import tensorly as tlTensor Factorisation
Interactive tutorial on tensor factorisation with practical implementations and visualizations
import cvxpy as cp
import numpy as np
# Ensure repeatably random problem data.
np.random.seed(0)
# Generate random data matrix A.
m = 10
n = 10
o = 5
k = 2
D = 10*np.ones((m, n, o)) + np.random.randn(m, n, o)
# Initialize Y randomly.
A_init = 10*np.ones((m, k))
B_init = 10*np.ones((n, k))
C_init = 10*np.ones((o, k))
Pred_A = np.einsum('ir, jr, kr ->ijk', A_init, B_init, C_init)# Ensure same initial random Y, rather than generate new one
# when executing this cell.
B = B_init
C = C_init
# Perform alternating minimization.
MAX_ITERS = 100
residual = np.zeros(MAX_ITERS)
for iter_num in range(0, 1+MAX_ITERS):
if iter_num % 3 == 0:
A = cp.Variable(shape=(n, k))
constraint = [A >= 0]
prediction = A@tl.tenalg.khatri_rao([C, B]).T
elif iter_num % 3 == 1:
B = cp.Variable(shape=(m, k))
constraint = [B >= 0]
prediction = B@tl.tenalg.khatri_rao([A, C]).T
elif iter_num % 3 == 2:
C = cp.Variable(shape=(o, k))
constraint = [C >= 0]
prediction = C@tl.tenalg.khatri_rao([B, A]).T
obj = cp.Minimize(cp.norm(D.reshape(prediction.shape) - prediction, 'fro')/D.size)
prob = cp.Problem(obj, constraint)
prob.solve(solver=cp.SCS, max_iters=10000)
if prob.status != cp.OPTIMAL:
raise Exception("Solver did not converge!")
print('Iteration {}, residual norm {}'.format(iter_num, prob.value))
residual[iter_num-1] = prob.value
# Convert variable to NumPy array constant for next iteration.
if iter_num % 3 == 0:
A = A.value
elif iter_num%3 == 1:
B = B.value
else:
C = C.valueIteration 0, residual norm 0.044229038768601577
Iteration 1, residual norm 0.04438975125966638
Iteration 2, residual norm 0.04485089174072711
Iteration 3, residual norm 0.0446730384004453
Iteration 4, residual norm 0.044526862069177754
Iteration 5, residual norm 0.04484264445045543
Iteration 6, residual norm 0.044478708695822676
Iteration 7, residual norm 0.04447482085818169
Iteration 8, residual norm 0.045090403949033964
Iteration 9, residual norm 0.04454108258260972
Iteration 10, residual norm 0.04409564845828368
Iteration 11, residual norm 0.04513476609369982
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Iteration 99, residual norm 0.04411809866902199
Iteration 100, residual norm 0.044273830016112556Aarray([[ 1.23599056e-01, 4.95799879e-02],
[-6.88417340e-12, 4.89807637e-02],
[ 1.97771012e-01, 5.00354889e-02],
[ 2.97660174e-11, 4.86588823e-02],
[ 1.16488475e-01, 4.82973254e-02],
[-1.07464945e-11, 4.91216434e-02],
[ 2.41321912e-11, 4.81319502e-02],
[ 1.23285226e-01, 4.79485790e-02],
[ 8.32457971e-12, 4.89433882e-02],
[ 1.25287913e-11, 4.91104662e-02]])Barray([[ 9.47630862e+00, 1.31432989e+01],
[ 2.21280935e+00, 1.29931743e+01],
[ 5.84494148e-10, 1.33764365e+01],
[ 1.08369019e+01, 1.28286679e+01],
[ 5.85242755e+00, 1.28260099e+01],
[-2.53650233e-09, 1.30457870e+01],
[ 2.49310302e+00, 1.27637902e+01],
[-9.13914054e-10, 1.27890647e+01],
[ 1.19440017e+00, 1.29894214e+01],
[-5.49265493e-10, 1.30485092e+01]])Carray([[ 1.52713520e-01, 1.58149369e+01],
[ 4.52202894e-01, 1.58153740e+01],
[ 5.73957401e-10, 1.56441552e+01],
[-1.73226998e-12, 1.54265628e+01],
[-1.68743313e-10, 1.57148110e+01]])np.einsum('ir, jr, kr ->ijk', A, B, C)array([[[10.48458589, 10.83565147, 10.19442928, 10.05263637,
10.24047173],
[10.22977218, 10.31196443, 10.07798707, 9.93781374,
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10.42211858],
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9.99533009],
[10.16739655, 10.38431148, 9.94832818, 9.80995826,
9.99325913],
[10.22925871, 10.22954142, 10.11879543, 9.97805451,
10.16449628],
[10.05520169, 10.1477645 , 9.90006825, 9.76236957,
9.94478124],
[10.02796162, 10.02823877, 9.9196721 , 9.78170076,
9.96447363],
[10.20760682, 10.25210095, 10.07507622, 9.93494338,
10.12057961],
[10.2313932 , 10.23167597, 10.12090687, 9.98013658,
10.16661726]],
[[10.18116321, 10.18144459, 10.07121931, 9.93114011,
10.11670529],
[10.06487253, 10.0651507 , 9.95618442, 9.81770523,
10.00115085],
[10.36175805, 10.36204442, 10.24986394, 10.1073 ,
10.29615676],
[ 9.93744133, 9.93771598, 9.83012932, 9.69340341,
9.87452643],
[ 9.93538237, 9.93565696, 9.82809259, 9.69139501,
9.87248051],
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10.04164808],
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9.82458851],
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9.84404291],
[10.06196547, 10.06224355, 9.95330875, 9.81486955,
9.99826219],
[10.10773648, 10.10801583, 9.99858549, 9.85951655,
10.04374343]],
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10.33455292],
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10.2165102 ],
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10.08506914],
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10.25787948],
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10.26001994]],
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10.15249244],
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