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This paper presents a new algorithm to model fast and accurate granular support vector machines (GSVMs) for biomedical binary classification problems. The algorithm, named GSVM-DC, splits the original training dataset into several highly overlapping granules, from which local support vectors (LSVs) are extracted. Then cross validation heuristic are adopted to optimize the SVM parameters. Finally, GSVM-DC combines these LSVs into a new compressed training dataset, on which a SVM with the optimized parameters is modeled for classification. The proposed GSVM-DC algorithm is fast due to the usually small size of LSVs. It is also expected to be accurate due to reservation of important data, which are essential for classification and elimination of large quantities of redundant data, which may confuse a classifier to find optimal decision boundary. The simulation results on three biomedical datasets prove that the expectation is reasonable. In general, GSVM provides an interesting new mechanism to address complex classification problems effectively and efficiently in the biomedical domain.