeList = []
kMeansTimeList = []
boundList = []
sinThetaList = []
i = 0
for subW in graphListIterator:
if __debug__:
Parameter.checkSymmetric(subW)
if self.logStep and i % self.logStep == 0:
logging.debug("Graph index: " + str(i))
logging.debug("Clustering graph of size " + str(subW.shape))
if self.alg != "efficientNystrom":
ABBA = GraphUtils.shiftLaplacian(subW)
# --- Eigen value decomposition ---
startTime = time.time()
if self.alg == "IASC":
if i % self.T != 0:
omega, Q = self.approxUpdateEig(subW, ABBA, omega, Q)
if self.computeBound:
inds = numpy.flipud(numpy.argsort(omega))
Q = Q[:, inds]
omega = omega[inds]
bounds = self.pertBound(omega, Q, omegaKbot, AKbot,
self.k2)
#boundList.append([i, bounds[0], bounds[1]])
#Now use accurate values of norm of R and delta
rank = Util.rank(ABBA.todense())
gamma, U = scipy.sparse.linalg.eigsh(ABBA,
rank - 1,
which="LM",
ncv=ABBA.shape[0])
#logging.debug("gamma=" + str(gamma))
bounds2 = self.realBound(omega, Q, gamma, AKbot,
self.k2)
boundList.append(
[bounds[0], bounds[1], bounds2[0], bounds2[1]])
else:
logging.debug("Computing exact eigenvectors")
self.storeInformation(subW, ABBA)
if self.computeBound:
#omega, Q = scipy.sparse.linalg.eigsh(ABBA, min(self.k2*2, ABBA.shape[0]-1), which="LM", ncv = min(10*self.k2, ABBA.shape[0]))
rank = Util.rank(ABBA.todense())
omega, Q = scipy.sparse.linalg.eigsh(ABBA,
rank - 1,
which="LM",
ncv=ABBA.shape[0])
inds = numpy.flipud(numpy.argsort(omega))
omegaKbot = omega[inds[self.k2:]]
QKbot = Q[:, inds[self.k2:]]
AKbot = (QKbot * omegaKbot).dot(QKbot.T)
omegaSort = numpy.flipud(numpy.sort(omega))
boundList.append([0] * 4)
else:
omega, Q = scipy.sparse.linalg.eigsh(
ABBA,
min(self.k2, ABBA.shape[0] - 1),
which="LM",
ncv=min(10 * self.k2, ABBA.shape[0]))
elif self.alg == "nystrom":
omega, Q = Nystrom.eigpsd(ABBA, self.k3)
elif self.alg == "exact":
omega, Q = scipy.sparse.linalg.eigsh(
ABBA,
min(self.k1, ABBA.shape[0] - 1),
which="LM",
ncv=min(15 * self.k1, ABBA.shape[0]))
elif self.alg == "efficientNystrom":
omega, Q = EfficientNystrom.eigWeight(subW, self.k2, self.k1)
elif self.alg == "randomisedSvd":
Q, omega, R = RandomisedSVD.svd(ABBA, self.k4)
else:
raise ValueError("Invalid Algorithm: " + str(self.alg))
if self.computeSinTheta:
omegaExact, QExact = scipy.linalg.eigh(ABBA.todense())
inds = numpy.flipud(numpy.argsort(omegaExact))
QExactKbot = QExact[:, inds[self.k1:]]
inds = numpy.flipud(numpy.argsort(omega))
QApproxK = Q[:, inds[:self.k1]]
sinThetaList.append(
scipy.linalg.norm(QExactKbot.T.dot(QApproxK)))
decompositionTimeList.append(time.time() - startTime)
if self.alg == "IASC":
self.storeInformation(subW, ABBA)
# --- Kmeans ---
startTime = time.time()
inds = numpy.flipud(numpy.argsort(omega))
standardiser = Standardiser()
#For some very strange reason we get an overflow when computing the
#norm of the rows of Q even though its elements are bounded by 1.
#We'll ignore it for now
try:
V = standardiser.normaliseArray(Q[:, inds[0:self.k1]].real.T).T
except FloatingPointError as e:
logging.warn("FloatingPointError: " + str(e))
V = VqUtils.whiten(V)
if i == 0:
centroids, distortion = vq.kmeans(V,
self.k1,
iter=self.nb_iter_kmeans)
else:
centroids = self.findCentroids(V, clusters[:subW.shape[0]])
if centroids.shape[0] < self.k1:
nb_missing_centroids = self.k1 - centroids.shape[0]
random_centroids = V[numpy.random.randint(
0, V.shape[0], nb_missing_centroids), :]
centroids = numpy.vstack((centroids, random_centroids))
centroids, distortion = vq.kmeans(
V, centroids) #iter can only be 1
clusters, distortion = vq.vq(V, centroids)
kMeansTimeList.append(time.time() - startTime)
clustersList.append(clusters)
#logging.debug("subW.shape: " + str(subW.shape))
#logging.debug("len(clusters): " + str(len(clusters)))
#from sandbox.util.ProfileUtils import ProfileUtils
#logging.debug("Total memory usage: " + str(ProfileUtils.memory()/10**6) + "MB")
if ProfileUtils.memory() > 10**9:
ProfileUtils.memDisplay(locals())
i += 1
if verbose:
eigenQuality = {
"boundList": boundList,
"sinThetaList": sinThetaList
}
return clustersList, numpy.array(
(decompositionTimeList, kMeansTimeList)).T, eigenQuality
else:
return clustersList
def clusterFromIterator(self, graphListIterator, verbose=False):
"""
Find a set of clusters for the graphs given by the iterator. If verbose
is true the each iteration is timed and bounded the results are returned
as lists.
The difference between a weight matrix and the previous one should be
positive.
"""
clustersList = []
decompositionTimeList = []
kMeansTimeList = []
boundList = []
sinThetaList = []
i = 0
for subW in graphListIterator:
if __debug__:
Parameter.checkSymmetric(subW)
if self.logStep and i % self.logStep == 0:
logging.debug("Graph index: " + str(i))
logging.debug("Clustering graph of size " + str(subW.shape))
if self.alg!="efficientNystrom":
ABBA = GraphUtils.shiftLaplacian(subW)
# --- Eigen value decomposition ---
startTime = time.time()
if self.alg=="IASC":
if i % self.T != 0:
omega, Q = self.approxUpdateEig(subW, ABBA, omega, Q)
if self.computeBound:
inds = numpy.flipud(numpy.argsort(omega))
Q = Q[:, inds]
omega = omega[inds]
bounds = self.pertBound(omega, Q, omegaKbot, AKbot, self.k2)
#boundList.append([i, bounds[0], bounds[1]])
#Now use accurate values of norm of R and delta
rank = Util.rank(ABBA.todense())
gamma, U = scipy.sparse.linalg.eigsh(ABBA, rank-1, which="LM", ncv = ABBA.shape[0])
#logging.debug("gamma=" + str(gamma))
bounds2 = self.realBound(omega, Q, gamma, AKbot, self.k2)
boundList.append([bounds[0], bounds[1], bounds2[0], bounds2[1]])
else:
logging.debug("Computing exact eigenvectors")
self.storeInformation(subW, ABBA)
if self.computeBound:
#omega, Q = scipy.sparse.linalg.eigsh(ABBA, min(self.k2*2, ABBA.shape[0]-1), which="LM", ncv = min(10*self.k2, ABBA.shape[0]))
rank = Util.rank(ABBA.todense())
omega, Q = scipy.sparse.linalg.eigsh(ABBA, rank-1, which="LM", ncv = ABBA.shape[0])
inds = numpy.flipud(numpy.argsort(omega))
omegaKbot = omega[inds[self.k2:]]
QKbot = Q[:, inds[self.k2:]]
AKbot = (QKbot*omegaKbot).dot(QKbot.T)
omegaSort = numpy.flipud(numpy.sort(omega))
boundList.append([0]*4)
else:
omega, Q = scipy.sparse.linalg.eigsh(ABBA, min(self.k2, ABBA.shape[0]-1), which="LM", ncv = min(10*self.k2, ABBA.shape[0]))
elif self.alg == "nystrom":
omega, Q = Nystrom.eigpsd(ABBA, self.k3)
elif self.alg == "exact":
omega, Q = scipy.sparse.linalg.eigsh(ABBA, min(self.k1, ABBA.shape[0]-1), which="LM", ncv = min(15*self.k1, ABBA.shape[0]))
elif self.alg == "efficientNystrom":
omega, Q = EfficientNystrom.eigWeight(subW, self.k2, self.k1)
elif self.alg == "randomisedSvd":
Q, omega, R = RandomisedSVD.svd(ABBA, self.k4)
else:
raise ValueError("Invalid Algorithm: " + str(self.alg))
if self.computeSinTheta:
omegaExact, QExact = scipy.linalg.eigh(ABBA.todense())
inds = numpy.flipud(numpy.argsort(omegaExact))
QExactKbot = QExact[:, inds[self.k1:]]
inds = numpy.flipud(numpy.argsort(omega))
QApproxK = Q[:,inds[:self.k1]]
sinThetaList.append(scipy.linalg.norm(QExactKbot.T.dot(QApproxK)))
decompositionTimeList.append(time.time()-startTime)
if self.alg=="IASC":
self.storeInformation(subW, ABBA)
# --- Kmeans ---
startTime = time.time()
inds = numpy.flipud(numpy.argsort(omega))
standardiser = Standardiser()
#For some very strange reason we get an overflow when computing the
#norm of the rows of Q even though its elements are bounded by 1.
#We'll ignore it for now
try:
V = standardiser.normaliseArray(Q[:, inds[0:self.k1]].real.T).T
except FloatingPointError as e:
logging.warn("FloatingPointError: " + str(e))
V = VqUtils.whiten(V)
if i == 0:
centroids, distortion = vq.kmeans(V, self.k1, iter=self.nb_iter_kmeans)
else:
centroids = self.findCentroids(V, clusters[:subW.shape[0]])
if centroids.shape[0] < self.k1:
nb_missing_centroids = self.k1 - centroids.shape[0]
random_centroids = V[numpy.random.randint(0, V.shape[0], nb_missing_centroids),:]
centroids = numpy.vstack((centroids, random_centroids))
centroids, distortion = vq.kmeans(V, centroids) #iter can only be 1
clusters, distortion = vq.vq(V, centroids)
kMeansTimeList.append(time.time()-startTime)
clustersList.append(clusters)
#logging.debug("subW.shape: " + str(subW.shape))
#logging.debug("len(clusters): " + str(len(clusters)))
#from sandbox.util.ProfileUtils import ProfileUtils
#logging.debug("Total memory usage: " + str(ProfileUtils.memory()/10**6) + "MB")
if ProfileUtils.memory() > 10**9:
ProfileUtils.memDisplay(locals())
i += 1
if verbose:
eigenQuality = {"boundList" : boundList, "sinThetaList" : sinThetaList}
return clustersList, numpy.array((decompositionTimeList, kMeansTimeList)).T, eigenQuality
else:
return clustersList
