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Meter data collection and management in smart grid has the potential for underlying security risks, e.g., low-sparsity unobservable attacks. Thus, it is crucial to investigate the vulnerability of smart grid through various exposure tests associated with these unobservable attacks. Recently, much attention has been paid to low-sparsity unobservable attacks with complete knowledge of the system matrix. In this paper, the unobservable attack exposure analysis is based on a relaxed condition, i.e., an incomplete knowledge of the system matrix. Furthermore, a data-driven attack scheme is designed to demonstrate that such knowledge can be learned with a two-stage strategy. In the first stage, a sequence of intercepted meter data is utilized to learn about the incomplete system matrix with a blind identification approach. In the second stage, the estimated system matrix at hand is used for the attack vector construction with a sparsity-exploiting method. Finally, the validity of the proposed data-driven attack scheme is tested through various experiments. The proposed result reveals the potential risk of meter data leakage to the security of the smart grid.