def test_missingness(algname):
# Random data tensor.
shape = (15, 16, 17)
rank = 3
if algname == "mcp_als":
X = tt.randn_ktensor(shape, rank=rank, random_state=data_seed).full()
elif algname == "ncp_hals":
X = tt.rand_ktensor(shape, rank=rank, random_state=data_seed).full()
# Random missingness mask.
mask = np.random.binomial(1, .5, size=X.shape).astype(bool)
# Create second tensor with corrupted entries.
Y = X.copy()
Y[~mask] = 999.
# Algorithm fitting options.
options = dict(rank=rank,
mask=mask,
verbose=False,
tol=1e-6,
random_state=alg_seed)
# Fit decompositions for both X and Y.
resultX = getattr(tt, algname)(X, **options)
resultY = getattr(tt, algname)(Y, **options)
# Test that learning curves are identical.
assert np.allclose(resultX.obj_hist, resultY.obj_hist)
# Test that final factors are identical.
for uX, uY in zip(resultX.factors, resultY.factors):
assert np.allclose(uX, uY)
def cp_als_test():
# Create synthetic dataset.
I, J, K, R = 25, 25, 25, 3 # dimensions and rank parameters
# Create a random tensor consisting of a low-rank component and noise.
X = tensortools.randn_ktensor((I, J, K), rank=R).full()
X += np.random.randn(I, J, K) # add some random noise
# Perform CP tensor decomposition.
U = tensortools.cp_als(X, rank=R, verbose=True)
V = tensortools.cp_als(X, rank=R, verbose=True)
# Compare the low-dimensional factors from the two fits.
fig, _, _ = tensortools.plot_factors(U.factors)
tensortools.plot_factors(V.factors, fig=fig)
# Align the two fits and print a similarity score.
similarity_score = tensortools.kruskal_align(U.factors,
V.factors,
permute_U=True,
permute_V=True)
print(similarity_score)
# Plot the results to see alignment.
fig, ax, po = tensortools.plot_factors(U.factors)
tensortools.plot_factors(V.factors, fig=fig)
plt.show()
def test_align():
# Generate random KTensor.
I, J, K, R = 15, 16, 17, 4
U = tt.randn_ktensor((I, J, K), rank=R)
X = U.full() # Dense representation of U.
# Enumerate all permutations of factors and test that
# kruskal_align appropriately inverts this permutation.
for prm in itertools.permutations(range(R)):
V = U.copy()
V.permute(prm)
assert (tt.kruskal_align(U, V) - 1) < atol_float64
assert linalg.norm(X - U.full()) < atol_float64
assert linalg.norm(X - V.full()) < atol_float64
# Test that second input to kruskal_align is correctly permuted.
for prm in itertools.permutations(range(R)):
V = U.copy()
V.permute(prm)
tt.kruskal_align(U, V, permute_V=True)
for fU, fV in zip(U, V):
assert linalg.norm(fU - fV) < atol_float64
assert linalg.norm(X - U.full()) < atol_float64
assert linalg.norm(X - V.full()) < atol_float64
# Test that first input to kruskal_align is correctly permuted.
for prm in itertools.permutations(range(R)):
V = U.copy()
V.permute(prm)
tt.kruskal_align(V, U, permute_U=True)
for fU, fV in zip(U, V):
assert linalg.norm(fU - fV) < atol_float64
assert linalg.norm(X - U.full()) < atol_float64
assert linalg.norm(X - V.full()) < atol_float64
def test_objective_decreases(algname, shape, rank):
# Generate data. If algorithm is made for nonnegative tensor decomposition
# then generate nonnegative data.
if algname in ['ncp_hals, ncp_bcd']:
X = tt.rand_ktensor(shape, rank=rank, random_state=data_seed).full()
else:
X = tt.randn_ktensor(shape, rank=rank, random_state=data_seed).full()
# Fit model.
f = getattr(tt, algname)
result = f(X, rank=rank, verbose=False, tol=1e-6, random_state=alg_seed)
# Test that objective function monotonically decreases.
assert np.all(np.diff(result.obj_hist) < obj_decreased_tol)
def test_objective_decreases(algname, shape, rank):
# Generate data. If algorithm is made for nonnegative tensor decomposition
# then generate nonnegative data.
if algname in ['ncp_hals, ncp_bcd']:
X = tt.rand_ktensor(shape, rank=rank, random_state=data_seed).full()
else:
X = tt.randn_ktensor(shape, rank=rank, random_state=data_seed).full()
# Algorithm fitting options.
options = dict(rank=rank, verbose=False, tol=1e-6, random_state=alg_seed)
# Add special options for particular algorithms.
if algname == 'mcp_als':
options['mask'] = np.ones_like(X).astype(bool)
# Fit model.
result = getattr(tt, algname)(X, **options)
# Test that objective function monotonically decreases.
assert np.all(np.diff(result.obj_hist) < obj_decreased_tol)
def test_nonneg(algname, neg_modes):
# Random data tensor.
shape = (15, 16, 17)
rank = 3
X = tt.randn_ktensor(shape, rank=rank, random_state=data_seed).full()
# Algorithm fitting options.
options = dict(rank=rank,
negative_modes=neg_modes,
verbose=False,
tol=1e-6,
random_state=alg_seed)
# Fit decomposition.
result = getattr(tt, algname)(X, **options)
for mode, factor in enumerate(result.factors):
if mode in neg_modes:
assert factor.min() < 0 # this should be true for most datasets
else:
assert factor.min() >= 0
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Jan 21 13:07:43 2019 @author: abuzarmahmood """ import tensortools as tt import numpy as np import matplotlib.pyplot as plt # Make synthetic dataset. I, J, K, R = 25, 25, 25, 4 # dimensions and rank X = tt.randn_ktensor((I, J, K), rank=R).full() X += np.random.randn(I, J, K) # add noise # Fit CP tensor decomposition (two times). U = tt.cp_als(X, rank=R, verbose=True) V = tt.cp_als(X, rank=R, verbose=True) # Compare the low-dimensional factors from the two fits. fig, _, _ = tt.plot_factors(U.factors) tt.plot_factors(V.factors, fig=fig) # Align the two fits and print a similarity score. sim = tt.kruskal_align(U.factors, V.factors, permute_U=True, permute_V=True) print(sim) # Plot the results again to see alignment. fig, ax, po = tt.plot_factors(U.factors)
