MATH AS A CRIME FIGHTING TOOL

Let’s hope they get the math right.

FIGHTING VIOLENT GANG CRIME WITH MATH
UCLA mathematicians working with the Los Angeles Police Department to analyze crime patterns have designed a mathematical algorithm to identify street gangs involved in unsolved violent crimes. Their research is based on patterns of known criminal activity between gangs, and represents the first scholarly study of gang violence of its kind.

By Stuart Wolpert

PhysOrg.com
October 31, 2011

The research appears today on the website of the peer-reviewed mathematical journal Inverse Problems and will be published in a future print edition.

In developing their algorithm, the mathematicians analyzed more than 1,000 gang crimes and suspected gang crimes, about half of them unsolved, that occurred over a 10-year period in an East Los Angeles police district known as Hollenbeck, a small area in which there are some 30 gangs and nearly 70 gang rivalries.

To test the algorithm, the researchers created a set of simulated data that closely mimicked the crime patterns of the Hollenbeck gang network. They then dropped some of the key information out — at times the victim, the perpetrator or both — and tested how well the algorithm could calculate the missing information.

"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," said the study's senior author, Andrea Bertozzi, a professor of mathematics and director of applied mathematics at UCLA.

About 80 percent of the time, the mathematicians could narrow it down to three gang rivalries that were most likely involved in a crime.

"Our algorithm placed the correct gang rivalry within the top three most likely rivalries 80 percent of the time, which is significantly better than chance," said Martin Short, a UCLA adjunct assistant professor of mathematics and co-author of the study. "That narrows it down quite a bit, and that is when we don't know anything about the crime victim or perpetrator."

The mathematicians also found that the correct gang was ranked No. 1 — rather than just among the top three — 50 percent of the time, compared with just 17 percent by chance.

Police can investigate further when the gangs are narrowed down.

"We can do even better," Bertozzi said. "This is the first paper that takes this new approach. We can only improve on that 80 percent by developing more sophisticated methods.

"Our algorithm exploits gang activity patterns to produce the best probability of which gang, or which three gangs, may have been responsible for the crimes," she said.

The new research is federally funded by the National Science Foundation, the U.S. Army Research Office's mathematics division, the U.S. Office of Naval Research, and the U.S. Air Force Office of Scientific Research.