Abstract
In "decomposition/reconstruction" strategy, we can solve a complex problem by 1) decomposing the problem into simpler sub-problems, 2) solving sub-problems with simpler systems (sub-systems) and 3) combining the results of sub-systems to solve the original problem. In a classification task we may have "label complexity" which is due to high number of possible classes, "function complexity" which means the existence of complex input-output relationship, and "input complexity" which is due to requirement of a huge feature set to represent patterns. Error Correcting Output Code (ECOC) is a technique to reduce the label complexity in which a multi-class problem will be decomposed into a set of binary sub-problems, based oil the sequence of "0"s and "1"s of the columns of a decomposition (code) matrix. Then a given pattern can be assigned to the class having minimum distance to the results of sub-problems. The lack of knowledge about the relationship between distance measurement and class score (like posterior probabilities) has caused some essential shortcomings to answering questions about "source of effectiveness", "error analysis", " code selecting ", and " alternative reconstruction methods" in previous works. Proposing a theoretical framework in this thesis to specify this relationship, our main contributions in this subject are to: 1) explain the theoretical reasons for code selection conditions 2) suggest new conditions for code generation (equidistance code)which minimise reconstruction error and address a search technique for code selection 3) provide an analysis to show the effect of different kinds of error on final performance 4) suggest a novel combining method to reduce the effect of code word selection in non-optimum codes 5) suggest novel reconstruction frameworks to combine the component outputs. Some experiments on artificial and real benchmarks demonstrate significant improvement achieved in multi-class problems when simple feed forward neural networks are arranged based on suggested framework To solve the problem of function complexity we considered AdaBoost, as a technique which can be fused with ECOC to overcome its shortcoming for binary problems. And to handle the problems of huge feature sets, we have suggested a multi-net structure with local back propagation. To demonstrate these improvements on realistic problems a face recognition application is considered. Key words: decomposition/ reconstruction, reconstruction error, error correcting output codes, bias-variance decomposition.