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)
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)
from numpy.random import seed from scipy.sandbox.pyem import GM, GMM, EM import copy seed(2) k = 4 d = 2 mode = 'diag' nframes = 1e3 #+++++++++++++++++++++++++++++++++++++++++++ # Create an artificial GMM model, samples it #+++++++++++++++++++++++++++++++++++++++++++ w, mu, va = GM.gen_param(d, k, mode, spread = 1.0) gm = GM.fromvalues(w, mu, va) # Sample nframes frames from the model data = gm.sample(nframes) #++++++++++++++++++++++++ # Learn the model with EM #++++++++++++++++++++++++ # List of learned mixtures lgm[i] is a mixture with i+1 components lgm = [] kmax = 6 bics = N.zeros(kmax) em = EM() for i in range(kmax):
#+++++++++++++++++++++++++++++ # 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 #++++++++++++++++++++++++ # Init the model lgm = GM(d, k, mode) gmm = GMM(lgm, 'kmean') gmm.init(data) # Keep a copy for drawing later
#+++++++++++++++++++++++++++++
# 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 = 4
d = 2
mode = 'diag'
nframes = 1e3
#+++++++++++++++++++++++++++++++++++++++++++
# Create an artificial GMM model, samples it
#+++++++++++++++++++++++++++++++++++++++++++
w, mu, va = GM.gen_param(d, k, mode, spread = 1.0)
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
#+++++++++++++++++++++++++++++ # 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 #++++++++++++++++++++++++ # Init the model lgm = GM(d, k, mode) gmm = GMM(lgm, 'kmean') gmm.init(data) # Keep a copy for drawing later
#------------------------------------------------------- # 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)