Multivariate Pattern Analysis in Python

# Simple Plotting of Classifier Behavior

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`).