With the advent of big data, there is an urgent need for methods and tools for integrative analyses of multi-modal or multi-view data. Of particular interest are unsupervised methods for parsimonious selection of non-redundant, complementary, and information-rich features from multi-view data. We introduce Adaptive Structural Co-Regularization Algorithm (ASCRA) for unsupervised multi-view feature selection. ASCRA jointly optimizes the embeddings of the different views so as to maximize their agreement with a consensus embedding which aims to simultaneously recover the latent cluster structure in the multi-view data while accounting for correlations between views. ASCRA uses the consensus embedding to guide efficient selection of features that preserve the latent cluster structure of the multi-view data. We establish ASCRA's convergence properties and analyze its computational complexity. The results of our experiments using several real-world and synthetic data sets suggest that ASCRA outperforms or is competitive with state-of-the-art unsupervised multi-view feature selection methods.