This example runs a number of classifiers on a simple 2D dataset and plots the decision surface of each classifier.
First compose some sample data – no PyMVPA involved.
import numpy as np
# set up the labeled data
# two skewed 2-D distributions
num_dat = 200
dist = 4
# Absolute max value allowed. Just to assure proper plots
xyamax = 10
feat_pos=np.random.randn(2, num_dat)
feat_pos[0, :] *= 2.
feat_pos[1, :] *= .5
feat_pos[0, :] += dist
feat_pos = feat_pos.clip(-xyamax, xyamax)
feat_neg=np.random.randn(2, num_dat)
feat_neg[0, :] *= .5
feat_neg[1, :] *= 2.
feat_neg[0, :] -= dist
feat_neg = feat_neg.clip(-xyamax, xyamax)
# set up the testing features
npoints = 101
x1 = np.linspace(-xyamax, xyamax, npoints)
x2 = np.linspace(-xyamax, xyamax, npoints)
x,y = np.meshgrid(x1, x2);
feat_test = np.array((np.ravel(x), np.ravel(y)))
Now load PyMVPA and convert the data into a proper Dataset.
from mvpa2.suite import *
# create the pymvpa dataset from the labeled features
patternsPos = dataset_wizard(samples=feat_pos.T, targets=1)
patternsNeg = dataset_wizard(samples=feat_neg.T, targets=0)
ds_lin = vstack((patternsPos, patternsNeg))
Let’s add another dataset: XOR. This problem is not linear separable and therefore need a non-linear classifier to be solved. The dataset is provided by the PyMVPA dataset warehouse.
# 30 samples per condition, SNR 2
ds_nl = pure_multivariate_signal(30, 2)
l1 = ds_nl.sa['targets'].unique[1]
datasets = {'linear': ds_lin, 'non-linear': ds_nl}
This demo utilizes a number of classifiers. The instantiation of a classifier involves almost no runtime costs, so it is easily possible compile a long list, if necessary.
# set up classifiers to try out
clfs = {
'Ridge Regression': RidgeReg(),
'Linear SVM': LinearNuSVMC(probability=1,
enable_ca=['probabilities']),
'RBF SVM': RbfNuSVMC(probability=1,
enable_ca=['probabilities']),
'SMLR': SMLR(lm=0.01),
'Logistic Regression': PLR(criterion=0.00001),
'3-Nearest-Neighbour': kNN(k=3),
'10-Nearest-Neighbour': kNN(k=10),
'GNB': GNB(common_variance=True),
'GNB(common_variance=False)': GNB(common_variance=False),
'LDA': LDA(),
'QDA': QDA(),
}
# How many rows/columns we need
nx = int(ceil(np.sqrt(len(clfs))))
ny = int(ceil(len(clfs)/float(nx)))
Now we are ready to run the classifiers. The following loop trains and queries each classifier to finally generate a nice plot showing the decision surface of each individual classifier, both for the linear and the non-linear dataset.
for id, ds in datasets.iteritems():
# loop over classifiers and show how they do
fig = 0
# make a new figure
pl.figure(figsize=(nx*4, ny*4))
print "Processing %s problem..." % id
for c in sorted(clfs):
# tell which one we are doing
print "Running %s classifier..." % (c)
# make a new subplot for each classifier
fig += 1
pl.subplot(ny, nx, fig)
# select the clasifier
clf = clfs[c]
# enable saving of the estimates used for the prediction
clf.ca.enable('estimates')
# train with the known points
clf.train(ds)
# run the predictions on the test values
pre = clf.predict(feat_test.T)
# if ridge, use the prediction, otherwise use the values
if c == 'Ridge Regression':
# use the prediction
res = np.asarray(pre)
elif 'Nearest-Ne' in c:
# Use the dictionaries with votes
res = np.array([e[l1] for e in clf.ca.estimates]) \
/ np.sum([e.values() for e in clf.ca.estimates], axis=1)
elif c == 'Logistic Regression':
# get out the values used for the prediction
res = np.asarray(clf.ca.estimates)
elif c in ['SMLR']:
res = np.asarray(clf.ca.estimates[:, 1])
elif c in ['LDA', 'QDA'] or c.startswith('GNB'):
# Since probabilities are logprobs -- just for
# visualization of trade-off just plot relative
# "trade-off" which determines decision boundaries if an
# alternative log-odd value was chosen for a cutoff
res = np.asarray(clf.ca.estimates[:, 1]
- clf.ca.estimates[:, 0])
# Scale and position around 0.5
res = 0.5 + res/max(np.abs(res))
else:
# get the probabilities from the svm
res = np.asarray([(q[1][1] - q[1][0] + 1) / 2
for q in clf.ca.probabilities])
# reshape the results
z = np.asarray(res).reshape((npoints, npoints))
# plot the predictions
pl.pcolor(x, y, z, shading='interp')
pl.clim(0, 1)
pl.colorbar()
# plot decision surfaces at few levels to emphasize the
# topology
pl.contour(x, y, z, [0.1, 0.4, 0.5, 0.6, 0.9],
linestyles=['dotted', 'dashed', 'solid', 'dashed', 'dotted'],
linewidths=1, colors='black', hold=True)
# plot the training points
pl.plot(ds.samples[ds.targets == 1, 0],
ds.samples[ds.targets == 1, 1],
"r.")
pl.plot(ds.samples[ds.targets == 0, 0],
ds.samples[ds.targets == 0, 1],
"b.")
pl.axis('tight')
# add the title
pl.title(c)
See also
The full source code of this example is included in the PyMVPA source distribution (doc/examples/pylab_2d.py).
