def bench1(mode='diag'):
#===========================================
# GMM of 20 comp, 20 dimension, 1e4 frames
#===========================================
d = 15
k = 30
nframes = 1e5
niter = 10
mode = 'diag'
print "============================================================="
print "(%d dim, %d components) GMM with %d iterations, for %d frames" \
% (d, k, niter, nframes)
#+++++++++++++++++++++++++++++++++++++++++++
# Create an artificial GMM model, samples it
#+++++++++++++++++++++++++++++++++++++++++++
print "Generating the mixture"
# Generate a model with k components, d dimensions
w, mu, va = GM.gen_param(d, k, mode, spread=3)
# gm = GM(d, k, mode)
# gm.set_param(w, mu, va)
gm = GM.fromvalues(w, mu, va)
# Sample nframes frames from the model
data = gm.sample(nframes)
#++++++++++++++++++++++++
# Learn the model with EM
#++++++++++++++++++++++++
# Init the model
print "Init a model for learning, with kmean for initialization"
lgm = GM(d, k, mode)
gmm = GMM(lgm, 'kmean')
gmm.init(data)
# Keep the initialized model for drawing
gm0 = copy.copy(lgm)
# The actual EM, with likelihood computation
like = N.zeros(niter)
print "computing..."
for i in range(niter):
print "iteration %d" % i
g, tgd = gmm.sufficient_statistics(data)
like[i] = N.sum(N.log(N.sum(tgd, 1)))
gmm.update_em(data, g)
#+++++++++++++++++++++++++++++++++++++++++++ # 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 #++++++++++++++++++++++++ # Init the model lgm = GM(d, k, mode) gmm = GMM(lgm, 'kmean') gmm.init(data) # Keep a copy for drawing later gm0 = copy.copy(lgm) # The actual EM, with likelihood computation. The threshold # is compared to the (linearly appromixated) derivative of the likelihood em = EM() like = em.train(data, gmm, maxiter=30, thresh=1e-8) #+++++++++++++++ # Draw the model #+++++++++++++++ import pylab as P
gm = GM.fromvalues(w, mu, va)
# Sample nframes frames from the model
data = gm.sample(nframes)
#++++++++++++++++++++++++
# Learn the model with EM
#++++++++++++++++++++++++
lgm = []
kmax = 6
bics = N.zeros(kmax)
for i in range(kmax):
# Init the model with an empty Gaussian Mixture, and create a Gaussian
# Mixture Model from it
lgm.append(GM(d, i+1, mode))
gmm = GMM(lgm[i], 'kmean')
# The actual EM, with likelihood computation. The threshold
# is compared to the (linearly appromixated) derivative of the likelihood
em = EM()
em.train(data, gmm, maxiter = 30, thresh = 1e-10)
bics[i] = gmm.bic(data)
print "Original model has %d clusters, bics says %d" % (k, N.argmax(bics)+1)
#+++++++++++++++
# Draw the model
#+++++++++++++++
import pylab as P
P.subplot(3, 2, 1)