Using line search with PARAFAC

Example on how to use tensorly.decomposition.parafac with line search to accelerate convergence.

plot cp line search
import matplotlib.pyplot as plt

from time import time
import numpy as np
import tensorly as tl
from tensorly.random import random_cp
from tensorly.decomposition import CP, parafac

tol = np.logspace(-1, -9)
err = np.empty_like(tol)
err_ls = np.empty_like(tol)
tt = np.empty_like(tol)
tt_ls = np.empty_like(tol)
tensor = random_cp((10, 10, 10), 3, random_state=1234, full=True)

# Get a high-accuracy decomposition for comparison
fac = parafac(tensor, rank=3, n_iter_max=2000000, tol=1.0e-15, linesearch=True)
err_min = tl.norm(tl.cp_to_tensor(fac) - tensor)

for ii, toll in enumerate(tol):
    # Run PARAFAC decomposition without line search and time
    start = time()
    cp = CP(rank=3, n_iter_max=2000000, tol=toll, linesearch=False)
    fac = cp.fit_transform(tensor)
    tt[ii] = time() - start
    err[ii] = tl.norm(tl.cp_to_tensor(fac) - tensor)

# Run PARAFAC decomposition with line search and time
for ii, toll in enumerate(tol):
    start = time()
    cp = CP(rank=3, n_iter_max=2000000, tol=toll, linesearch=True)
    fac_ls = cp.fit_transform(tensor)
    tt_ls[ii] = time() - start

    # Calculate the error of both decompositions
    err_ls[ii] = tl.norm(tl.cp_to_tensor(fac_ls) - tensor)

fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.loglog(tt, err - err_min, '.', label="No line search")
ax.loglog(tt_ls, err_ls - err_min, '.r', label="Line search")

Total running time of the script: ( 0 minutes 8.314 seconds)

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