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# Classification with Feed-Forward Neural Networks

This tutorial walks you through the process of setting up a dataset for classification, and train a network on it while visualizing the results online.

First we need to import the necessary components from PyBrain.

    from pybrain.datasets            import ClassificationDataSet
    from pybrain.utilities           import percentError
    from pybrain.tools.shortcuts     import buildNetwork
    from pybrain.supervised.trainers import BackpropTrainer
    from pybrain.structure.modules   import SoftmaxLayer

Furthermore, pylab is needed for the graphical output.

    from pylab import ion, ioff, figure, draw, contourf, clf, show, hold, plot
    from scipy import diag, arange, meshgrid, where
    from numpy.random import multivariate_normal

To have a nice dataset for visualization, we produce a set of points in 2D belonging to three different classes. You could also read in your data from a file, e.g. using pylab.load().

    means = [(-1,0),(2,4),(3,1)]
    cov = [diag([1,1]), diag([0.5,1.2]), diag([1.5,0.7])]
    alldata = ClassificationDataSet(2, 1, nb_classes=3)
    for n in xrange(400):
        for klass in range(3):
            input = multivariate_normal(means[klass],cov[klass])
            alldata.addSample(input, [klass])

Randomly split the dataset into 75% training and 25% test data sets. Of course, we could also have created two different datasets to begin with.

    tstdata, trndata = alldata.splitWithProportion( 0.25 )

For neural network classification, it is highly advisable to encode classes with one output neuron per class. Note that this operation duplicates the original targets and stores them in an (integer) field named ‘class’.

    trndata._convertToOneOfMany( )
    tstdata._convertToOneOfMany( )

Test our dataset by printing a little information about it.

    print "Number of training patterns: ", len(trndata)
    print "Input and output dimensions: ", trndata.indim, trndata.outdim
    print "First sample (input, target, class):"
    print trndata['input'][0], trndata['target'][0], trndata['class'][0]

Now build a feed-forward network with 5 hidden units. We use the shortcut `buildNetwork()` for this. The input and output layer size must match the dataset’s input and target dimension. You could add additional hidden layers by inserting more numbers giving the desired layer sizes.

The output layer uses a softmax function because we are doing classification. There are more options to explore here, e.g. try changing the hidden layer transfer function to linear instead of (the default) sigmoid.

See also

Description `buildNetwork()` for more info on options, and the Network tutorial Building Networks with Modules and Connections for info on how to build your own non-standard networks.

    fnn = buildNetwork( trndata.indim, 5, trndata.outdim, outclass=SoftmaxLayer )

Set up a trainer that basically takes the network and training dataset as input. For a list of trainers, see `trainers`. We are using a `BackpropTrainer` for this.

    trainer = BackpropTrainer( fnn, dataset=trndata, momentum=0.1, verbose=True, weightdecay=0.01)

Now generate a square grid of data points and put it into a dataset, which we can then classify to obtain a nice contour field for visualization. Therefore the target values for this data set can be ignored.

    ticks = arange(-3.,6.,0.2)
    X, Y = meshgrid(ticks, ticks)
    # need column vectors in dataset, not arrays
    griddata = ClassificationDataSet(2,1, nb_classes=3)
    for i in xrange(X.size):
        griddata.addSample([X.ravel()[i],Y.ravel()[i]], [0])
    griddata._convertToOneOfMany()  # this is still needed to make the fnn feel comfy

Start the training iterations.

    for i in range(20):

Train the network for some epochs. Usually you would set something like 5 here, but for visualization purposes we do this one epoch at a time.

    ...
        trainer.trainEpochs( 1 )

Evaluate the network on the training and test data. There are several ways to do this - check out the `pybrain.tools.validation` module, for instance. Here we let the trainer do the test.

    ...
        trnresult = percentError( trainer.testOnClassData(),
                                  trndata['class'] )
        tstresult = percentError( trainer.testOnClassData(
               dataset=tstdata ), tstdata['class'] )

        print "epoch: %4d" % trainer.totalepochs, \
              "  train error: %5.2f%%" % trnresult, \
              "  test error: %5.2f%%" % tstresult

Run our grid data through the FNN, get the most likely class and shape it into a square array again.

    ...
        out = fnn.activateOnDataset(griddata)
        out = out.argmax(axis=1)  # the highest output activation gives the class
        out = out.reshape(X.shape)

Now plot the test data and the underlying grid as a filled contour.

    ...
        figure(1)
        ioff()  # interactive graphics off
        clf()   # clear the plot
        hold(True) # overplot on
        for c in [0,1,2]:
            here, _ = where(tstdata['class']==c)
            plot(tstdata['input'][here,0],tstdata['input'][here,1],'o')
        if out.max()!=out.min():  # safety check against flat field
            contourf(X, Y, out)   # plot the contour
        ion()   # interactive graphics on
        draw()  # update the plot

Finally, keep showing the plot until user kills it.

    ioff()
    show()

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