Feature Extraction and DTW

Feature Selection

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The raw signature data available from the tablet consists of three dimensional series data; Where x(t), y(t) is the pen position at time (t) and p(t) є {0,1,…,1024} represents the pen pressure.

For this system the following three local features and three features derived from the local features are used to obtain minimum error rate.

1. ∆x: Change of x between two successive sampling points
2. Δy: Change of y between two successive sampling points
3. Δp: Change of p between two successive sampling points
4. Δy/Δx: Ratio of Δy to Δx
5. Δp/Δx: Ratio of Δp to Δx
6. v: Change of speed between two successive sampling points

The x and y coordinate differences between two consecutive points (Δx, Δy) give the lowest error rates. Note that the Δx, Δy features are invariant with respect to translation.

Enrollment

While enrollment the user supplies a number of signatures which is used in measuring the variation in a user’s signature and it is later used for training and verification process. Firstly the supplied signatures are aligned pairwise to find the distance between each pair. Using these alignment scores, first the selection of the reference signature with the minimum average distance to all other supplied signatures and R_ID, computation of average values over the reference set, for:

* Distances of reference signatures to their nearest neighbor ((d_min ) ̅(R_ID))
* Distances of reference signatures to their farthest neighbor ((d_max ) ̅(R_ID))
* Distances of reference signatures to the template signature ((d_temp ) ̅(R_ID ))

The computed average distance values describe the user’s variation to some extent and are selected so as to be used in normalizing a signature’s min, max and template distances to its reference set. By normalizing these distances by the corresponding reference set averages, the need to calculate user-dependent thresholds is eliminated.

Dynamic Time Warping (DTW)

In both training and verification stages, the need to align the signatures to calculate their distances is present. In order to compare and calculate distance between signatures of different lengths, the Dynamic Time Warping (DTW) algorithm is used, which is a widely used algorithm for aligning vectors of different lengths.