  Data imputation, the process of filling in missing feature elements for
incomplete data sets, plays a crucial role in data-driven learning. A
fundamental belief is that data imputation is helpful for learning performance,
and it follows that the pursuit of better classification can guide the data
imputation process. While some works consider using label information to assist
in this task, their simplistic utilization of labels lacks flexibility and may
rely on strict assumptions. In this paper, we propose a new framework that
effectively leverages supervision information to complete missing data in a
manner conducive to classification. Specifically, this framework operates in
two stages. Firstly, it leverages labels to supervise the optimization of
similarity relationships among data, represented by the kernel matrix, with the
goal of enhancing classification accuracy. To mitigate overfitting that may
occur during this process, a perturbation variable is introduced to improve the
robustness of the framework. Secondly, the learned kernel matrix serves as
additional supervision information to guide data imputation through regression,
utilizing the block coordinate descent method. The superiority of the proposed
method is evaluated on four real-world data sets by comparing it with
state-of-the-art imputation methods. Remarkably, our algorithm significantly
outperforms other methods when the data is missing more than 60\% of the
features
