As data sources become ever more numerous with increased feature dimensionality, feature selection for multiview data has become an important technique in machine learning. Semi-supervised multiview feature selection (SMFS) focuses on the problem of how to obtain a discriminative feature subset from heterogeneous feature spaces in the case of abundant unlabeled data with little labeled data. Most existing methods suffer from unreliable similarity graph structure across different views since they separate the graph construction from feature selection and use the fixed graphs that are susceptible to noisy features. Furthermore, they directly concatenate multiple feature projections for feature selection, neglecting the contribution diversity among projections. To alleviate these problems, we present an SMFS to simultaneously select informative features and learn a unified graph through the data fusion from aspects of feature projection and similarity graph. Specifically, SMFS adaptively weights different feature projections and flexibly fuses them to form a joint weighted projection, preserving the complementarity and consensus of the original views. Moreover, an implicit graph fusion is devised to dynamically learn a compatible graph across views according to the similarity structure in the learned projection subspace, where the undesirable effects of noisy features are largely alleviated. A convergent method is derived to iteratively optimize SMFS. Experiments on various datasets validate the effectiveness and superiority of SMFS over state-of-the-art methods.