Singhal & Wu's four regions benchmark for nonlinear classification algorithms, in Python/NumPy.

fourregions.py

#!/usr/bin/env python
"""
NumPy implementation of the classic 'four regions' benchmark.
By David Warde-Farley -- user AT cs dot toronto dot edu (user = dwf)

Redistributable under the terms of the 3-clause BSD license 
(see http://www.opensource.org/licenses/bsd-license.php for details)
"""

import numpy as np

def fourregions_labels(points):
    """
    Returns labels for points in [-1,1]^2 from the "four regions" benchmark
    classification task first described by Singhal and Wu.
    
    'points' is a Nx2 rank-2 array (or numpy.matrix)
    
    For more information see:
        S. Singhal and L. Wu, "Training multilayer perceptrons with the 
        extended Kalman algorithm". Advances in Neural Information 
        Processing Systems, Proceedings of the 1988 Conference, pp133-140.
        http://books.nips.cc/papers/files/nips01/0133.pdf
    """
    region = np.zeros(points.shape[0])
    tophalf = points[:, 1] > 0
    righthalf = points[:, 0] > 0
    dists = np.sqrt(np.sum(points**2, axis=1))
    
    # The easy ones -- the outer shelf.
    region[dists > np.sqrt(2)] = np.nan
    outer = dists > 5./6.
    region[np.logical_and(tophalf, outer)] = 3
    region[np.logical_and(np.logical_not(tophalf), outer)] = 4
    
    firstring = np.logical_and(dists > 1./6., dists <= 1./2.)
    secondring = np.logical_and(dists > 1./2., dists <= 5./6.)
    
    # Region 2 -- right inner and left outer, excluding center nut
    region[np.logical_and(firstring, righthalf)] = 2
    region[np.logical_and(secondring, np.logical_not(righthalf))] = 2
    
    # Region 1 -- left inner and right outer, including center nut
    region[np.logical_and(secondring, righthalf)] = 1
    region[np.logical_and(np.logical_not(righthalf), dists < 1./2.)] = 1
    region[np.logical_and(righthalf, dists < 1./6.)] = 1
    assert(np.all(region > 0))
    return region


def demo():
    """Run a little demo, if matplotlib is available."""
    import matplotlib.pyplot as plt
    x = np.random.rand(90000, 2) * 2 - 1
    plt.scatter(x[:, 0], x[:, 1], 10, fourregions_labels(x), cmap='gray')
    plt.axis('equal')
    plt.title('90000 samples from the four regions benchmark')
    plt.show()

if __name__ == "__main__":
    #try:
    #    demo()
    #except:
    #    pass
    demo()