A Multi-objective Optimization Approach for the Synthesis of Granular Computing-Based Classification Systems in the Graph Domain

The synthesis of a pattern recognition system usually aims at the optimization of a given performance index. However, in many real-world scenarios, there exist other desired facets to take into account. In this regard, multi-objective optimization acts as the main tool for the optimization of different (and possibly conflicting) objective functions in order to seek for potential trade-offs among them. In this paper, we propose a three-objective optimization problem for the synthesis of a granular computing-based pattern recognition system in the graph domain. The core pattern recognition engine searches for suitable information granules (i.e., recurrent and/or meaningful subgraphs from the training data) on the top of which the graph embedding procedure towards the Euclidean space is performed. In the latter, any classification system can be employed. The optimization problem aims at jointly optimizing the performance of the classifier, the number of information granules and the structural complexity of the classification model. Furthermore, we address the problem of selecting a suitable number of solutions from the resulting Pareto Fronts in order to compose an ensemble of classifiers to be tested on previously unseen data. To perform such selection, we employed a multi-criteria decision making routine by analyzing different case studies that differ on how much each objective function weights in the ranking process. Results on five open-access datasets of fully labeled graphs show that exploiting the ensemble is effective (especially when the structural complexity of the model plays a minor role in the decision making process) if compared against the baseline solution that solely aims at maximizing the performances.