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#! /usr/bin/env python
# Example of use of pyem toolbox. Feel free to change parameters
# such as dimension, number of components, mode of covariance.
#
# You can also try less trivial things such as adding outliers, sampling
# a mixture with full covariance and estimating it with a mixture with diagonal
# gaussians (replace the mode of the learned model lgm)
#
# Later, I hope to add functions for number of component estimation using eg BIC
import numpy as N
from numpy.random import seed
from scipy.sandbox.pyem import GM, GMM, EM
import copy
seed(1)
#+++++++++++++++++++++++++++++
# 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
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
P.subplot(2, 1, 1)
# Level is the confidence level for confidence ellipsoids: 1.0 means that
# all points will be (almost surely) inside the ellipsoid
level = 0.8
if not d == 1:
P.plot(data[:, 0], data[:, 1], '.', label = '_nolegend_')
# h keeps the handles of the plot, so that you can modify
# its parameters like label or color
h = gm.plot(level = level)
[i.set_color('g') for i in h]
h[0].set_label('true confidence ellipsoides')
# Initial confidence ellipses as found by kmean
h = gm0.plot(level = level)
[i.set_color('k') for i in h]
h[0].set_label('kmean confidence ellipsoides')
# Values found by EM
h = lgm.plot(level = level)
[i.set_color('r') for i in h]
h[0].set_label('EM confidence ellipsoides')
P.legend(loc = 0)
else:
# The 1d plotting function is quite elaborate: the confidence
# interval are represented by filled areas, the pdf of the mixture and
# the pdf of each component is drawn (optional)
h = gm.plot1d(level = level)
[i.set_color('g') for i in h['pdf']]
h['pdf'][0].set_label('true pdf')
h0 = gm0.plot1d(level = level)
[i.set_color('k') for i in h0['pdf']]
h0['pdf'][0].set_label('initial pdf')
hl = lgm.plot1d(fill = 1, level = level)
[i.set_color('r') for i in hl['pdf']]
hl['pdf'][0].set_label('pdf found by EM')
P.legend(loc = 0)
P.subplot(2, 1, 2)
P.plot(like)
P.title('log likelihood')
P.show()
# P.save('2d diag.png')
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