UCLA's Crime Fighting Mathematicians

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A team of mathematicians at UCLA have created an algorithm that can identify with relative accuracy which Los Angeles gang is responsible for an unsolved crime. When tested against cases with a known culprit, the mathematicians could correctly list the gang rivalry involved (out of the three most likely rivalries) about 80 percent of the time. Of these options, they ranked the responsible gang first about 50 percent of the time.

To develop their technique, the mathematicians studied a combination of solved and unsolved gang crimes throughout East L.A. over ten years. Explaining the process, author Andrea Bertozzi, director of applied mathematics at UCLA, says:

If police believe a crime might have been committed by one of seven or eight rival gangs, our method would look at recent historical events in the area and compute probabilities as to which of these gangs are most likely to have committed crime.

Bertozzi believes that their algorithm could apply to all sorts of problems that involve activity on social networks:

You have events — they could be crimes or something else — that occur in a time series and a known network. There is activity between nodes, in this case a gang attacking another gang. With some of these activities, you know exactly who was involved and with others, you do not. The challenge is how to make the best educated judgment as to who was involved in the unknown activities. We believe there are a number of social networks that have this same kind of pattern.

Bertozzi is optimistic about the future of mathematicians as crime fighters. “We can do even better,” she says. “This is the first paper that takes this new approach. We can only improve on that 80 percent by developing more sophisticated methods.”

This is the UCLA math department’s second foray into crime investigations; last year, Bertozzi and her colleagues created a model to analyze crime “hot spots” in Los Angeles.