def testUncentre(self):
shape = (50, 10)
r = 5
k = 100
X, U, s, V = SparseUtils.generateSparseLowRank(shape, r, k, verbose=True)
rowInds, colInds = X.nonzero()
Y = X.copy()
inds = X.nonzero()
X, mu1 = SparseUtils.centerRows(X)
X, mu2 = SparseUtils.centerCols(X, inds=inds)
cX = X.copy()
Y2 = SparseUtils.uncenter(X, mu1, mu2)
nptst.assert_array_almost_equal(Y.todense(), Y2.todense(), 3)
#We try softImpute on a centered matrix and check if the results are the same
lmbdas = numpy.array([0.1])
softImpute = SoftImpute(lmbdas)
Z = softImpute.learnModel(cX, fullMatrices=False)
Z = softImpute.predict([Z], cX.nonzero())[0]
error1 = MCEvaluator.rootMeanSqError(cX, Z)
X = SparseUtils.uncenter(cX, mu1, mu2)
Z2 = SparseUtils.uncenter(Z, mu1, mu2)
error2 = MCEvaluator.rootMeanSqError(X, Z2)
self.assertAlmostEquals(error1, error2)
def testLearnModel2(self):
#Test the SVD updating solution in the case where we get an exact solution
lmbda = 0.0
eps = 0.1
k = 20
matrixIterator = iter(self.matrixList)
iterativeSoftImpute = IterativeSoftImpute(lmbda, k=k, eps=eps, svdAlg="rsvd")
ZList = iterativeSoftImpute.learnModel(matrixIterator)
#Check that ZList is the same as XList
for i, Z in enumerate(ZList):
U, s, V = Z
Xhat = (U*s).dot(V.T)
nptst.assert_array_almost_equal(Xhat, self.matrixList[i].todense())
#Compare solution with that of SoftImpute class
rhoList = [0.1, 0.2, 0.5, 1.0]
for rho in rhoList:
iterativeSoftImpute = IterativeSoftImpute(rho, k=k, eps=eps, svdAlg="rsvd", updateAlg="zero")
matrixIterator = iter(self.matrixList)
ZList = iterativeSoftImpute.learnModel(matrixIterator)
rhos = numpy.array([rho])
softImpute = SoftImpute(rhos, k=k, eps=eps)
Z1 = softImpute.learnModel(self.matrixList[0])
Z2 = softImpute.learnModel(self.matrixList[1])
Z3 = softImpute.learnModel(self.matrixList[2])
ZList2 = [Z1, Z2, Z3]
for j, Zhat in enumerate(ZList):
U, s, V = Zhat
Z = (U*s).dot(V.T)
nptst.assert_array_almost_equal(Z, ZList2[j].todense())
#Also test with true solution Z = S_lambda(X + Z^\bot_\omega)
Zomega = numpy.zeros(self.matrixList[j].shape)
rowInds, colInds = self.matrixList[j].nonzero()
for i in range(self.matrixList[j].nonzero()[0].shape[0]):
Zomega[rowInds[i], colInds[i]] = Z[rowInds[i], colInds[i]]
U, s, V = ExpSU.SparseUtils.svdArpack(self.matrixList[j], 1, kmax=20)
lmbda = rho*numpy.max(s)
U, s, V = ExpSU.SparseUtils.svdSoft(numpy.array(self.matrixList[j]-Zomega+Z), lmbda)
tol = 0.1
self.assertTrue(numpy.linalg.norm(Z -(U*s).dot(V.T))**2 < tol)
def testLearnModel(self):
lmbda = 0.0
eps = 0.1
k = 10
matrixIterator = iter(self.matrixList)
iterativeSoftImpute = IterativeSoftImpute(lmbda, k=k, eps=eps, svdAlg="propack")
ZList = iterativeSoftImpute.learnModel(matrixIterator)
#Check that ZList is the same as XList
for i, Z in enumerate(ZList):
U, s, V = Z
Xhat = (U*s).dot(V.T)
nptst.assert_array_almost_equal(Xhat, numpy.array(self.matrixList[i].todense()))
#Compare solution with that of SoftImpute class
lmbdaList = [0.1, 0.2, 0.5, 1.0]
for lmbda in lmbdaList:
iterativeSoftImpute = IterativeSoftImpute(lmbda, k=k, eps=eps, svdAlg="propack", updateAlg="zero")
matrixIterator = iter(self.matrixList)
ZList = iterativeSoftImpute.learnModel(matrixIterator)
lmbdas = numpy.array([lmbda])
softImpute = SoftImpute(lmbdas, k=k, eps=eps)
Z1 = softImpute.learnModel(self.matrixList[0])
Z2 = softImpute.learnModel(self.matrixList[1])
Z3 = softImpute.learnModel(self.matrixList[2])
ZList2 = [Z1, Z2, Z3]
for j, Zhat in enumerate(ZList):
U, s, V = Zhat
Z = (U*s).dot(V.T)
nptst.assert_array_almost_equal(Z, ZList2[j].todense())
#Also test with true solution Z = S_lambda(X + Z^\bot_\omega)
Zomega = numpy.zeros(self.matrixList[j].shape)
rowInds, colInds = self.matrixList[j].nonzero()
for i in range(self.matrixList[j].nonzero()[0].shape[0]):
Zomega[rowInds[i], colInds[i]] = Z[rowInds[i], colInds[i]]
U, s, V = ExpSU.SparseUtils.svdSoft(numpy.array(self.matrixList[j]-Zomega+Z), lmbda)
tol = 0.1
self.assertTrue(numpy.linalg.norm(Z -(U*s).dot(V.T))**2 < tol)
def testModelSelect(self):
lmbda = 0.1
shape = (20, 20)
r = 20
numInds = 100
noise = 0.2
X = ExpSU.SparseUtils.generateSparseLowRank(shape, r, numInds, noise)
U, s, V = numpy.linalg.svd(X.todense())
k = 15
iterativeSoftImpute = IterativeSoftImpute(lmbda, k=None, svdAlg="propack", updateAlg="zero")
iterativeSoftImpute.numProcesses = 1
rhos = numpy.linspace(0.5, 0.001, 20)
ks = numpy.array([k], numpy.int)
folds = 3
cvInds = Sampling.randCrossValidation(folds, X.nnz)
meanTestErrors, meanTrainErrors = iterativeSoftImpute.modelSelect(X, rhos, ks, cvInds)
#Now do model selection manually
(rowInds, colInds) = X.nonzero()
trainErrors = numpy.zeros((rhos.shape[0], len(cvInds)))
testErrors = numpy.zeros((rhos.shape[0], len(cvInds)))
for i, rho in enumerate(rhos):
for j, (trainInds, testInds) in enumerate(cvInds):
trainX = scipy.sparse.csc_matrix(X.shape)
testX = scipy.sparse.csc_matrix(X.shape)
for p in trainInds:
trainX[rowInds[p], colInds[p]] = X[rowInds[p], colInds[p]]
for p in testInds:
testX[rowInds[p], colInds[p]] = X[rowInds[p], colInds[p]]
softImpute = SoftImpute(numpy.array([rho]), k=ks[0])
ZList = [softImpute.learnModel(trainX, fullMatrices=False)]
predTrainX = softImpute.predict(ZList, trainX.nonzero())[0]
predX = softImpute.predict(ZList, testX.nonzero())[0]
testErrors[i, j] = MCEvaluator.rootMeanSqError(testX, predX)
trainErrors[i, j] = MCEvaluator.rootMeanSqError(trainX, predTrainX)
meanTestErrors2 = testErrors.mean(1)
meanTrainErrors2 = trainErrors.mean(1)
nptst.assert_array_almost_equal(meanTestErrors.ravel(), meanTestErrors2, 1)
def testPredict(self):
X = scipy.sparse.rand(10, 10, 0.2)
X = X.tocsc()
lmbdas = numpy.array([2.0, 1.5, 1.0, 0.5, 0.2, 0.1])
eps = 0.001
k = 9
#Check out singular values
U, s, V = sparsesvd(X.tocsc(), k)
softImpute = SoftImpute(lmbdas, eps, k)
ZList = softImpute.learnModel(X, fullMatrices=False)
inds = X.nonzero()
predXList = softImpute.predict(ZList, inds)
U, s, V = ZList[0]
for predX in predXList:
nptst.assert_array_equal(predX.nonzero()[0], inds[0])
nptst.assert_array_equal(predX.nonzero()[1], inds[1])
def testPredict(self):
X = scipy.sparse.rand(10, 10, 0.2)
X = X.tocsc()
lmbdas = numpy.array([2.0, 1.5, 1.0, 0.5, 0.2, 0.1])
eps = 0.001
k = 9
#Check out singular values
U, s, V = sparsesvd(X.tocsc(), k)
softImpute = SoftImpute(lmbdas, eps, k)
ZList = softImpute.learnModel(X, fullMatrices=False)
inds = X.nonzero()
predXList = softImpute.predict(ZList, inds)
U, s, V = ZList[0]
for predX in predXList:
nptst.assert_array_equal(predX.nonzero()[0], inds[0])
nptst.assert_array_equal(predX.nonzero()[1], inds[1])
def testLearnModel2(self):
X = scipy.sparse.rand(10, 10, 0.2)
X = X.tocsc()
lmbdas = numpy.array([10.0, 0.0])
eps = 0.01
k = 9
#Check out singular values
U, s, V = sparsesvd(X.tocsc(), k)
softImpute = SoftImpute(lmbdas, eps, k)
ZList = softImpute.learnModel2(X)
#Test that when lambda=0 get approx original matrix back
X2 = ZList[1].todense()
nptst.assert_almost_equal(X.todense(), X2)
#When lambda is greater or equal to largest singular value, get 0
U, s, V = sparsesvd(X.tocsc(), k)
lmbdas = numpy.array([numpy.max(s)])
softImpute = SoftImpute(lmbdas, eps, k)
Z = softImpute.learnModel2(X)
self.assertEquals(numpy.linalg.norm(Z.todense()), 0)
#Check solution for medium values of lambda
eps = 0.1
lmbdas = numpy.array([0.1, 0.2, 0.5, 1.0])
softImpute = SoftImpute(lmbdas, eps, k)
ZList = softImpute.learnModel2(X)
for j, Z in enumerate(ZList):
Z = Z.todense()
Zomega = numpy.zeros(X.shape)
rowInds, colInds = X.nonzero()
for i in range(X.nonzero()[0].shape[0]):
Zomega[rowInds[i], colInds[i]] = Z[rowInds[i], colInds[i]]
U, s, V = ExpSU.SparseUtils.svdSoft(numpy.array(X - Zomega + Z),
lmbdas[j])
tol = 0.1
self.assertTrue(numpy.linalg.norm(Z - (U * s).dot(V.T))**2 < tol)
def testUncentre(self):
shape = (50, 10)
r = 5
k = 100
X, U, s, V = SparseUtils.generateSparseLowRank(shape,
r,
k,
verbose=True)
rowInds, colInds = X.nonzero()
Y = X.copy()
inds = X.nonzero()
X, mu1 = SparseUtils.centerRows(X)
X, mu2 = SparseUtils.centerCols(X, inds=inds)
cX = X.copy()
Y2 = SparseUtils.uncenter(X, mu1, mu2)
nptst.assert_array_almost_equal(Y.todense(), Y2.todense(), 3)
#We try softImpute on a centered matrix and check if the results are the same
lmbdas = numpy.array([0.1])
softImpute = SoftImpute(lmbdas)
Z = softImpute.learnModel(cX, fullMatrices=False)
Z = softImpute.predict([Z], cX.nonzero())[0]
error1 = MCEvaluator.rootMeanSqError(cX, Z)
X = SparseUtils.uncenter(cX, mu1, mu2)
Z2 = SparseUtils.uncenter(Z, mu1, mu2)
error2 = MCEvaluator.rootMeanSqError(X, Z2)
self.assertAlmostEquals(error1, error2)
def testLearnModel2(self):
X = scipy.sparse.rand(10, 10, 0.2)
X = X.tocsc()
lmbdas = numpy.array([10.0, 0.0])
eps = 0.01
k = 9
#Check out singular values
U, s, V = sparsesvd(X.tocsc(), k)
softImpute = SoftImpute(lmbdas, eps, k)
ZList = softImpute.learnModel2(X)
#Test that when lambda=0 get approx original matrix back
X2 = ZList[1].todense()
nptst.assert_almost_equal(X.todense(), X2)
#When lambda is greater or equal to largest singular value, get 0
U, s, V = sparsesvd(X.tocsc(), k)
lmbdas = numpy.array([numpy.max(s)])
softImpute = SoftImpute(lmbdas, eps, k)
Z = softImpute.learnModel2(X)
self.assertEquals(numpy.linalg.norm(Z.todense()), 0)
#Check solution for medium values of lambda
eps = 0.1
lmbdas = numpy.array([0.1, 0.2, 0.5, 1.0])
softImpute = SoftImpute(lmbdas, eps, k)
ZList = softImpute.learnModel2(X)
for j, Z in enumerate(ZList):
Z = Z.todense()
Zomega = numpy.zeros(X.shape)
rowInds, colInds = X.nonzero()
for i in range(X.nonzero()[0].shape[0]):
Zomega[rowInds[i], colInds[i]] = Z[rowInds[i], colInds[i]]
U, s, V = ExpSU.SparseUtils.svdSoft(numpy.array(X-Zomega+Z), lmbdas[j])
tol = 0.1
self.assertTrue(numpy.linalg.norm(Z -(U*s).dot(V.T))**2 < tol)
def profileLearnModel(self):
lmbdas = numpy.array([0.5])
softImpute = SoftImpute(lmbdas)
ProfileUtils.profile('softImpute.learnModel(self.X, False)', globals(),
locals())
