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Data reduction plays an important role in machine learning and pattern recognition with a high-dimensional data. In real-world applications data usually exists with hybrid formats, and a unified data reducing technique for hybrid data is desirable. In this paper, an information measure is proposed to computing discernibility power of a crisp equivalence relation or a fuzzy one, which is the key concept in classical rough set model and fuzzy-rough set model. Based on the information measure, a general definition of significance of nominal, numeric and fuzzy attributes is presented. We redefine the independence of hybrid attribute subset, reduct, and relative reduct. Then two greedy reduction algorithms for unsupervised and supervised data dimensionality reduction based on the proposed information measure are constructed. Experiments show the reducts found by the proposed algorithms get a better performance …