# [Scipy-svn] r3134 - trunk/Lib/sandbox/pyem/examples

scipy-svn@scip... scipy-svn@scip...
Mon Jul 2 03:07:09 CDT 2007

```Author: cdavid
Date: 2007-07-02 03:07:01 -0500 (Mon, 02 Jul 2007)
New Revision: 3134

trunk/Lib/sandbox/pyem/examples/regularized_example.py
Log:
Forgot to add the file implementing regularized example...

===================================================================
--- trunk/Lib/sandbox/pyem/examples/regularized_example.py	2007-07-02 08:06:13 UTC (rev 3133)
+++ trunk/Lib/sandbox/pyem/examples/regularized_example.py	2007-07-02 08:07:01 UTC (rev 3134)
@@ -0,0 +1,69 @@
+#! /usr/bin/env python
+# Last Change: Mon Jul 02 04:00 PM 2007 J
+
+__doc__ = """Example of using RegularizedEM with pendigits data.
+
+If you want to do discriminant analysis with pendigits, you quickly have
+problems with EM if you use directly the coordinates, because some points are
+likely to be on the border, hence the corresponding component can have a
+covariance matrix which easily becomes singular. Regularized EM avoids this
+problem by using simple regularization on the mixture. You can play with pcount
+and pval to see the effect on pdf estimation.
+
+For now, regularized EM is pretty crude, but is enough for simple cases where
+you need to avoid singular covariance matrices."""
+
+import numpy as N
+import pylab as P
+
+#from scipy.sandbox import pyem
+from gauss_mix import GM
+from gmm_em import GMM, EM, RegularizedEM
+import utils
+
+x, y = utils.get_pendigits()
+
+# Take only the first point of pendigits for pdf estimation
+dt1 = N.concatenate([x[:, :1], y[:, :1]], 1)
+dt1 = utils.scale(dt1.astype(N.float))
+
+# pcnt is the poportion of samples to use as prior count. Eg if you have 1000
+# samples, and pcn is 0.1, then the prior count would be 100, and 1100 samples
+# will be considered as overall when regularizing the parameters.
+pcnt = 0.05
+# You should try different values of pval. If pval is 0.1, then the
+# regularization will be strong. If you use something like 0.01, really sharp
+# components will appear. If the values are too small, the regularizer may not
+# work (singular covariance matrices).
+pval = 0.05
+
+# This function train a mixture model with k components, returns the trained
+# model and the BIC
+def cluster(data, k, mode = 'full'):
+    d = data.shape[1]
+    gm = GM(d, k, mode)
+    gmm = GMM(gm, 'random')
+    em = RegularizedEM(pcnt = pcnt, pval = pval)
+    em.train(data, gmm, maxiter = 20)
+    return gm, gmm.bic(data)
+
+# bc will contain a list of BIC values for each model trained
+N.seterr(all = 'warn')
+bc = []
+mode = 'full'
+
+P.figure()
+for k in range(1, 5):
+    # Train a model of k component, and plots isodensity curve
+    P.subplot(2, 2, k)
+    gm, b = cluster(dt1, k = k, mode = mode)
+    bc.append(b)
+
+    X, Y, Z, V = gm.density_on_grid(nl = 20)
+    P.contour(X, Y, Z, V)
+    P.plot(dt1[:, 0], dt1[:, 1], '.')
+    P.xlabel('x coordinate (scaled)')
+    P.ylabel('y coordinate (scaled)')
+
+print "According to the BIC, model with %d components is better" % (N.argmax(bc) + 1)
+P.show()

```