Conclusion
Having performed studies of the relative performance of the three selection methods implemented in our applet we can conclude the following:
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Brute force method is highly impractical because the time complexity increases as gd, where g is the granularity along each feature axis and d is the number of features. High granularity is needed if we want to obtain a near-optimal result, so the running time diverges.
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Neural networks yield good results and training is relatively quick, especially as we are using a single perceptron and not a complicated network with many neurons. Convergence is, unfortunately, not robust as the learning seems to be dependent on both the learning rate and the initial network configuration (the weights and the threshold are initiated with random values). Also, there is a problem of falling into a local minimum corresponding to sub-optimal performance. As a consequence, a classifier of poor performance can be obtained even after long training.
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The classified based on a genetic algorithm offers a compromise. Speed of convergence of a neural network (there is, at least in our configuration, a larger overhead associated with the colony propagation than with perceptron training) is sacrificed, but the chance of being trapped in a local minimum is greatly reduced. One could imagine merging the two methods by first performing a coarse search of the global minimum by a genetic algorithm and then refining the solution by a neural network approach.