Exponential
Most fuzzy matching scores are linear - the penalty for being different by 1 unit is 1, by 2 units is 2 etc.
However, some penalties can be set to be exponential, meaning the difference is squared.
In these cases, a difference of 1 will still be 1, but a difference of 2 will have a score penalty of 4, a difference of 3 will have a penalty of 9, and so on.
Usage
Exponential penalties are ideal for removing outliers from matches.
They're often used when you have two or more of a particular attribute that has the same penalty - for example, you might have four different sensors measuring the height of a cake leaving your bakery oven.
We want to search for the cake with the perfect size - let's say 25% of the way up the tin. We've captured two examples of product runs in the captures below…
| Sensor | Capture A | Capture B |
|---|---|---|
| 1 | 1 | 30 |
| 2 | 1 | 32 |
| 3 | 1 | 30 |
| 4 | 100 | 35 |
Capture A is obviously a terrible shape for a cake to be in. But mathematically, the average for Capture A is around 25%, while Capture B is almost 32%. Using linear penalties, the system would pick Capture A as a better fit than Capture B.
But using exponential penalties, Capture B is much better than Capture A.
Warnings
If you are mixing linear and exponential values, be aware of the possibility of a smaller, less significant scoring factor dominating one that is supposed to be more important.
We normally suggest giving exponential values small multipliers to reduce the chances of this happening.