Feature selection has been proven to be effective and efficient in preparing high-dimensional data for data mining and machine learning problems. Since real-world data is usually unlabeled, unsupervised feature selection has received increasing attention in recent years. Without label information, unsupervised feature selection needs alternative criteria to define feature relevance. Recently, data reconstruction error emerged as a new criterion for unsupervised feature selection, which defines feature relevance as the capability of features to approximate original data via a reconstruction function. Most existing algorithms in this family assume predefined, linear reconstruction functions. However, the reconstruction function should be data dependent and may not always be linear especially when the original data is high-dimensional. In this paper, we investigate how to learn the reconstruction function from the data automatically for unsupervised feature selection, and propose a novel reconstruction-based unsupervised feature selection framework REFS, which embeds the reconstruction function learning process into feature selection. Experiments on various types of realworld datasets demonstrate the effectiveness of the proposed framework REFS.