A0 /= A0.sum(axis=1)[:, None]
S0 = np.random.rand(k, n)
# mixture model: amplitudes positive
# and sum up to one at every pixel
pA = partial(proxmin.operators.prox_unity_plus, axis=1)
pS = proxmin.operators.prox_plus
if problem == "nmf":
prox = [pS, pS]
elif problem == "mixmf":
prox = [pA, pS]
grad = partial(proxmin.nmf.grad_likelihood, Y=Y)
traceback = Traceback()
all_args = {"prox": prox, "max_iter": 1000, "callback": traceback, "e_rel": 1e-4}
b1 = 0.9
b2 = 0.999
pgm_args = {"accelerated": True}
adaprox_args = {"b1": b1, "b2": b2, "prox_max_iter": 100}
runs = (
(proxmin.pgm, dict(all_args, **pgm_args), "PGM"),
(proxmin.adaprox, dict(all_args, **adaprox_args, scheme="adam"), "Adam"),
(
proxmin.adaprox,
dict(all_args, **adaprox_args, scheme="padam", p=0.125),
"PAdam",
),
(proxmin.adaprox, dict(all_args, **adaprox_args, scheme="amsgrad"), "AMSGrad"),
)
np.random.seed(101)
# set up test data
trueA = np.array([generateAmplitudes(k) for i in range(b)])
trueS = np.array([generateComponent(n) for i in range(k)])
trueY = np.dot(trueA, trueS)
Y = add_noise(trueY, noise)
# if noise is variable, specify variance matrix of the same shape as Y
W = None
# initialize and run NMF
A0 = np.array([generateAmplitudes(k) for i in range(b)])
S0 = np.array([generateComponent(n) for i in range(k)])
p1 = partial(po.prox_unity_plus, axis=1)
proxs_g = [[p1], None]
tr = Traceback(2)
A, S = nmf(Y,
A0,
S0,
W=W,
prox_A=p1,
e_rel=1e-6,
e_abs=1e-6 / noise**2,
traceback=tr)
# sort components to best match inputs
A, S = match(A, S, trueS)
# show data and model
fig = plt.figure(figsize=(6, 7))
ax = fig.add_subplot(311)
ax.set_title("True Components S")
if len(sys.argv)==2:
boundary = sys.argv[1]
if boundary not in ["line", "circle"]:
raise ValueError("Expected either 'line' or 'circle' as an argument")
else:
boundary = "circle"
max_iter = 100
# step sizes and proximal operators for boundary
step_f = steps_f12()
prox_g = partial(prox_lim, boundary=boundary)
prox_gradf_ = partial(prox_gradf_lim, boundary=boundary)
# PGM without boundary
tr = Traceback()
xy = xy0.copy()
pa.pgm(xy, prox_gradf, step_f, max_iter=max_iter, relax=1, traceback=tr)
plotResults(tr, "PGM no boundary")
# PGM
tr = Traceback()
xy = xy0.copy()
pa.pgm(xy, prox_gradf_, step_f, max_iter=max_iter, traceback=tr)
plotResults(tr, "PGM", boundary=boundary)
# APGM
tr = Traceback()
xy = xy0.copy()
pa.pgm(xy, prox_gradf_, step_f, max_iter=max_iter, accelerated=True, traceback=tr)
plotResults(tr, "PGM accelerated", boundary=boundary)