def testComputeKClusterBound2(self):
# Try strange case where bound is less than continuous solution
# ValueError: Bound is smaller than real solution: 127.7443918 29.6138874353
U = numpy.load("/home/dhanjalc/Documents/Postdoc/Code/APGL/repo/exp/sandbox/badMatrix.npy")
delta = numpy.load("/home/dhanjalc/Documents/Postdoc/Code/APGL/repo/exp/sandbox/badDelta.npy")
k = 3
obj, bestSigma = ClusterBound.computeKClusterBound(U, delta, k)
X, a, Y = numpy.linalg.svd(U)
a = numpy.flipud(numpy.sort(a))
self.assertTrue(obj > 127.7443918)
def testComputeKClusterBound2(self):
#Try strange case where bound is less than continuous solution
#ValueError: Bound is smaller than real solution: 127.7443918 29.6138874353
U = numpy.load(
"/home/dhanjalc/Documents/Postdoc/Code/APGL/repo/exp/sandbox/badMatrix.npy"
)
delta = numpy.load(
"/home/dhanjalc/Documents/Postdoc/Code/APGL/repo/exp/sandbox/badDelta.npy"
)
k = 3
obj, bestSigma = ClusterBound.computeKClusterBound(U, delta, k)
X, a, Y = numpy.linalg.svd(U)
a = numpy.flipud(numpy.sort(a))
self.assertTrue(obj > 127.7443918)
def testComputeKClusterBound(self):
numExamples = 100
numFeatures = 2
#Test some 2 cluster examples
for i in range(50):
V = numpy.random.rand(numExamples, numFeatures)
numCluster1 = numpy.random.randint(5, numExamples)
V[0:numCluster1, :] += numpy.random.randn()
U = V - numpy.mean(V)
delta = numpy.linalg.norm(U) * 0.1
k = 2
obj, bestSigma = ClusterBound.computeKClusterBound(U, delta, k)
obj2, bestSigma2 = ClusterBound.compute2ClusterBound(U, delta)
self.assertAlmostEquals(obj, obj2)
#Now use more clusters
numExamples = 30
numFeatures = 5
V = numpy.zeros((numExamples, numFeatures))
V[0:10, :] = numpy.random.randn(10, numFeatures) + numpy.array(
[1, 2, -1, 5, -4])
V[10:20, :] = numpy.random.randn(10, numFeatures) + numpy.array(
[1, 1, -1, 5, -4])
V[20:30, :] = numpy.random.randn(10, numFeatures) + numpy.array(
[-3, 4, -0.1, 0.5, 2])
U = V - numpy.mean(V)
delta = numpy.linalg.norm(U) * 0.1
k = 4
#In delta=0 case the sigmas are the same as the a_is
for k in range(2, 5):
obj, bestSigma = ClusterBound.computeKClusterBound(U, 0, k)
X, a, Y = numpy.linalg.svd(U)
a = numpy.flipud(numpy.sort(a))
self.assertAlmostEquals(obj, (a[k - 1:]**2).sum(), 4)
self.assertAlmostEquals(obj, (bestSigma[k - 1:]**2).sum(), 4)
#delta != 0
delta = numpy.linalg.norm(U) * 0.1
obj, bestSigma = ClusterBound.computeKClusterBound(U, 0, k)
self.assertAlmostEquals(obj, (bestSigma[k - 1:]**2).sum(), 4)
#Do some random tests
for i in range(20):
V = numpy.zeros((numExamples, numFeatures))
V[0:10, :] = numpy.random.randn(
10, numFeatures) + numpy.random.rand(numFeatures)
V[10:20, :] = numpy.random.randn(
10, numFeatures) + numpy.random.rand(numFeatures)
V[20:30, :] = numpy.random.randn(
10, numFeatures) + numpy.random.rand(numFeatures)
U = V - numpy.mean(V)
delta = numpy.linalg.norm(U) * 0.1
for k in range(2, 5):
obj, bestSigma = ClusterBound.computeKClusterBound(U, delta, k)
self.assertAlmostEquals(obj, (bestSigma[k - 1:]**2).sum(), 4)
self.assertTrue((bestSigma[0:k - 1] >= bestSigma[k - 1]).all()
and (bestSigma[k:] <= bestSigma[k - 1]).all())
#Try on a simple toy example for which we know the answer
U = numpy.array([[5, 0], [0, 1]])
delta = 1
k = 2
obj, bestSigma = ClusterBound.computeKClusterBound(U, delta, k)
self.assertEquals(obj, 4)
nptst.assert_array_equal(bestSigma, numpy.array([5, 2]))
U = numpy.array([[5, 0], [0, 1]])
delta = 4
k = 2
obj, bestSigma = ClusterBound.computeKClusterBound(U, delta, k)
self.assertAlmostEquals(obj, 9)
nptst.assert_array_almost_equal(bestSigma, numpy.array([5, 3]))
#Now try on 3-cluster example
U = numpy.array([[5, 0, 0], [0, 2, 0], [0, 0, 1]])
delta = 0
k = 3
obj, bestSigma = ClusterBound.computeKClusterBound(U, delta, k)
self.assertEquals(obj, 1)
nptst.assert_array_equal(bestSigma, numpy.array([5, 2, 1]))
U = numpy.array([[5, 0, 0], [0, 2, 0], [0, 0, 1]])
delta = 1
k = 3
obj, bestSigma = ClusterBound.computeKClusterBound(U, delta, k)
self.assertEquals(obj, 4)
nptst.assert_array_equal(bestSigma, numpy.array([5, 2, 2]))
U = numpy.array([[5, 0, 0], [0, 2, 0], [0, 0, 1]])
delta = 2
k = 3
obj, bestSigma = ClusterBound.computeKClusterBound(U, delta, k)
#To solve this we look at sigmak(sigmak-4) + sigmak(sigmak-2) = -3
sigmak = 3.0**(1.0 / 2.0) / 2.0 + 3.0 / 2.0
self.assertAlmostEquals(obj, sigmak**2)
nptst.assert_array_almost_equal(bestSigma,
numpy.array([5, sigmak, sigmak]))
def testComputeKClusterBound(self):
numExamples = 100
numFeatures = 2
# Test some 2 cluster examples
for i in range(50):
V = numpy.random.rand(numExamples, numFeatures)
numCluster1 = numpy.random.randint(5, numExamples)
V[0:numCluster1, :] += numpy.random.randn()
U = V - numpy.mean(V)
delta = numpy.linalg.norm(U) * 0.1
k = 2
obj, bestSigma = ClusterBound.computeKClusterBound(U, delta, k)
obj2, bestSigma2 = ClusterBound.compute2ClusterBound(U, delta)
self.assertAlmostEquals(obj, obj2)
# Now use more clusters
numExamples = 30
numFeatures = 5
V = numpy.zeros((numExamples, numFeatures))
V[0:10, :] = numpy.random.randn(10, numFeatures) + numpy.array([1, 2, -1, 5, -4])
V[10:20, :] = numpy.random.randn(10, numFeatures) + numpy.array([1, 1, -1, 5, -4])
V[20:30, :] = numpy.random.randn(10, numFeatures) + numpy.array([-3, 4, -0.1, 0.5, 2])
U = V - numpy.mean(V)
delta = numpy.linalg.norm(U) * 0.1
k = 4
# In delta=0 case the sigmas are the same as the a_is
for k in range(2, 5):
obj, bestSigma = ClusterBound.computeKClusterBound(U, 0, k)
X, a, Y = numpy.linalg.svd(U)
a = numpy.flipud(numpy.sort(a))
self.assertAlmostEquals(obj, (a[k - 1 :] ** 2).sum(), 4)
self.assertAlmostEquals(obj, (bestSigma[k - 1 :] ** 2).sum(), 4)
# delta != 0
delta = numpy.linalg.norm(U) * 0.1
obj, bestSigma = ClusterBound.computeKClusterBound(U, 0, k)
self.assertAlmostEquals(obj, (bestSigma[k - 1 :] ** 2).sum(), 4)
# Do some random tests
for i in range(20):
V = numpy.zeros((numExamples, numFeatures))
V[0:10, :] = numpy.random.randn(10, numFeatures) + numpy.random.rand(numFeatures)
V[10:20, :] = numpy.random.randn(10, numFeatures) + numpy.random.rand(numFeatures)
V[20:30, :] = numpy.random.randn(10, numFeatures) + numpy.random.rand(numFeatures)
U = V - numpy.mean(V)
delta = numpy.linalg.norm(U) * 0.1
for k in range(2, 5):
obj, bestSigma = ClusterBound.computeKClusterBound(U, delta, k)
self.assertAlmostEquals(obj, (bestSigma[k - 1 :] ** 2).sum(), 4)
self.assertTrue(
(bestSigma[0 : k - 1] >= bestSigma[k - 1]).all() and (bestSigma[k:] <= bestSigma[k - 1]).all()
)
# Try on a simple toy example for which we know the answer
U = numpy.array([[5, 0], [0, 1]])
delta = 1
k = 2
obj, bestSigma = ClusterBound.computeKClusterBound(U, delta, k)
self.assertEquals(obj, 4)
nptst.assert_array_equal(bestSigma, numpy.array([5, 2]))
U = numpy.array([[5, 0], [0, 1]])
delta = 4
k = 2
obj, bestSigma = ClusterBound.computeKClusterBound(U, delta, k)
self.assertAlmostEquals(obj, 9)
nptst.assert_array_almost_equal(bestSigma, numpy.array([5, 3]))
# Now try on 3-cluster example
U = numpy.array([[5, 0, 0], [0, 2, 0], [0, 0, 1]])
delta = 0
k = 3
obj, bestSigma = ClusterBound.computeKClusterBound(U, delta, k)
self.assertEquals(obj, 1)
nptst.assert_array_equal(bestSigma, numpy.array([5, 2, 1]))
U = numpy.array([[5, 0, 0], [0, 2, 0], [0, 0, 1]])
delta = 1
k = 3
obj, bestSigma = ClusterBound.computeKClusterBound(U, delta, k)
self.assertEquals(obj, 4)
nptst.assert_array_equal(bestSigma, numpy.array([5, 2, 2]))
U = numpy.array([[5, 0, 0], [0, 2, 0], [0, 0, 1]])
delta = 2
k = 3
obj, bestSigma = ClusterBound.computeKClusterBound(U, delta, k)
# To solve this we look at sigmak(sigmak-4) + sigmak(sigmak-2) = -3
sigmak = 3.0 ** (1.0 / 2.0) / 2.0 + 3.0 / 2.0
self.assertAlmostEquals(obj, sigmak ** 2)
nptst.assert_array_almost_equal(bestSigma, numpy.array([5, sigmak, sigmak]))
