Feature selection has been proven to be efficient in preparing high dimensional data for data mining and machine learning. As most data is unlabeled, unsupervised feature selection has attracted more and more attention in recent years. Discriminant analysis has been proven to be a powerful technique to select discriminative features for supervised feature selection. To apply discriminant analysis, we usually need label information which is absent for unlabeled data. This gap makes it challenging to apply discriminant analysis for unsupervised feature selection. In this paper, we investigate how to exploit discriminant analysis in unsupervised scenarios to select discriminative features. We introduce the concept of pseudo labels, which enable discriminant analysis on unlabeled data, propose a novel unsupervised feature selection framework DisUFS which incorporates learning discriminative features with generating pseudo labels, and develop an effective algorithm for DisUFS. Experimental results on different types of real-world data demonstrate the effectiveness of the proposed framework DisUFS.