For many textual collections, the number of features is often overly large. These features can be very redundant, it is therefore desirable to have a small, succinct, yet highly informative collection of features that describes the key characteristics of a dataset. Information theory is one such tool for us to obtain this feature collection. With this paper, we mainly contribute to the improvement of efficiency for the process of selecting the most informative feature set over high-dimensional unlabeled data. We propose a heuristic theory for informative feature set selection from high dimensional data. Moreover, we design data structures that enable us to compute the entropies of the candidate feature sets efficiently. We also develop a simple pruning strategy that eliminates the hopeless candidates at each forward selection step. We test our method through experiments on real-world data sets, showing that our proposal is very efficient.