Offline Handwritten Signature Verification - Literature Review <s> Ensemble of classifiers <s> Much of previous attention on decision trees focuses on the splitting criteria and optimization of tree sizes. The dilemma between overfitting and achieving maximum accuracy is seldom resolved. A method to construct a decision tree based classifier is proposed that maintains highest accuracy on training data and improves on generalization accuracy as it grows in complexity. The classifier consists of multiple trees constructed systematically by pseudorandomly selecting subsets of components of the feature vector, that is, trees constructed in randomly chosen subspaces. The subspace method is compared to single-tree classifiers and other forest construction methods by experiments on publicly available datasets, where the method's superiority is demonstrated. We also discuss independence between trees in a forest and relate that to the combined classification accuracy. <s> BIB001 </s> Offline Handwritten Signature Verification - Literature Review <s> Ensemble of classifiers <s> In this work we address two important issues of off-line signature verification. The first one regards feature extraction. We introduce a new graphometric feature set that considers the curvature of the most important segments, perceptually speaking, of the signature. The idea is to simulate the shape of the signature by using Bezier curves and then extract features from these curves. The second important aspect is the use of an ensemble of classifiers based on graphometric features to improve the reliability of the classification, hence reducing the false acceptance. The ensemble was built using a standard genetic algorithm and different fitness functions were assessed to drive the search. Two different scenarios were considered in our experiments. In the former, we assume that only genuine signatures and random forgeries are available to guide the search. In the latter, on the other hand, we assume that simple and simulated forgeries also are available during the optimization of the ensemble. The pool of base classifiers is trained using only genuine signatures and random forgeries. Thorough experiments were conduct on a database composed of 100 writers and the results compare favorably. <s> BIB002 </s> Offline Handwritten Signature Verification - Literature Review <s> Ensemble of classifiers <s> In a multiple classifier system, dynamic selection (DS) has been used successfully to choose only the best subset of classifiers to recognize the test samples. Dos Santos et al's approach (DSA) looks very promising in performing DS, since it presents a general solution for a wide range of classifiers. Aiming to improve the performance of DSA, we propose a context-based framework that exploits the internal sources of knowledge embedded in this method. Named $\mbox{DSA}^{c}$, the proposed approach takes advantage of the evidences provided by the base classifiers to define the best set of ensembles of classifiers to recognize each test samples, by means of contextual information provided by the validation set. In addition, we propose a switch mechanism to deal with tie-breaking and low-margin decisions. Experiments on two handwriting recognition problems have demonstrated that the proposed approach generally presents better results than DSA, showing the effectiveness of the proposed enhancements. In addition, we demonstrate that the proposed method can be used, without changing the parameters of the base classifiers, in an incremental learning (IL) scenario, suggesting that it is also a promising general IL approach. And the use of a filtering method shows that we can significantly reduce the complexity of $\mbox{DSA}^{c}$ in the same IL scenario and even resulting in an increase in the final performance. <s> BIB003 </s> Offline Handwritten Signature Verification - Literature Review <s> Ensemble of classifiers <s> In practice, each writer provides only a limited number of signature samples to design a signature verification (SV) system. Hybrid generative-discriminative ensembles of classifiers (EoCs) are proposed in this paper to design an off-line SV system from few samples, where the classifier selection process is performed dynamically. To design the generative stage, multiple discrete left-to-right Hidden Markov Models (HMMs) are trained using a different number of states and codebook sizes, allowing the system to learn signatures at different levels of perception. To design the discriminative stage, HMM likelihoods are measured for each training signature, and assembled into feature vectors that are used to train a diversified pool of two-class classifiers through a specialized Random Subspace Method. During verification, a new dynamic selection strategy based on the K-nearest-oracles (KNORA) algorithm and on Output Profiles selects the most accurate EoCs to classify a given input signature. This SV system is suitable for incremental learning of new signature samples. Experiments performed with real-world signature data (composed of genuine samples, and random, simple and skilled forgeries) indicate that the proposed dynamic selection strategy can significantly reduce the overall error rates, with respect to other EoCs formed using well-known dynamic and static selection strategies. Moreover, the performance of the SV system proposed in this paper is significantly greater than or comparable to that of related systems found in the literature. <s> BIB004
Instead of simply training one classifier for the task, some authors have adopted strategies to train multiple classifiers, and combine their predictions when classifying a new sample. Bertollini et al. BIB002 used a static ensemble selection with graphometric features, to reduce forgeries in a writer-independent classification. They apply a strategy of "overproduce and choose", by generating a large pool of classifiers (trained with different grid sizes), and used a genetic algorithm to select a subset of the models, building an ensemble of classifiers. They performed this optimization (ensemble selection) using two fitness functions: maximize the Area Under the Curve (AUC) and maximize the True Positive Rate, given a fixed False Positive Rate. This strategy was used to obtain state-of-the-art results on the GPDS and Brazilian datasets. Batista et al BIB004 used dynamic selection of classifiers for building a writer-dependent system. First, a bank of HMMs (M ) = λ 1 , ..., λ N is trained, using different number of observations (i.e. dividing the signature image into different number of columns), different codebook sizes, and considering two types of HMMs: one to model the genuine class (trained with genuine samples), and one to model the forgery class (trained with random forgeries). For a given sample, the posterior likelihood P (O|λ i ) is calculated for all HMMs. The set of likelihoods is considered as a feature vector, and a specialized random subspace method (based on BIB001 ) is used to train an ensemble of classifiers (each classifier in a subspace of the features). Two strategies for dynamic selection of classifiers, based on Output Profiles BIB003 , are used, to select which classifiers should be used for a given query signature. After the ensemble is selected, the output of the classifiers in the ensemble is combined using a majority vote, yielding a final classification label for the sample.