def distance2(self, graph1, graph2, permutation):
"""
Compute a graph distance metric between two graphs give a permutation
vector. This is given by F(P) = (1-alpha)/(||W1||^2_F + ||W2||^2_F)
(||W1 - P W2 P.T||^2_F) - alpha 1/(||V1||_F^2 + ||V2||_F^2) ||V1 - P.T V2||^2_F
and is bounded between 0 and 1.
:param graph1: A graph object
:param graph2: The second graph object to match
:param permutation: An array of permutation indices matching the first to second graph
:type permutation: `numpy.ndarray`
"""
if self.useWeightM:
W1 = graph1.getWeightMatrix()
W2 = graph2.getWeightMatrix()
else:
W1 = graph1.adjacencyMatrix()
W2 = graph2.adjacencyMatrix()
if W1.shape[0] < W2.shape[0]:
W1 = Util.extendArray(W1, W2.shape)
elif W2.shape[0] < W1.shape[0]:
W2 = Util.extendArray(W2, W1.shape)
n = W1.shape[0]
P = numpy.zeros((n, n))
P[(numpy.arange(n), permutation)] = 1
dist1 = numpy.linalg.norm(W1 - P.dot(W2).dot(P.T))**2
#Now compute the vertex similarities distance
V1 = graph1.getVertexList().getVertices()
V2 = graph2.getVertexList().getVertices()
if V1.shape[0] < V2.shape[0]:
V1 = Util.extendArray(V1, V2.shape)
elif V2.shape[0] < V1.shape[0]:
V2 = Util.extendArray(V2, V1.shape)
dist2 = numpy.sum((V1 - P.T.dot(V2))**2)
norm1 = ((W1**2).sum() + (W2**2).sum())
norm2 = ((V1**2).sum() + (V2**2).sum())
if norm1 != 0:
dist1 = dist1 / norm1
if norm2 != 0:
dist2 = dist2 / norm2
dist = (1 - self.alpha) * dist1 + self.alpha * dist2
return dist
def distance2(self, graph1, graph2, permutation):
"""
Compute a graph distance metric between two graphs give a permutation
vector. This is given by F(P) = (1-alpha)/(||W1||^2_F + ||W2||^2_F)
(||W1 - P W2 P.T||^2_F) - alpha 1/(||V1||_F^2 + ||V2||_F^2) ||V1 - P.T V2||^2_F
and is bounded between 0 and 1.
:param graph1: A graph object
:param graph2: The second graph object to match
:param permutation: An array of permutation indices matching the first to second graph
:type permutation: `numpy.ndarray`
"""
if self.useWeightM:
W1 = graph1.getWeightMatrix()
W2 = graph2.getWeightMatrix()
else:
W1 = graph1.adjacencyMatrix()
W2 = graph2.adjacencyMatrix()
if W1.shape[0] < W2.shape[0]:
W1 = Util.extendArray(W1, W2.shape)
elif W2.shape[0] < W1.shape[0]:
W2 = Util.extendArray(W2, W1.shape)
n = W1.shape[0]
P = numpy.zeros((n, n))
P[(numpy.arange(n), permutation)] = 1
dist1 = numpy.linalg.norm(W1 - P.dot(W2).dot(P.T)) ** 2
# Now compute the vertex similarities distance
V1 = graph1.getVertexList().getVertices()
V2 = graph2.getVertexList().getVertices()
if V1.shape[0] < V2.shape[0]:
V1 = Util.extendArray(V1, V2.shape)
elif V2.shape[0] < V1.shape[0]:
V2 = Util.extendArray(V2, V1.shape)
dist2 = numpy.sum((V1 - P.T.dot(V2)) ** 2)
norm1 = (W1 ** 2).sum() + (W2 ** 2).sum()
norm2 = (V1 ** 2).sum() + (V2 ** 2).sum()
if norm1 != 0:
dist1 = dist1 / norm1
if norm2 != 0:
dist2 = dist2 / norm2
dist = (1 - self.alpha) * dist1 + self.alpha * dist2
return dist
def testExtendArray(self):
X = numpy.random.rand(5, 5)
X2 = Util.extendArray(X, (10, 5))
nptst.assert_array_equal(X, X2[0:5, :])
nptst.assert_array_equal(0, X2[5:, :])
X2 = Util.extendArray(X, (10, 5), 1.23)
nptst.assert_array_equal(X, X2[0:5, :])
nptst.assert_array_equal(1.23, X2[5:, :])
#Now try extending using an array
X2 = Util.extendArray(X, (10, 5), numpy.array([1, 2, 3, 4, 5]))
nptst.assert_array_equal(X, X2[0:5, :])
for i in range(5, 10):
nptst.assert_array_equal(numpy.array([1, 2, 3, 4, 5]), X2[i, :])
def testExtendArray(self):
X = numpy.random.rand(5, 5)
X2 = Util.extendArray(X, (10, 5))
nptst.assert_array_equal(X, X2[0:5, :])
nptst.assert_array_equal(0, X2[5:, :])
X2 = Util.extendArray(X, (10, 5), 1.23)
nptst.assert_array_equal(X, X2[0:5, :])
nptst.assert_array_equal(1.23, X2[5:, :])
#Now try extending using an array
X2 = Util.extendArray(X, (10, 5), numpy.array([1, 2, 3, 4, 5]))
nptst.assert_array_equal(X, X2[0:5, :])
for i in range(5, 10):
nptst.assert_array_equal(numpy.array([1, 2, 3, 4, 5]), X2[i, :])
def distance(self, graph1, graph2, permutation, normalised=False, nonNeg=False, verbose=False):
"""
Compute the graph distance metric between two graphs given a permutation
vector. This is given by F(P) = (1-alpha)/(||W1||^2_F + ||W2||^2_F)(||W1 - P W2 P.T||^2_F)
- alpha 1/||C||_F tr(C.T P) in the normalised case. If we want an unnormalised
solution it is computed as (1-alpha)/(||W1 - P W2 P.T||^2_F) - alpha tr C.T P
and finally there is a standardised case in which the distance is between
0 and 1, where ||C||_F is used to normalise the vertex similarities and
we assume 0 <= C_ij <= 1.
:param graph1: A graph object
:param graph2: The second graph object to match
:param permutation: An array of permutation indices matching the first to second graph
:type permutation: `numpy.ndarray`
:param normalised: Specify whether to normalise the objective function
:type normalised: `bool`
:param nonNeg: Specify whether we want a non-negative solution.
:type nonNeg: `bool`
:param verbose: Specify whether to return graph and label distance
:type nonNeg: `bool`
"""
if graph1.size == 0 and graph2.size == 0:
if not verbose:
return 0.0
else:
return 0.0, 0.0, 0.0
elif graph1.size == 0 or graph2.size == 0:
if normalised:
if not verbose:
return 1 - self.alpha
else:
return 1 - self.alpha, 1 - self.alpha, 0.0
else:
raise ValueError("Unsupported case")
if self.useWeightM:
W1 = graph1.getWeightMatrix()
W2 = graph2.getWeightMatrix()
else:
W1 = graph1.adjacencyMatrix()
W2 = graph2.adjacencyMatrix()
if W1.shape[0] < W2.shape[0]:
W1 = Util.extendArray(W1, W2.shape, self.rho)
elif W2.shape[0] < W1.shape[0]:
W2 = Util.extendArray(W2, W1.shape, self.rho)
n = W1.shape[0]
P = numpy.zeros((n, n))
P[(numpy.arange(n), permutation)] = 1
dist1 = numpy.linalg.norm(W1 - P.dot(W2).dot(P.T)) ** 2
# Now compute the vertex similarities trace
C = self.vertexSimilarities(graph1, graph2)
minC = numpy.min(C)
maxC = numpy.max(C)
C = Util.extendArray(C, (n, n), minC + self.gamma * (maxC - minC))
dist2 = numpy.trace(C.T.dot(P))
if normalised:
norm1 = (W1 ** 2).sum() + (W2 ** 2).sum()
norm2 = numpy.linalg.norm(C)
if norm1 != 0:
dist1 = dist1 / norm1
if norm2 != 0:
dist2 = dist2 / norm2
dist = (1 - self.alpha) * dist1 - self.alpha * dist2
# If nonNeg = True then we add a term to the distance to ensure it is
# always positive. The numerator is an upper bound on tr(C.T P)
if nonNeg and normalised:
normC = norm2
logging.debug(
"Graph distance: "
+ str(dist1)
+ " label distance: "
+ str(dist2)
+ " distance offset: "
+ str(self.alpha * n / normC)
+ " graph sizes: "
+ str((graph1.size, graph2.size))
)
if normC != 0:
dist = dist + self.alpha * n / normC
else:
logging.debug(
"Graph objective: "
+ str(dist1)
+ " label objective: "
+ str(dist2)
+ " weighted objective: "
+ str(dist)
+ " graph sizes: "
+ str((graph1.size, graph2.size))
)
if verbose:
return dist, dist1, dist2
else:
return dist
def distance(self,
graph1,
graph2,
permutation,
normalised=False,
nonNeg=False,
verbose=False):
"""
Compute the graph distance metric between two graphs given a permutation
vector. This is given by F(P) = (1-alpha)/(||W1||^2_F + ||W2||^2_F)(||W1 - P W2 P.T||^2_F)
- alpha 1/||C||_F tr(C.T P) in the normalised case. If we want an unnormalised
solution it is computed as (1-alpha)/(||W1 - P W2 P.T||^2_F) - alpha tr C.T P
and finally there is a standardised case in which the distance is between
0 and 1, where ||C||_F is used to normalise the vertex similarities and
we assume 0 <= C_ij <= 1.
:param graph1: A graph object
:param graph2: The second graph object to match
:param permutation: An array of permutation indices matching the first to second graph
:type permutation: `numpy.ndarray`
:param normalised: Specify whether to normalise the objective function
:type normalised: `bool`
:param nonNeg: Specify whether we want a non-negative solution.
:type nonNeg: `bool`
:param verbose: Specify whether to return graph and label distance
:type nonNeg: `bool`
"""
if graph1.size == 0 and graph2.size == 0:
if not verbose:
return 0.0
else:
return 0.0, 0.0, 0.0
elif graph1.size == 0 or graph2.size == 0:
if normalised:
if not verbose:
return 1 - self.alpha
else:
return 1 - self.alpha, 1 - self.alpha, 0.0
else:
raise ValueError("Unsupported case")
if self.useWeightM:
W1 = graph1.getWeightMatrix()
W2 = graph2.getWeightMatrix()
else:
W1 = graph1.adjacencyMatrix()
W2 = graph2.adjacencyMatrix()
if W1.shape[0] < W2.shape[0]:
W1 = Util.extendArray(W1, W2.shape, self.rho)
elif W2.shape[0] < W1.shape[0]:
W2 = Util.extendArray(W2, W1.shape, self.rho)
n = W1.shape[0]
P = numpy.zeros((n, n))
P[(numpy.arange(n), permutation)] = 1
dist1 = numpy.linalg.norm(W1 - P.dot(W2).dot(P.T))**2
#Now compute the vertex similarities trace
C = self.vertexSimilarities(graph1, graph2)
minC = numpy.min(C)
maxC = numpy.max(C)
C = Util.extendArray(C, (n, n), minC + self.gamma * (maxC - minC))
dist2 = numpy.trace(C.T.dot(P))
if normalised:
norm1 = ((W1**2).sum() + (W2**2).sum())
norm2 = numpy.linalg.norm(C)
if norm1 != 0:
dist1 = dist1 / norm1
if norm2 != 0:
dist2 = dist2 / norm2
dist = (1 - self.alpha) * dist1 - self.alpha * dist2
#If nonNeg = True then we add a term to the distance to ensure it is
#always positive. The numerator is an upper bound on tr(C.T P)
if nonNeg and normalised:
normC = norm2
logging.debug("Graph distance: " + str(dist1) +
" label distance: " + str(dist2) +
" distance offset: " + str(self.alpha * n / normC) +
" graph sizes: " + str((graph1.size, graph2.size)))
if normC != 0:
dist = dist + self.alpha * n / normC
else:
logging.debug("Graph objective: " + str(dist1) +
" label objective: " + str(dist2) +
" weighted objective: " + str(dist) +
" graph sizes: " + str((graph1.size, graph2.size)))
if verbose:
return dist, dist1, dist2
else:
return dist
def next(self):
X = self.XIterator.next()
logging.debug("Learning on matrix with shape: " +
str(X.shape) + " and " + str(X.nnz) +
" non-zeros")
if self.iterativeSoftImpute.weighted:
#Compute row and col probabilities
up, vp = SparseUtils.nonzeroRowColsProbs(X)
nzuInds = up == 0
nzvInds = vp == 0
u = numpy.sqrt(1 / (up + numpy.array(nzuInds, numpy.int)))
v = numpy.sqrt(1 / (vp + numpy.array(nzvInds, numpy.int)))
u[nzuInds] = 0
v[nzvInds] = 0
if self.rhos != None:
self.iterativeSoftImpute.setRho(self.rhos.next())
if not scipy.sparse.isspmatrix_csc(X):
raise ValueError("X must be a csc_matrix not " +
str(type(X)))
#Figure out what lambda should be
#PROPACK has problems with convergence
Y = scipy.sparse.csc_matrix(X, dtype=numpy.float)
U, s, V = ExpSU.SparseUtils.svdArpack(Y, 1, kmax=20)
del Y
#U, s, V = SparseUtils.svdPropack(X, 1, kmax=20)
maxS = s[0]
logging.debug("Largest singular value : " + str(maxS))
(n, m) = X.shape
if self.j == 0:
self.oldU = numpy.zeros((n, 1))
self.oldS = numpy.zeros(1)
self.oldV = numpy.zeros((m, 1))
else:
oldN = self.oldU.shape[0]
oldM = self.oldV.shape[0]
if self.iterativeSoftImpute.updateAlg == "initial":
if n > oldN:
self.oldU = Util.extendArray(
self.oldU, (n, self.oldU.shape[1]))
elif n < oldN:
self.oldU = self.oldU[0:n, :]
if m > oldM:
self.oldV = Util.extendArray(
self.oldV, (m, self.oldV.shape[1]))
elif m < oldN:
self.oldV = self.oldV[0:m, :]
elif self.iterativeSoftImpute.updateAlg == "zero":
self.oldU = numpy.zeros((n, 1))
self.oldS = numpy.zeros(1)
self.oldV = numpy.zeros((m, 1))
else:
raise ValueError("Unknown SVD update algorithm: " +
self.updateAlg)
rowInds, colInds = X.nonzero()
gamma = self.iterativeSoftImpute.eps + 1
i = 0
self.iterativeSoftImpute.measures = numpy.zeros(
(self.iterativeSoftImpute.maxIterations, 4))
while gamma > self.iterativeSoftImpute.eps:
if i == self.iterativeSoftImpute.maxIterations:
logging.debug("Maximum number of iterations reached")
break
ZOmega = SparseUtilsCython.partialReconstructPQ(
(rowInds, colInds), self.oldU * self.oldS, self.oldV)
Y = X - ZOmega
#Y = Y.tocsc()
#del ZOmega
Y = csarray(Y, storagetype="row")
gc.collect()
#os.system('taskset -p 0xffffffff %d' % os.getpid())
if self.iterativeSoftImpute.svdAlg == "propack":
L = LinOperatorUtils.sparseLowRankOp(Y,
self.oldU,
self.oldS,
self.oldV,
parallel=False)
newU, newS, newV = SparseUtils.svdPropack(
L,
k=self.iterativeSoftImpute.k,
kmax=self.iterativeSoftImpute.kmax)
elif self.iterativeSoftImpute.svdAlg == "arpack":
L = LinOperatorUtils.sparseLowRankOp(Y,
self.oldU,
self.oldS,
self.oldV,
parallel=False)
newU, newS, newV = SparseUtils.svdArpack(
L,
k=self.iterativeSoftImpute.k,
kmax=self.iterativeSoftImpute.kmax)
elif self.iterativeSoftImpute.svdAlg == "svdUpdate":
newU, newS, newV = SVDUpdate.addSparseProjected(
self.oldU, self.oldS, self.oldV, Y,
self.iterativeSoftImpute.k)
elif self.iterativeSoftImpute.svdAlg == "rsvd":
L = LinOperatorUtils.sparseLowRankOp(Y,
self.oldU,
self.oldS,
self.oldV,
parallel=True)
newU, newS, newV = RandomisedSVD.svd(
L,
self.iterativeSoftImpute.k,
p=self.iterativeSoftImpute.p,
q=self.iterativeSoftImpute.q)
elif self.iterativeSoftImpute.svdAlg == "rsvdUpdate":
L = LinOperatorUtils.sparseLowRankOp(Y,
self.oldU,
self.oldS,
self.oldV,
parallel=True)
if self.j == 0:
newU, newS, newV = RandomisedSVD.svd(
L,
self.iterativeSoftImpute.k,
p=self.iterativeSoftImpute.p,
q=self.iterativeSoftImpute.q)
else:
newU, newS, newV = RandomisedSVD.svd(
L,
self.iterativeSoftImpute.k,
p=self.iterativeSoftImpute.p,
q=self.iterativeSoftImpute.qu,
omega=self.oldV)
elif self.iterativeSoftImpute.svdAlg == "rsvdUpdate2":
if self.j == 0:
L = LinOperatorUtils.sparseLowRankOp(Y,
self.oldU,
self.oldS,
self.oldV,
parallel=True)
newU, newS, newV = RandomisedSVD.svd(
L,
self.iterativeSoftImpute.k,
p=self.iterativeSoftImpute.p,
q=self.iterativeSoftImpute.q)
else:
#Need linear operator which is U s V
L = LinOperatorUtils.lowRankOp(
self.oldU, self.oldS, self.oldV)
Y = GeneralLinearOperator.asLinearOperator(
Y, parallel=True)
newU, newS, newV = RandomisedSVD.updateSvd(
L,
self.oldU,
self.oldS,
self.oldV,
Y,
self.iterativeSoftImpute.k,
p=self.iterativeSoftImpute.p)
else:
raise ValueError("Unknown SVD algorithm: " +
self.iterativeSoftImpute.svdAlg)
if self.iterativeSoftImpute.weighted and i == 0:
delta = numpy.diag((u * newU.T).dot(newU))
pi = numpy.diag((v * newV.T).dot(newV))
lmbda = (maxS / numpy.max(
delta * pi)) * self.iterativeSoftImpute.rho
lmbdav = lmbda * delta * pi
elif not self.iterativeSoftImpute.weighted:
lmbda = maxS * self.iterativeSoftImpute.rho
if i == 0:
logging.debug("lambda: " + str(lmbda))
lmbdav = lmbda
newS = newS - lmbdav
#Soft threshold
newS = numpy.clip(newS, 0, numpy.max(newS))
normOldZ = (self.oldS**2).sum()
normNewZmOldZ = (self.oldS**2).sum() + (
newS**2).sum() - 2 * numpy.trace(
(self.oldV.T.dot(newV * newS)).dot(
newU.T.dot(self.oldU * self.oldS)))
#We can get newZ == oldZ in which case we break
if normNewZmOldZ < self.tol:
gamma = 0
elif abs(normOldZ) < self.tol:
gamma = self.iterativeSoftImpute.eps + 1
else:
gamma = normNewZmOldZ / normOldZ
if self.iterativeSoftImpute.verbose:
theta1 = (
self.iterativeSoftImpute.k -
numpy.linalg.norm(self.oldU.T.dot(newU), 'fro')**
2) / self.iterativeSoftImpute.k
theta2 = (
self.iterativeSoftImpute.k -
numpy.linalg.norm(self.oldV.T.dot(newV), 'fro')**
2) / self.iterativeSoftImpute.k
thetaS = numpy.linalg.norm(
newS - self.oldS)**2 / numpy.linalg.norm(newS)**2
self.iterativeSoftImpute.measures[i, :] = numpy.array(
[gamma, theta1, theta2, thetaS])
self.oldU = newU.copy()
self.oldS = newS.copy()
self.oldV = newV.copy()
logging.debug("Iteration " + str(i) + " gamma=" +
str(gamma))
i += 1
if self.iterativeSoftImpute.postProcess:
#Add the mean vectors
previousS = newS
newU = numpy.c_[newU, numpy.array(X.mean(1)).ravel()]
newV = numpy.c_[newV, numpy.array(X.mean(0)).ravel()]
newS = self.iterativeSoftImpute.unshrink(X, newU, newV)
#Note that this increases the rank of U and V by 1
#print("Difference in s after postprocessing: " + str(numpy.linalg.norm(previousS - newS[0:-1])))
logging.debug("Difference in s after postprocessing: " +
str(numpy.linalg.norm(previousS -
newS[0:-1])))
logging.debug("Number of iterations for rho=" +
str(self.iterativeSoftImpute.rho) + ": " +
str(i))
self.j += 1
return (newU, newS, newV)
def next(self):
X = self.XIterator.next()
logging.debug("Learning on matrix with shape: " + str(X.shape) + " and " + str(X.nnz) + " non-zeros")
if self.iterativeSoftImpute.weighted:
#Compute row and col probabilities
up, vp = SparseUtils.nonzeroRowColsProbs(X)
nzuInds = up==0
nzvInds = vp==0
u = numpy.sqrt(1/(up + numpy.array(nzuInds, numpy.int)))
v = numpy.sqrt(1/(vp + numpy.array(nzvInds, numpy.int)))
u[nzuInds] = 0
v[nzvInds] = 0
if self.rhos != None:
self.iterativeSoftImpute.setRho(self.rhos.next())
if not scipy.sparse.isspmatrix_csc(X):
raise ValueError("X must be a csc_matrix not " + str(type(X)))
#Figure out what lambda should be
#PROPACK has problems with convergence
Y = scipy.sparse.csc_matrix(X, dtype=numpy.float)
U, s, V = ExpSU.SparseUtils.svdArpack(Y, 1, kmax=20)
del Y
#U, s, V = SparseUtils.svdPropack(X, 1, kmax=20)
maxS = s[0]
logging.debug("Largest singular value : " + str(maxS))
(n, m) = X.shape
if self.j == 0:
self.oldU = numpy.zeros((n, 1))
self.oldS = numpy.zeros(1)
self.oldV = numpy.zeros((m, 1))
else:
oldN = self.oldU.shape[0]
oldM = self.oldV.shape[0]
if self.iterativeSoftImpute.updateAlg == "initial":
if n > oldN:
self.oldU = Util.extendArray(self.oldU, (n, self.oldU.shape[1]))
elif n < oldN:
self.oldU = self.oldU[0:n, :]
if m > oldM:
self.oldV = Util.extendArray(self.oldV, (m, self.oldV.shape[1]))
elif m < oldN:
self.oldV = self.oldV[0:m, :]
elif self.iterativeSoftImpute.updateAlg == "zero":
self.oldU = numpy.zeros((n, 1))
self.oldS = numpy.zeros(1)
self.oldV = numpy.zeros((m, 1))
else:
raise ValueError("Unknown SVD update algorithm: " + self.updateAlg)
rowInds, colInds = X.nonzero()
gamma = self.iterativeSoftImpute.eps + 1
i = 0
self.iterativeSoftImpute.measures = numpy.zeros((self.iterativeSoftImpute.maxIterations, 4))
while gamma > self.iterativeSoftImpute.eps:
if i == self.iterativeSoftImpute.maxIterations:
logging.debug("Maximum number of iterations reached")
break
ZOmega = SparseUtilsCython.partialReconstructPQ((rowInds, colInds), self.oldU*self.oldS, self.oldV)
Y = X - ZOmega
#Y = Y.tocsc()
#del ZOmega
Y = csarray(Y, storagetype="row")
gc.collect()
#os.system('taskset -p 0xffffffff %d' % os.getpid())
if self.iterativeSoftImpute.svdAlg=="propack":
L = LinOperatorUtils.sparseLowRankOp(Y, self.oldU, self.oldS, self.oldV, parallel=False)
newU, newS, newV = SparseUtils.svdPropack(L, k=self.iterativeSoftImpute.k, kmax=self.iterativeSoftImpute.kmax)
elif self.iterativeSoftImpute.svdAlg=="arpack":
L = LinOperatorUtils.sparseLowRankOp(Y, self.oldU, self.oldS, self.oldV, parallel=False)
newU, newS, newV = SparseUtils.svdArpack(L, k=self.iterativeSoftImpute.k, kmax=self.iterativeSoftImpute.kmax)
elif self.iterativeSoftImpute.svdAlg=="svdUpdate":
newU, newS, newV = SVDUpdate.addSparseProjected(self.oldU, self.oldS, self.oldV, Y, self.iterativeSoftImpute.k)
elif self.iterativeSoftImpute.svdAlg=="rsvd":
L = LinOperatorUtils.sparseLowRankOp(Y, self.oldU, self.oldS, self.oldV, parallel=True)
newU, newS, newV = RandomisedSVD.svd(L, self.iterativeSoftImpute.k, p=self.iterativeSoftImpute.p, q=self.iterativeSoftImpute.q)
elif self.iterativeSoftImpute.svdAlg=="rsvdUpdate":
L = LinOperatorUtils.sparseLowRankOp(Y, self.oldU, self.oldS, self.oldV, parallel=True)
if self.j == 0:
newU, newS, newV = RandomisedSVD.svd(L, self.iterativeSoftImpute.k, p=self.iterativeSoftImpute.p, q=self.iterativeSoftImpute.q)
else:
newU, newS, newV = RandomisedSVD.svd(L, self.iterativeSoftImpute.k, p=self.iterativeSoftImpute.p, q=self.iterativeSoftImpute.qu, omega=self.oldV)
elif self.iterativeSoftImpute.svdAlg=="rsvdUpdate2":
if self.j == 0:
L = LinOperatorUtils.sparseLowRankOp(Y, self.oldU, self.oldS, self.oldV, parallel=True)
newU, newS, newV = RandomisedSVD.svd(L, self.iterativeSoftImpute.k, p=self.iterativeSoftImpute.p, q=self.iterativeSoftImpute.q)
else:
#Need linear operator which is U s V
L = LinOperatorUtils.lowRankOp(self.oldU, self.oldS, self.oldV)
Y = GeneralLinearOperator.asLinearOperator(Y, parallel=True)
newU, newS, newV = RandomisedSVD.updateSvd(L, self.oldU, self.oldS, self.oldV, Y, self.iterativeSoftImpute.k, p=self.iterativeSoftImpute.p)
else:
raise ValueError("Unknown SVD algorithm: " + self.iterativeSoftImpute.svdAlg)
if self.iterativeSoftImpute.weighted and i==0:
delta = numpy.diag((u*newU.T).dot(newU))
pi = numpy.diag((v*newV.T).dot(newV))
lmbda = (maxS/numpy.max(delta*pi))*self.iterativeSoftImpute.rho
lmbdav = lmbda*delta*pi
elif not self.iterativeSoftImpute.weighted:
lmbda = maxS*self.iterativeSoftImpute.rho
if i==0:
logging.debug("lambda: " + str(lmbda))
lmbdav = lmbda
newS = newS - lmbdav
#Soft threshold
newS = numpy.clip(newS, 0, numpy.max(newS))
normOldZ = (self.oldS**2).sum()
normNewZmOldZ = (self.oldS**2).sum() + (newS**2).sum() - 2*numpy.trace((self.oldV.T.dot(newV*newS)).dot(newU.T.dot(self.oldU*self.oldS)))
#We can get newZ == oldZ in which case we break
if normNewZmOldZ < self.tol:
gamma = 0
elif abs(normOldZ) < self.tol:
gamma = self.iterativeSoftImpute.eps + 1
else:
gamma = normNewZmOldZ/normOldZ
if self.iterativeSoftImpute.verbose:
theta1 = (self.iterativeSoftImpute.k - numpy.linalg.norm(self.oldU.T.dot(newU), 'fro')**2)/self.iterativeSoftImpute.k
theta2 = (self.iterativeSoftImpute.k - numpy.linalg.norm(self.oldV.T.dot(newV), 'fro')**2)/self.iterativeSoftImpute.k
thetaS = numpy.linalg.norm(newS - self.oldS)**2/numpy.linalg.norm(newS)**2
self.iterativeSoftImpute.measures[i, :] = numpy.array([gamma, theta1, theta2, thetaS])
self.oldU = newU.copy()
self.oldS = newS.copy()
self.oldV = newV.copy()
logging.debug("Iteration " + str(i) + " gamma="+str(gamma))
i += 1
if self.iterativeSoftImpute.postProcess:
#Add the mean vectors
previousS = newS
newU = numpy.c_[newU, numpy.array(X.mean(1)).ravel()]
newV = numpy.c_[newV, numpy.array(X.mean(0)).ravel()]
newS = self.iterativeSoftImpute.unshrink(X, newU, newV)
#Note that this increases the rank of U and V by 1
#print("Difference in s after postprocessing: " + str(numpy.linalg.norm(previousS - newS[0:-1])))
logging.debug("Difference in s after postprocessing: " + str(numpy.linalg.norm(previousS - newS[0:-1])))
logging.debug("Number of iterations for rho="+str(self.iterativeSoftImpute.rho) + ": " + str(i))
self.j += 1
return (newU, newS, newV)
