[Note for Numb3rs]101:Pilot

Key words: Rossmo’s formula

[from Wikipedia]

$\displaystyle p_{i,j}=k \sum_{n=1}^{\text{total crimes}}[\frac{\phi}{(|X_i-x_n|+|Y_j-y_n|)^f}+\frac{(1-\phi)B^{g-f}}{(2B-|X_i-x_n|-|Y_j-y_n|)^g}]$

where $X_i\neq x_n$ and $Y_j\neq y_n$.

and $\phi=1,\quad\text{if } (|X_i-x_n|+|Y_j-y_n|)>B$, otherwise $\phi=0$.

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 $\phi$ is used to put more weight on one of the two ideas. The variable $B$ describes the radius of the buffer zone. The constant $k$ 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 $f$ can be chosen so that it works best on data of past crimes. The same idea goes for the variable $g$.

The distance is calculated with the Manhattan distance formula.