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Missing data are frequently encountered in reality, which inevitably poses great challenges to data mining techniques devoted to data structure identification. In view of the fact that missing data generally exhibits high uncertainty, this paper first introduces the concept of information granule, and performs granular imputation on missing data in a more abstract and inclusive way. With the tolerant nature of the information granule to uncertainty, the error of data imputation and the adverse effects on the subsequent research caused by the low-quality data can be largely reduced. Second, the initial data structure (including granular cluster centers and numeric partition matrix) of the data set with missing values is identified by performing fuzzy clustering on the mixed data set (including both numeric values and information granules) formed by imputation. Third, the bounds of granular cluster centers are further optimized by using the principle of justifiable granularity, and a more robust and reliable granular partition matrix is formed subsequently. Finally, by constructing a reconstruction criterion for mixed data, clustering performance and the optimization of some critical parameters (e.g., the cluster number) used in the proposed method could be investigated. This paper conducts comprehensive experimental studies on both synthetic and publicly available data sets to show the feasibility and effectiveness of the proposed data structure exploration method. [ABSTRACT FROM AUTHOR]