Rossmo's formula explained
Rossmo's formula is a geographic profiling formula to predict where a serial criminal lives. It relies upon the tendency of criminals to not commit crimes near places where they might be recognized, but also to not travel excessively long distances. The formula was developed and patented in 1996 by criminologist Kim Rossmo and integrated into a specialized crime analysis software product called Rigel.[1] The Rigel product is developed by the software company Environmental Criminology Research Inc. (ECRI), which Rossmo co-founded.[2]
Formula
Imagine a map with an overlaying grid of little squares named sectors. If this map is a raster image file on a computer, these sectors are pixels. A sector
is the square on row
i and column
j, located at coordinates
.The following function gives the probability
of the position of the serial criminal residing within a specific sector (or point)
:
[3]
where:
\phiij=
\begin{cases}
1,& if (\midXi-xn\mid+\midYj-yn\mid)>B \\
0,& else
\end{cases}
Here the summation is over past crimes located at coordinates
,
, where
is the number of past crimes. Furthermore,
is an
indicator function that returns 0 when a point
is an element of the buffer zone B (the neighborhood of a criminal residence that is swept out by a radius of B from its center). The indicator
allows the computation to switch between the two terms.If a crime occurs within the buffer zone, then
and, thus, the first term does not contribute to the overall result.This is a prerogative for defining the first term in the case when the distance between a point (or pixel) becomes equal to zero.When
, the 1st term is used to calculate
.
\midXi-xn\mid+\midYj-yn\mid
is the
Manhattan distance between a point
and the
n-th crime site
,
.
Finally,
is an appopriately selected normalization constant to ensure that
.
Explanation
The summation in the formula consists of two terms. The first term describes the idea of decreasing probability with increasing distance. The second term deals with the concept of a buffer zone. The variable
is used to put more weight on one of the two ideas. The variable
describes the radius of the buffer zone. The constant
is empirically determined.
The main idea of the formula is that the probability of crimes first increases as one moves through the buffer zone away from the hotzone, but decreases afterwards. The variable
can be chosen so that it works best on data of past crimes. The same idea goes for the variable
.
The distance is calculated with the Manhattan distance formula.
Applications
The formula has been applied to fields other than forensics.[4] Because of the buffer zone idea, the formula works well for studies concerning predatory animals such as white sharks.[5]
This formula and math behind it were used in crime detecting in the Pilot episode of the TV series Numb3rs and in the 100th episode of the same show, called "Disturbed".
Further reading
- Book: The numbers behind NUMB3RS: solving crime with mathematics. Devlin. Keith J.. Gary Lorden. Lorden. Gary. 978-0-452-28857-7. 2007. Plumer. illustrated. 1–12. NUMB3RS.
- Book: Rossmo
, Kim D.
. Geographic profiling. 978-0-8493-8129-4. 2000. CRC Press. illustrated.
Notes and References
- Web site: Rigel Analyst . . en-US . 2019-02-12 . Geographic Profiling - Crime Analysis.
- Web site: Rich . T. . Shively . M . December 2004 . A Methodology for Evaluating Geographic Profiling Software . U.S. Department of Justice . 14.
- Rossmo . Kim D. . Kim Rossmo . 1995 . Geographic profiling: target patterns of serial murderers . . 225.
- Le Comber . S. C. . Stevenson . 2012 . From Jack the Ripper to epidemiology and ecology . Trends in Ecology & Evolution . 27 . 6 . 307–308 . 10.1016/j.tree.2012.03.004 . 22494610 .
- Martin . R. A. . Rossmo . D. K. . Kim Rossmo . Hammerschlag . N. . 2009 . Hunting patterns and geographic profiling of white shark predation . dead . Journal of Zoology . 279 . 2 . 111–118 . 10.1111/j.1469-7998.2009.00586.x . https://web.archive.org/web/20100612035446/http://www.rjd.miami.edu/scientific-publications/pdf/Martin_Rossmo_Hammerschlag_2009_JZool.pdf . 2010-06-12.