Rossmo's formula
Encyclopedia
Rossmo's formula is a geographic profiling
formula to predict where a serial criminal lives. The formula was developed by criminologist Kim Rossmo
.
is the square on row i and column j, located at coordinates (Xi,Yj).
The following function gives the probability
of the position of the serial criminal residing within a specific sector (or point) 
:
Where:
Here the summation is over past crimes located at coordinates (xn,yn).
is a characteristic 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). 
allows p to switch between the two terms. When 
, then the 1st term is nullified, allowing the 2nd term to be used to calculate the 
. When 
, the 1st term is used to calculate 
.
is the Manhattan distance between a point
and the nth crime site 
becomes undefined when the distance between a point (or pixel) is zero.
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
.
This formula and math behind it were used in crime detecting in Pilot
episode of
TV-series Numb3rs
and in the 100th episode, called Disturbed
.
Geographic profiling
Geographic profiling is a criminal investigative methodology that analyzes the locations of a connected series of crimes to determine the most probable area of offender residence. By incorporating both qualitative and quantitative methods, it assists in understanding spatial behaviour of an...
formula to predict where a serial criminal lives. The formula was developed by criminologist Kim Rossmo
Kim Rossmo
D. Kim Rossmo is a Canadian criminologist specializing in geographic profiling. He joined the Vancouver Police Department as a civilian employee in 1978 and became a sworn officer in 1980. In 1987 he received a Master's degree in criminology from Simon Fraser University and in 1995 became the first...
.
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 (Xi,Yj).The following function gives the probability
of the position of the serial criminal residing within a specific sector (or point) :Where:
Here the summation is over past crimes located at coordinates (xn,yn).
is a characteristic functionCharacteristic function
In mathematics, characteristic function can refer to any of several distinct concepts:* The most common and universal usage is as a synonym for indicator function, that is the function* In probability theory, the characteristic function of any probability distribution on the real line is given by...
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). allows p to switch between the two terms. When , then the 1st term is nullified, allowing the 2nd term to be used to calculate the . When , the 1st term is used to calculate .is the Manhattan distance between a point
and the nth crime site becomes undefined when the distance between a point (or pixel) is zero.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
Taxicab geometry
Taxicab geometry, considered by Hermann Minkowski in the 19th century, is a form of geometry in which the usual distance function or metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the absolute differences of their coordinates...
.
Applications
The formula has been applied to fields other than forensics. Because of the buffer zone idea, the formula works well for studies concerning predatory animals such as white sharks.This formula and math behind it were used in crime detecting in Pilot
Pilot (Numb3rs)
"Pilot" is the first episode of the American television show Numb3rs. Based on a real-life serial rape case, "Pilot" features two brothers, an agent with the Federal Bureau of Investigation and a mathematics professor at a Southern California university, using their individual skills to capture a...
episode of
TV-series Numb3rs
NUMB3RS
Numb3rs is an American television drama which premiered on CBS on January 23, 2005, and concluded on March 12, 2010. The series was created by Nicolas Falacci and Cheryl Heuton, and follows FBI Special Agent Don Eppes and his mathematical genius brother, Charlie Eppes , who helps Don solve crimes...
and in the 100th episode, called Disturbed
Disturbed (Numb3rs)
"Disturbed" is the 21st episode of the fifth season of the American television show Numb3rs. In the episode written by series creators/executive producers Cheryl Heuton and Nicolas Falacci, skeptical Federal Bureau of Investigation agents track an undetected serial killer while their math...
.