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Classification, as one of the main task of machine learning, corresponds to the core work of granular computing, namely granulation. Most of granular computing models and related classification methods are uniquely classifying by granule features, but not considering granule structure, especially in information area with widespread application of algebraic structure. In this paper, we propose a granular computing based classification method from algebraic granule structure. First of all, to pre-process the original data in the algebraic granule structure area, we formulate the algebraic structure based granularity with granule structure of an algebraic binary operator. Then, we propose a novel granular computing based classification method as well as related classifying algorithm with congruence partitioning granules and homomorphicly projecting granule structure. Finally, compared with tolerance neighborhood model and quotient space model, we prove that the proposed classification method is much more effective and robust while classifying the algebraic structure based granularity. The proposed granular computing based classification method provides an approach for classifying algebraic structure based granularity, and combines granular computing theory and classification theory of machine learning.

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