| Handwritten Signature Verification is one of the biometrics technologies to carry out identity authentication by using people's behavior characteristics. In order to obtain the abundant signature characteristics, the method that we generally adopt is on-line handwritten signature verification technology. Such characteristics of handwritten signature as the shape, pressure and the time can be gathered by the special handwritten inputting equipment and used for distinguishing the true and false of the signature in real time.Currently, various researches on on-line handwritten signature verification have developed their own different ways, with varying results. But because the signatures have different languages, different habits of writing, and the types and numbers of the characteristics of the acquisition are different, it is difficult to say which method is better directly from the test results. This paper presents a idea to solve: give theoretical analysis of the error of a recognition algorithm; then seek an algorithm, which adaptively changes in accordance with specific training sample under the guidance of error analysis, to achieve optimal results.The main task of this paper is divided into two parts, one of which is constructed of a widely applicable algorithm framework of its theoretical error analysis, the framework of this algorithm is to use kernel methods, wavelet transform, principal component analysis, clustering, support vector and other theoretical structure; and the other, how this algorithm based on actual data adaptive regulation is discussed. The general pattern recognition algorithm contains feature extraction, classifier design as its two parts. In this paper, methods are constructed under the concept of kernel methods to facilitate the estimation of theoretical error. And, the method of generalized algorithm provides a framework conditions, or may choose different kernel structure to adapt to different sign language or writing habits of the characteristics of expression.Wavelet transform is widely used because of its superior performance as a feature extraction tool. In this paper, the framework of the algorithm uses the wavelet transform theory to describe the characteristics of samples. Then the choice of various components after wavelet transform is made to a certain way of thinking principal component analysis. Thereby the dimension of features is reduced, and the clustering is made easier as the samples are concentrated in a sub-sample space. We use the smallest ultra-ball clustering method. After the clustering features are extracted, we use the samples to train the classifier using Support Vector Machine method. In Clustering and Support Vector Machine classifier training, you can choose or structure different kernel functions; the ultimate error rate can be easily analyzed with any kernel function.The Analysis of Theoretical ErrorError analysis of the algorithm has to judge whether each step of the algorithm is stabile, besides using support vector machines to build classification error estimation theory. It has to make sure that the final data for the training of SVM classifier are representative of samples of the real distribution in great significance.Analysis of stability exists at each step of the algorithm. The stability analysis of least super-sphere cluster and kernel PCA with different kernels has universally applicable estimates. This paper analyses the wavelet transform combining with PCA method (In this article it's called WPCA) .The stability of this method proves that the characteristics are indeed on behalf of the original samples to a large extend, and with high efficiency.As the stability of the algorithm is guaranteed, the estimate of the error rate of the whole verification algorithm can be obtained using the error estimating theory of SVM method.Construction of Adaptive Algorithm with SRMError rate of the algorithm reveals various factors that impact the rate, and it has played a guiding role to structure various adaptive algorithms. These factors include whether it is appropriate to do wavelet principal component analysis by a certain proportion of components, whether the sensitivity to outlier values in clustering is reasonable, and most critically the relationship between the kernel function and the corresponding margin of the classifier. The adjustment of the algorithm is designed to reduce the error rate sector.This paper proposes the establishment of a kernel family, from which the function class can be chosen as subsets of the family, while adjusting the algorithm. The subsets are chosen in the theory of Structure Risk Minimum, from large to small, from complex to simple. In this way, an adaptive algorithm is built and the kernel family's performance can get tested.In this paper, experiments on actual data are made. The experiments show that, the classifier in accordance with theoretical error control method can get appreciated actual error. And apparently, its theoretical error rate can be guaranteed.Summary and OutlookA theoretical framework of a kind of algorithm is established in this paper. This framework includes feature extraction, feature selection and classification design, has a reliable theoretical an adaptive algorithm which adjusts the parameters according to the theoretical error. The algorithm has obtained good results about specific data.The work in this paper is primarily broad and instructive. The estimation of theoretical error rate requires to be further refined, and the relationship between the error rate and the training samples need to be more quantitatively descript. Of course, to on-line signature verification, finding an appropriate family of kernel functions is also very important.It can be believed that the framework proposed in this paper can provide an idea of the overall awareness about recognition algorithms and their comparisons, and also gives error analysis of the theory to some existing algorithms. And the theory itself will be further developed and improved. |
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