def calculateError(partition):
"""
Calculate Frobenius Norm of difference between tensor slices and decomposed tensor.
"""
ret = []
rows = list(partition)
normX = 0.0
error = 0.0
for row in rows:
Xi = row[1]
Ci = row[2]
normX = normX + np.square(norm(Xi, 2))
error = error + np.square(norm(Xi - kruskal_to_tensor([Ci, A, B]), 2))
'''
(Ki,I,J) = Xi.shape
for i in range(0,I):
for j in range(0,J):
for k in range(0,Ki):
sum = 0.0
for r in range(0,R):
sum = sum + A.item(i,r) * B.item(j,r) * Ci.item(k,r)
x = Xi.item((k,i,j))
error = error + np.square(sum) - (2.0*sum*x)
normX = normX + np.square(x)
'''
ret.append(['error',error])
ret.append(['normX',normX])
return ret
def createTensorSlice(partition):
ret = []
rows = list(partition)
rowCount = len(rows)
stepSize = rowCount
for row in rows:
if c > 0:
Ci = createCollinearMatrix(Ki, R, c)
else:
Ci = np.random.rand(Ki, R)
#Xi = outerProduct (A, B, Ci)
Xi = kruskal_to_tensor([Ci, A, B])
N1 = np.random.randn(Ki, I, J)
N2 = np.random.randn(Ki, I, J)
normXi = norm(Xi, 2)
normN1 = norm(N1, 2)
normN2 = norm(N2, 2)
filename = 'X-' + str(row * Ki)
for l1 in l1Range:
for l2 in l2Range:
add = '-C' + str(c) + '-L1_' + str(l1) + '-L2_' + str(
l2) + '-' + str(globalN) + '/'
newOutputDir = outputDir + add
newHDFSDir = hdfsDir + add
if l1 > 0:
Xi1 = Xi + math.pow(
((100 / l1) - 1), -0.5) * (normXi / normN1) * N1
else:
Xi1 = Xi
if l2 > 0:
N2Xi1 = N2 * Xi1
Xi2 = Xi1 + math.pow(
((100 / l2) - 1),
-0.5) * (norm(Xi1, 2) / norm(N2Xi1, 2)) * N2Xi1
else:
Xi2 = Xi1
np.save(newOutputDir + filename, Xi2)
subprocess.call([
'hadoop fs -moveFromLocal ' + newOutputDir + filename +
'.npy ' + newHDFSDir
],
shell=True)
# print Xi.shape
ret.append(row)
return ret
def getTensorDimensions(partition):
"""
Spark job to process each slice and return its local tensor dimensions.
"""
# print '****** get tensor dim ******'
ret = []
rows = list(partition)
for row in rows:
Xi = row[1]
a = []
a.extend(Xi.shape)
a.append(np.square(norm(Xi, 2)))
ret.append(a)
return [tensorOps.getDim (ret)]
def calculateFNorm(partition):
"""
Calculate Frobenius Norm of tensor slices.
"""
ret = []
rows = list(partition)
normX = 0.0
for row in rows:
Xi = row[1]
normX = normX + np.square(norm(Xi, 2))
'''
(Ki,I,J) = Xi.shape
for i in range(0,I):
for j in range(0,J):
for k in range(0,Ki):
normX = normX + np.square(Xi.item((k,i,j)))
'''
return ([normX])
def saveFactorMatrices(partition):
"""
Spark job to solve for and save each Ci factor matrix.
"""
ret = []
rows = list(partition)
error = 0.0
for row in rows:
label = row[0]
Xi = row[1]
Ki = Xi.shape[0]
dashIdx = label.rindex('-')
dotIdx = label.rindex('.')
labelId = int(label[dashIdx + 1:dotIdx])
# solve for Ci
Ci = np.zeros((Ki, R))
ZiTZic = tensorOps.ZTZ(A, B)
XiZic = np.dot(unfold(Xi, 0), khatri_rao([Ci, A, B], skip_matrix=0))
if regularization > 0:
ZiTZic = ZiTZic + regulParam * eye
Ci = solve(ZiTZic.T, XiZic.T).T
#print Ci
if outputDir != '':
# save Ci
filename = './Ci-' + str(labelId)
np.save(filename, Ci)
# save A & B
if labelId == 0:
filename = './A'
np.save(filename, A)
filename = './B'
np.save(filename, B)
error = error + np.square(norm(Xi - kruskal_to_tensor([Ci, A, B]), 2))
if outputDir != '':
subprocess.call(['hadoop fs -moveFromLocal ' + './*.npy ' + outputDir],
shell=True)
ret.append(['error', error])
return ret
import numpy as np from tensorly.kruskal import kruskal_to_tensor from tensorly.tenalg import norm from tensortools.cpfit import _compute_squared_recon_error_naive, _compute_squared_recon_error # make factors dims = [20, 30, 40] ndim = len(dims) rank = 5 factors = [np.random.randn(n, rank) for n in dims] # make data tensor = kruskal_to_tensor(factors) norm_tensor = norm(tensor, 2) err1 = _compute_squared_recon_error_naive(tensor, factors, norm_tensor) err2 = _compute_squared_recon_error(tensor, factors, norm_tensor) f2 = [np.random.randn(n, rank) for n in dims] err3 = _compute_squared_recon_error_naive(tensor, f2, norm_tensor) err4 = _compute_squared_recon_error(tensor, f2, norm_tensor) assert (np.abs(err1 - err2) < 1e-6) assert (np.abs(err3 - err4) < 1e-6)
def singleModeALSstep(partition):
"""
Runs a single step of Alternating Least Squares to solve for one of A (mode = 1),
B (mode = 2), or C (mode = 3) matrix.
"""
'''
if decompMode == 1:
print 'Solving for A....'
elif decompMode == 2:
print 'Solving for B....'
elif decompMode == 3:
print 'Solving for Ci...'
'''
ret = []
rows = list(partition)
ZiTZi = 0
XiZi = 0
error = 0.0
for row in rows:
label = row[0]
Xi = row[1]
Ki = Xi.shape[0]
# make sure not to skip over slice if we're calculating error on full tensor
# if (sketching > 0 or (decompMode == 3 and errorCalcSketchingRate < 1)) and not (decompMode == 3 and errorCalcSketchingRate == 1) and not (decompMode == 3 and onUpdateWeightLoop):
if ((sketching > 0 and sketchingRate < 1.0) or (decompMode == 3 and errorCalcSketchingRate < 1)) and not (decompMode == 3 and errorCalcSketchingRate == 1) and not (decompMode == 3 and onUpdateWeightLoop):
dashIdx=label.rindex('-')
dotIdx=label.rindex('.')
labelId=int(label[dashIdx+1:dotIdx])
minIndex = labelId
maxIndex = labelId + Ki - 1
# dalia - IS THIS A PROBLEM? THIS WILL SELECT ROWS OF C WHEN CALCULATING FULL ERROR, BUT NOT SURE THESE ROWS ARE USED
selectRowsC = sketchingRowsC[(sketchingRowsC >= minIndex) & (sketchingRowsC <= maxIndex)]
selectRowsC = selectRowsC - minIndex
if len(selectRowsC) == 0:
continue;
# always solve for Ci first!
Ci = np.zeros((Ki,R))
# if sketching == 1 or sketching == 3:
# if (decompMode < 3 and (sketching == 1 or sketching >= 3)) or (decompMode == 3 and 0 < errorCalcSketchingRate < 1) and not onUpdateWeightLoop:
if (decompMode < 3 and (sketching == 1 or sketching >= 3) and sketchingRate < 1.0) or (decompMode == 3 and 0 < errorCalcSketchingRate < 1) and not onUpdateWeightLoop:
ZiTZic = tensorOps.ZTZ(A[sketchingRowsA,:], B[sketchingRowsB,:])
XiZic = np.dot(unfold(Xi[:,sketchingRowsA,:][:,:,sketchingRowsB], 0), khatri_rao([Ci, A[sketchingRowsA,:], B[sketchingRowsB,:]], skip_matrix=0))
'''
if (decompMode == 3):
print 'Solving for partial C'
'''
# don't need a sketching == 2, since else is the same
else:
'''
if (decompMode == 3):
print 'Solving for full C'
'''
ZiTZic = tensorOps.ZTZ(A, B)
XiZic = np.dot(unfold(Xi, 0), khatri_rao([Ci, A, B], skip_matrix=0))
#ZiTZic = tensorOps.ZTZ(A, B)
#XiZic = np.dot(unfold(Xi, 0), khatri_rao([Ci, A, B], skip_matrix=0))
if regularization > 0:
ZiTZic = ZiTZic + regulParam * eye
# I don't have Ci yet...
#if regularization == 2:
# XiZi = XiZi + regulParam * Ci
Ci = solve(ZiTZic.T, XiZic.T).T
# print 'Xi=\n',Xi
# print 'new Ci=\n',Ci
if decompMode == 1:
# if sketching == 1 or sketching >= 3:
if (sketching == 1 or sketching >= 3) and sketchingRate < 1.0:
ZiTZi = ZiTZi + tensorOps.ZTZ(B[sketchingRowsB,:], Ci[selectRowsC,:])
XiZi = XiZi + np.dot(unfold(Xi[selectRowsC,:,:][:,:,sketchingRowsB], 1), khatri_rao([Ci[selectRowsC,:], A, B[sketchingRowsB,:]], skip_matrix=1))
elif sketching == 2:
ZiTZi = ZiTZi + tensorOps.ZTZ(B, Ci[selectRowsC,:])
XiZi = XiZi + np.dot(unfold(Xi[selectRowsC,:,:], 1), khatri_rao([Ci[selectRowsC,:], A, B], skip_matrix=1))
else:
ZiTZi = ZiTZi + tensorOps.ZTZ(B, Ci)
# XiZi = XiZi + tensorOps.unfolded_3D_matrix_multiply(decompMode, Xi, Ci, B, I, J, Ki, R)
XiZi = XiZi + np.dot(unfold(Xi, 1), khatri_rao([Ci, A, B], skip_matrix=1))
elif decompMode == 2:
# if sketching == 1 or sketching >= 3:
if (sketching == 1 or sketching >= 3) and sketchingRate < 1.0:
ZiTZi = ZiTZi + tensorOps.ZTZ(A[sketchingRowsA,:], Ci[selectRowsC,:])
XiZi = XiZi + np.dot(unfold(Xi[selectRowsC,:,:][:,sketchingRowsA,:], 2), khatri_rao([Ci[selectRowsC,:], A[sketchingRowsA,:], B], skip_matrix=2))
elif sketching == 2:
ZiTZi = ZiTZi + tensorOps.ZTZ(A, Ci[selectRowsC,:])
XiZi = XiZi + np.dot(unfold(Xi[selectRowsC,:,:], 2), khatri_rao([Ci[selectRowsC,:], A, B], skip_matrix=2))
else:
ZiTZi = ZiTZi + tensorOps.ZTZ(A, Ci)
# XiZi = XiZi + tensorOps.unfolded_3D_matrix_multiply(decompMode, Xi, Ci, A, I, J, Ki, R)
XiZi = XiZi + np.dot(unfold(Xi, 2), khatri_rao([Ci, A, B], skip_matrix=2))
elif decompMode == 3:
# if sketching == 1 or sketching == 3:
if 0 < errorCalcSketchingRate < 1 and not onUpdateWeightLoop:
error = error + np.square(norm(Xi[selectRowsC,:,:][:,sketchingRowsA,:][:,:,sketchingRowsB] - kruskal_to_tensor([Ci[selectRowsC,:], A[sketchingRowsA,:], B[sketchingRowsB,:]]), 2))
#print 'Error calc with partial C'
elif sketching == 2:
error = error + np.square(norm(Xi[selectRowsC,:,:] - kruskal_to_tensor([Ci[selectRowsC,:], A, B]), 2))
else:
#print 'Error calc with full C'
error = error + np.square(norm(Xi - kruskal_to_tensor([Ci, A, B]), 2))
#print 'local error =',np.square(norm(Xi - kruskal_to_tensor([Ci, A, B]), 2))
else:
print 'Unknown decomposition mode. Catastrophic error. Failing now...'
if (len(rows) > 0) and (decompMode < 3):
ret.append(['ZTZ',ZiTZi])
ret.append(['XZ',XiZi])
elif (decompMode == 3):
ret.append(['error',error])
# print 'cumulative error =',error
del ZiTZi, XiZi
return ret
def HOOI(tensor, r1, r2, num_iter=500, error_print=True, tol=10e-5):
"""
U: [r1, S, 1, 1]
Core:[r2,r1, kernel_w, kernel_h]
V: [T, r2, 1, 1]
"""
w_out_channel, w_in_channel, kernel_w, kernel_h = [i for i in tensor.shape]
# compute sparse ratio of W
sparse_ratio = (tensor < 0.005).astype(np.float32).mean()
print 'sparse ratio is ', sparse_ratio
print tensor.shape, tensor.min(), tensor.max()
for i in np.arange(-0.1, 0.282, 0.03):
boolvalue = (tensor > i) & (tensor < (i + 0.03))
ratio = boolvalue.astype(np.float32).mean()
print ratio
# tucker-2 decomposition
ranks = [r2, r1]
### tucker step1: HOSVD init
factors = []
for mode in range(2):
eigenvecs, _, _ = partial_svd(unfold(tensor, mode),
n_eigenvecs=ranks[mode])
factors.append(eigenvecs)
factors.append(np.eye(kernel_w))
factors.append(np.eye(kernel_h))
### HOOI decomposition
rec_errors = []
norm_tensor = norm(tensor, 2)
for iteration in range(num_iter):
for mode in range(2):
core_approximation = tucker_to_tensor(tensor,
factors,
skip_factor=mode,
transpose_factors=True)
eigenvecs, _, _ = partial_svd(unfold(core_approximation, mode),
n_eigenvecs=ranks[mode])
factors[mode] = eigenvecs
core = tucker_to_tensor(tensor, factors, transpose_factors=True)
reconstruct_tensor = tucker_to_tensor(
core, factors, transpose_factors=False) # reconstruct tensor
rec_error1 = norm(tensor - reconstruct_tensor, 2) / norm_tensor
rec_errors.append(rec_error1)
if iteration > 1:
if error_print:
print('reconsturction error={}, norm_tensor={}, variation={}.'.
format(rec_errors[-1], rec_error1,
rec_errors[-2] - rec_errors[-1]))
if tol and abs(rec_errors[-2] - rec_errors[-1]) < tol:
if error_print:
print('converged in {} iterations.'.format(iteration))
break
#print tensor.shape,core.shape,factors[0].shape,factors[1].shape
Core = core
U = factors[1].transpose((1, 0)).reshape((r1, w_in_channel, 1, 1))
V = factors[0].reshape((w_out_channel, r2, 1, 1))
#print Core.shape,U.shape,V.shape
return Core, V, U
def singleModeALSstep(partition):
"""
Runs a single step of Alternating Least Squares to solve for one of A (mode = 1),
B (mode = 2), or C (mode = 3) matrix.
"""
'''
if decompMode == 1:
print 'Solving for A....'
elif decompMode == 2:
print 'Solving for B....'
elif decompMode == 3:
print 'Solving for Ci...'
'''
ret = []
rows = list(partition)
ZiTZi = 0
XiZi = 0
error = 0.0
for row in rows:
label = row[0]
Xi = row[1]
Ki = Xi.shape[0]
if sketching > 0:
dashIdx = label.rindex('-')
dotIdx = label.rindex('.')
labelId = int(label[dashIdx + 1:dotIdx])
minIndex = labelId
maxIndex = labelId + Ki - 1
selectRowsC = sketchingRowsC[(sketchingRowsC >= minIndex)
& (sketchingRowsC <= maxIndex)]
selectRowsC = selectRowsC - minIndex
if len(selectRowsC) == 0:
continue
# always solve for Ci first!
Ci = np.zeros((Ki, R))
if sketching == 1 or sketching == 3:
ZiTZic = tensorOps.ZTZ(A[sketchingRowsA, :], B[sketchingRowsB, :])
XiZic = np.dot(
unfold(Xi[:, sketchingRowsA, :][:, :, sketchingRowsB], 0),
khatri_rao([Ci, A[sketchingRowsA, :], B[sketchingRowsB, :]],
skip_matrix=0))
# don't need a sketching == 2, since else is the same
else:
ZiTZic = tensorOps.ZTZ(A, B)
XiZic = np.dot(unfold(Xi, 0), khatri_rao([Ci, A, B],
skip_matrix=0))
#ZiTZic = tensorOps.ZTZ(A, B)
#XiZic = np.dot(unfold(Xi, 0), khatri_rao([Ci, A, B], skip_matrix=0))
if regularization > 0:
ZiTZic = ZiTZic + regulParam * eye
# I don't have Ci yet...
#if regularization == 2:
# XiZi = XiZi + regulParam * Ci
Ci = solve(ZiTZic.T, XiZic.T).T
if decompMode == 1:
if sketching == 1 or sketching == 3:
ZiTZi = ZiTZi + tensorOps.ZTZ(B[sketchingRowsB, :],
Ci[selectRowsC, :])
XiZi = XiZi + np.dot(
unfold(Xi[selectRowsC, :, :][:, :, sketchingRowsB], 1),
khatri_rao([Ci[selectRowsC, :], A, B[sketchingRowsB, :]],
skip_matrix=1))
elif sketching == 2:
ZiTZi = ZiTZi + tensorOps.ZTZ(B, Ci[selectRowsC, :])
XiZi = XiZi + np.dot(
unfold(Xi[selectRowsC, :, :], 1),
khatri_rao([Ci[selectRowsC, :], A, B], skip_matrix=1))
else:
ZiTZi = ZiTZi + tensorOps.ZTZ(B, Ci)
# XiZi = XiZi + tensorOps.unfolded_3D_matrix_multiply(decompMode, Xi, Ci, B, I, J, Ki, R)
XiZi = XiZi + np.dot(unfold(Xi, 1),
khatri_rao([Ci, A, B], skip_matrix=1))
elif decompMode == 2:
if sketching == 1 or sketching == 3:
ZiTZi = ZiTZi + tensorOps.ZTZ(A[sketchingRowsA, :],
Ci[selectRowsC, :])
XiZi = XiZi + np.dot(
unfold(Xi[selectRowsC, :, :][:, sketchingRowsA, :], 2),
khatri_rao([Ci[selectRowsC, :], A[sketchingRowsA, :], B],
skip_matrix=2))
elif sketching == 2:
ZiTZi = ZiTZi + tensorOps.ZTZ(A, Ci[selectRowsC, :])
XiZi = XiZi + np.dot(
unfold(Xi[selectRowsC, :, :], 2),
khatri_rao([Ci[selectRowsC, :], A, B], skip_matrix=2))
else:
ZiTZi = ZiTZi + tensorOps.ZTZ(A, Ci)
# XiZi = XiZi + tensorOps.unfolded_3D_matrix_multiply(decompMode, Xi, Ci, A, I, J, Ki, R)
XiZi = XiZi + np.dot(unfold(Xi, 2),
khatri_rao([Ci, A, B], skip_matrix=2))
elif decompMode == 3:
if sketching == 1 or sketching == 3:
error = error + np.square(
norm(
Xi[selectRowsC, :, :][:, sketchingRowsA, :]
[:, :, sketchingRowsB] - kruskal_to_tensor([
Ci[selectRowsC, :], A[sketchingRowsA, :],
B[sketchingRowsB, :]
]), 2))
elif sketching == 2:
error = error + np.square(
norm(
Xi[selectRowsC, :, :] -
kruskal_to_tensor([Ci[selectRowsC, :], A, B]), 2))
else:
error = error + np.square(
norm(Xi - kruskal_to_tensor([Ci, A, B]), 2))
else:
print 'Unknown decomposition mode. Catastrophic error. Failing now...'
if (len(rows) > 0) and (decompMode < 3):
ret.append(['ZTZ', ZiTZi])
ret.append(['XZ', XiZi])
elif (decompMode == 3):
ret.append(['error', error])
del ZiTZi, XiZi
return ret
def calculateErrorTensorly(tensor, A, B, C):
return norm(tensor - kruskal_to_tensor([C, A, B]),
2) / calculateFNormXTensorly(tensor)
def calculateFNormXTensorly(tensor):
return norm(tensor, 2)