Online signature verification based on dynamic features from gene expression programming

Gene Expression Programming (GEP) is a powerful evolutionary algorithm with simple, linear and compact chromosomes, which has been applied in many fields to solve a large variety of complex problems such as logistic regression, function finding and time series prediction. Since online signature data are composed of discrete points, it is difficult to represent by functional forms, resulting in a limited amount of information used in calculating feature values. Hausdorff distance is utilized as a similarity measure to compute the maximum distance between two point sets, which reduces computational complexity compared with other distance measures. The main contributions of this work are: (1) In preprocessing stage, GEP is used to make signature curve continuous and control each parameter to obtain a fitting curve. Curve fitting is to find a suitable function that is the best fitting for a given set of data; (2) In feature extraction stage, curvature and torsion are utilized to construct eight feature sets for characterizing each user’s signatures, and then Hausdorff distance is proposed to calculate the distances between feature sets of two signatures to form an eight-dimensional feature vector; (3) In verification stage, combined with Feed-Forward BP Neural Network classifier, distance matrices consisting of feature vectors are trained and tested many times. The best performances can be provided with false rejection rate, false acceptance rate, average error rate and standard deviation. The experimental results implemented on three available online signature databases MCYT-100, SVC2004 and SUSIG indicate the effectiveness and robustness of our proposed method.