The Numbers Behind NUMB3RS

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Authors: Keith Devlin
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specific symptoms led her to make that conclusion.
    Much of the value of neural networks comes from the fact that they can acquire the ability to discern feature-patterns that no human could uncover. To take one example, typically just one credit card transaction among every 50,000 is fraudulent. No human could monitor that amount of activity to identify the frauds.
    On occasion, however, the very opacity of neural networks—the fact that they can uncover patterns that the human would not normally recognize as such—can lead to unanticipated results. According to one oft-repeated story, some years ago the U.S. Army trained a neural network to recognize tanks despite their being painted in camouflage colors to blend in with the background. The system was trained by showing it many photographs of scenes, some with tanks in, others with no tanks. After many training cycles, the network began to display extremely accurate tank recognition capacity. finally, the day came to test the system in the field, with real tanks in real locations. And to everyone’s surprise, it performed terribly, seeming quite unable to distinguish between a scene with tanks and one without. The red-faced system developers retreated to their research laboratory and struggled to find out what had gone wrong. Eventually, someone realized what the problem was. The photos used to train the system had been taken on two separate days. The photos with tanks in them had been taken on a sunny day, the tank-free photos on a cloudy day. The neural network had certainly learned the difference between the two sets of photos, but the pattern it had discerned had nothing to do with the presence or absence of tanks; rather, the system had learned to distinguish a sunny day scene from a cloudy day scene. The moral of this tale being, of course, that you have to be careful when interpreting exactly which pattern a neural network has identified. That caution aside, however, neural networks have proved themselves extremely useful both in industry and commerce, and in law enforcement and defense.
    Various network architectures have been developed to speed up the initial training process before a neural network can be put to work, but in most cases it still takes some time to complete. The principal exceptions are the Kohonen networks (named after Dr. Tevo Kohonen, who developed the idea), also known as Self-Organizing Maps (SOMs), which are used to identify clusters, and which we mentioned in Chapter 3 in connection with clustering crimes into groups that are likely to be the work of one individual or gang.
    Kohonen networks have an architecture that incorporates a form of distance measurement, so that they essentially train themselves, without the need for any external feedback. Because they do not require feedback, there is no need for a large body of prior data; they train themselves by cycling repeatedly through the application data. Nevertheless, they function by adjusting connection weights, just like the other, more frequently used neural networks.
    One advantage of neural networks over other data-mining systems is that they are much better able to handle the inevitable problem of missing data points that comes with any large body of human-gathered records.
    CRIME DATA MINING USING NEURAL NETWORKS
    Several commercial systems have been developed to help police solve—and on occasion even stop—crimes.
    One such is the Classification System for Serial Criminal Patterns (CSSCP), developed by computer scientists Tom Muscarello and Kamal Dahbur at DePaul University in Chicago. CSSCP sifts through all the case records available to it, assigning numerical values to different aspects of each crime, such as the kind of offence, the perpetrator’s sex, height, and age, and the type of weapon or getaway vehicle used. From these figures it builds a crime description profile. A Kohonen-type neural network program then uses this to seek out crimes with similar

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