Table 2: Confusion matrix with 93.30% rec. rate and 1.39% error rate. 9 Acknowledgments The authors thanks ELSAG S.p.A., Italy, for supplying the character database and all researchers and staa of IRST that have contributed to this work. 15 Figure 5: A random subsample of size normalized characters. Second, values of free parameters are learned through a gradient-descent based algorithm. The classiier has been applied to handwritten character recognition. A database of 67; 000 real life numeric characters was used and only a size and orientation normalization was performed on each isolated character. By using small bitmap portions as input features, state of art results were obtained. Experiments have shown, rst, that the Good-Turing formula provides better estimates than simply adding a costant to all frequencies. Second, that the introduction of exponent parameters, further improves classiication. Third, that the cross-validation technique provides an eeective way for monitoring generalization. Possible enhancements of the classiier will be considered in the next future. First, the feature extraction process will be improved in order to introduce more discriminant and task-dependent features. Second, some constraint on the parameters will be analized for the aim of generalization. Third, other optimization techniques will be investigated, in order to improve convergence and generalization. Fourth, performances assessment over larger corpora will be considered, in particular preliminar work has begun with the NIST 3 1,000,000 handwritten characters corpus. As a nal remark it is worth noticing that both the hardware requirements and the computational eecency of the training algorithms make this architecture a potential competitor of ANN. 14 error rate ranging from 1.0% and 2.0% are reported in Table 1. Best achieved performances were achieved by the rst set of weights. As the 93.30% of correct classiications with 1.39% of errors, and the 92.00% of correct classiications with 1.04% of errors. The confusion table of the rst result is shown in Table 2. By comparing results in Table 1, it clearly follows that the exponent learning algorithm considerably improves the generalization capabilities of the classiier when rejection critera are introduced. As a matter of fact, by making thresholds more and more selective about 1% of diierence between recognition rates is observable. In conclusion, results are promising if compared with those achievied with ANN 11, 12] if similar input patterns (i.e. raw character bitmaps) are used. 7 Time space complexity. An account of time and space complexity of the training and …
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