2.2.1. Preprocessing

As the variations in different signatures have different dynamic ranges, min–max normalization is implemented in their *X* and *Y* coordinates. One signature should be reprocessed as follows:

$$\text{Max}\_{i} = 2000 \times \frac{\text{x} - \min(\text{x})}{\max(\text{x}) - \min(\text{x})},\\ y\_{i} = 1000 \times \frac{\text{y} - \min(\text{y})}{\max(\text{y}) - \min(\text{y})} \tag{8}$$

where *x* and *y* are the original coordinates, and *xi* and *yi* are the normalized coordinates. The normalization scales of horizontal and vertical directions are different, and 2000 and 1000 are taken respectively to keep the original scale of the signature curve as much as possible.
