def generate_dataset(d, k, mode, nframes):
"""Generate a dataset useful for EM anf GMM testing.
returns:
data : ndarray
data from the true model.
tgm : GM
the true model (randomly generated)
gm0 : GM
the initial model
gm : GM
the trained model
"""
# Generate a model
w, mu, va = GM.gen_param(d, k, mode, spread=2.0)
tgm = GM.fromvalues(w, mu, va)
# Generate data from the model
data = tgm.sample(nframes)
# Run EM on the model, by running the initialization separetely.
gmm = GMM(GM(d, k, mode), 'test')
gmm.init_random(data)
gm0 = copy.copy(gmm.gm)
gmm = GMM(copy.copy(gmm.gm), 'test')
em = EM()
em.train(data, gmm)
return data, tgm, gm0, gmm.gm
def _create_model(self, d, k, mode, nframes, emiter):
#+++++++++++++++++++++++++++++++++++++++++++++++++
# Generate a model with k components, d dimensions
#+++++++++++++++++++++++++++++++++++++++++++++++++
w, mu, va = GM.gen_param(d, k, mode, spread=1.5)
gm = GM.fromvalues(w, mu, va)
# Sample nframes frames from the model
data = gm.sample(nframes)
#++++++++++++++++++++++++++++++++++++++++++
# Approximate the models with classical EM
#++++++++++++++++++++++++++++++++++++++++++
# Init the model
lgm = GM(d, k, mode)
gmm = GMM(lgm, 'kmean')
gmm.init(data, niter=KM_ITER)
self.gm0 = copy.copy(gmm.gm)
# The actual EM, with likelihood computation
for i in range(emiter):
g, tgd = gmm.compute_responsabilities(data)
gmm.update_em(data, g)
self.data = data
self.gm = lgm
def test_conf_ellip(self):
"""Only test whether the call succeed. To check wether the result is
OK, you have to plot the results."""
d = 3
k = 3
w, mu, va = GM.gen_param(d, k)
gm = GM.fromvalues(w, mu, va)
gm.conf_ellipses()
def _test(self, dataset, log):
dic = load_dataset(dataset)
gm = GM.fromvalues(dic['w0'], dic['mu0'], dic['va0'])
gmm = GMM(gm, 'test')
EM().train(dic['data'], gmm, log = log)
assert_array_almost_equal(gmm.gm.w, dic['w'], DEF_DEC)
assert_array_almost_equal(gmm.gm.mu, dic['mu'], DEF_DEC)
assert_array_almost_equal(gmm.gm.va, dic['va'], DEF_DEC)
def test_2d_diag_logpdf(self):
d = 2
w = N.array([0.4, 0.6])
mu = N.array([[0., 2], [-1, -2]])
va = N.array([[1, 0.5], [0.5, 1]])
x = N.random.randn(100, 2)
gm = GM.fromvalues(w, mu, va)
y1 = N.sum(multiple_gauss_den(x, mu, va) * w, 1)
y2 = gm.pdf(x, log=True)
assert_array_almost_equal(N.log(y1), y2)
def test_1d_bogus(self):
"""Check that functions which do not make sense for 1d fail nicely."""
d = 1
k = 2
w, mu, va = GM.gen_param(d, k)
gm = GM.fromvalues(w, mu, va)
try:
gm.conf_ellipses()
raise AssertionError("This should not work !")
except ValueError, e:
print "Ok, conf_ellipses failed as expected (with msg: " + str(
e) + ")"
def _create_model_and_run_em(self, d, k, mode, nframes):
#+++++++++++++++++++++++++++++++++++++++++++++++++
# Generate a model with k components, d dimensions
#+++++++++++++++++++++++++++++++++++++++++++++++++
w, mu, va = GM.gen_param(d, k, mode, spread = 1.5)
gm = GM.fromvalues(w, mu, va)
# Sample nframes frames from the model
data = gm.sample(nframes)
#++++++++++++++++++++++++++++++++++++++++++
# Approximate the models with classical EM
#++++++++++++++++++++++++++++++++++++++++++
# Init the model
lgm = GM(d, k, mode)
gmm = GMM(lgm, 'kmean')
em = EM()
lk = em.train(data, gmm)
def test_get_va(self):
"""Test _get_va for diag and full mode."""
d = 3
k = 2
ld = 2
dim = [0, 2]
w, mu, va = GM.gen_param(d, k, 'full')
va = N.arange(d * d * k).reshape(d * k, d)
gm = GM.fromvalues(w, mu, va)
tva = N.empty(ld * ld * k)
for i in range(k * ld * ld):
tva[i] = dim[i %
ld] + (i % 4) / ld * dim[1] * d + d * d * (i /
(ld * ld))
tva = tva.reshape(ld * k, ld)
sva = gm._get_va(dim)
assert N.all(sva == tva)
def _test_common(self, d, k, mode):
dic = load_dataset('%s_%dd_%dk.mat' % (mode, d, k))
gm = GM.fromvalues(dic['w0'], dic['mu0'], dic['va0'])
gmm = GMM(gm, 'test')
a, na = gmm.compute_responsabilities(dic['data'])
la, nla = gmm.compute_log_responsabilities(dic['data'])
ta = N.log(a)
tna = N.log(na)
if not N.all(N.isfinite(ta)):
print "precision problem for %s, %dd, %dk, test need fixing" % (mode, d, k)
else:
assert_array_almost_equal(ta, la, DEF_DEC)
if not N.all(N.isfinite(tna)):
print "precision problem for %s, %dd, %dk, test need fixing" % (mode, d, k)
else:
assert_array_almost_equal(tna, nla, DEF_DEC)
#------------------------------------------------------- # Values for weights, mean and (diagonal) variances # - the weights are an array of rank 1 # - mean is expected to be rank 2 with one row for one component # - variances are also expteced to be rank 2. For diagonal, one row # is one diagonal, for full, the first d rows are the first variance, # etc... In this case, the variance matrix should be k*d rows and d # colums w = N.array([0.2, 0.45, 0.35]) mu = N.array([[4.1, 3], [1, 5], [-2, -3]]) va = N.array([[1, 1.5], [3, 4], [2, 3.5]]) #----------------------------------------- # First method: directly from parameters: # Both methods are equivalents. gm = GM.fromvalues(w, mu, va) #------------------------------------- # Second method to build a GM instance: gm = GM(d, k, mode='diag') # The set_params checks that w, mu, and va corresponds to k, d and m gm.set_param(w, mu, va) # Once set_params is called, both methods are equivalent. The 2d # method is useful when using a GM object for learning (where # the learner class will set the params), whereas the first one # is useful when there is a need to quickly sample a model # from existing values, without a need to give the hyper parameters # Create a Gaussian Mixture from the parameters, and sample # 1000 items from it (one row = one 2 dimension sample)
# Meta parameters of the model # - k: Number of components # - d: dimension of each Gaussian # - mode: Mode of covariance matrix: full or diag (string) # - nframes: number of frames (frame = one data point = one # row of d elements) k = 2 d = 2 mode = 'diag' nframes = 1e3 #+++++++++++++++++++++++++++++++++++++++++++ # Create an artificial GM model, samples it #+++++++++++++++++++++++++++++++++++++++++++ w, mu, va = GM.gen_param(d, k, mode, spread = 1.5) gm = GM.fromvalues(w, mu, va) # Sample nframes frames from the model data = gm.sample(nframes) #++++++++++++++++++++++++ # Learn the model with EM #++++++++++++++++++++++++ # Create a Model from a Gaussian mixture with kmean initialization lgm = GM(d, k, mode) gmm = GMM(lgm, 'kmean') # The actual EM, with likelihood computation. The threshold # is compared to the (linearly appromixated) derivative of the likelihood em = EM()
