Data Fusion Mapping Estimation

Tech ID: 22308 / UC Case 2011-324-0


UCLA researchers in the Department of Mathematics have developed a novel probability density estimation method that incorporates geographical information.


High resolution and hyperspectral satellite images, city and county boundary maps, census data, and other types of geographical data provide much information about a given region. It is desirable to integrate this knowledge into models defining geographically dependent data. However, common methods of density estimation, such as Kernel Density Estimation, do not incorporate geographical information. Using such methods could result in predicting events in unrealistic or unreasonable geographic locations, such as residential burglary in the ocean.


UCLA researchers have developed a method that gives more geographically accurate probability density estimates. It uses a novel set of models that restrict the support of the density estimate to the valid region and ensure realistic behavior. This approach embodies new fast computational methods for density estimation using maximum penalized likelihood estimations.


This method can be used for such applications as:

  • Mapping threat level probabilities for crime
  • Solving geographic profiling problems
  • Ascertaining geographic location using wireless technology


Compared to current methods, it can give more geographically accurate probability density estimates.

State Of Development

Researchers have finished and published the computer model simulation results on a residential burglary dataset.

Patent Status

Country Type Number Dated Case
United States Of America Issued Patent 8,938,115 01/20/2015 2011-324

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  • Bertozzi, Andrea L.

Other Information


Crime mapping, probability analysis, density functions, geographical information systems, density estimation, maximum penalized likelihood estimation, geographic profiling

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