Feature selection is effective in preparing high-dimensional data for a variety of learning tasks such as classification, clustering and anomaly detection. A vast majority of existing feature selection methods assume that all instances share some common patterns manifested in a subset of shared features. However, this assumption is not necessarily true in many domains where data instances could show high individuality. For example, in the medical domain, we need to capture the heterogeneous nature of patients for personalized predictive modeling, which could be characterized by a subset of instance-specific features. Motivated by this, we propose to study a novel problem of personalized feature selection. In particular, we investigate the problem in an unsupervised scenario as label information is usually hard to obtain in practice. To be specific, we present a novel unsupervised personalized feature selection framework UPFS to find some shared features by all instances and instance-specific features tailored to each instance. We formulate the problem into a principled optimization framework and provide an effective algorithm to solve it. Experimental results on real-world datasets verify the effectiveness of the proposed UPFS framework.