The prevalent use of social media produces mountains of unlabeled, high-dimensional data. Feature selection has been shown effective in dealing with high-dimensional data for efficient data mining. Feature selection for unlabeled data remains a challenging task due to the absence of label information by which the feature relevance can be assessed. The unique characteristics of social media data further complicate the already challenging problem of unsupervised feature selection, (e.g., part of social media data is linked, which makes invalid the independent and identically distributed assumption), bringing about new challenges to traditional unsupervised feature selection algorithms. In this paper, we study the differences between social media data and traditional attribute-value data, investigate if the relations revealed in linked data can be used to help select relevant features, and propose a novel unsupervised feature selection framework, LUFS, for linked social media data. We perform experiments with real-world social media datasets to evaluate the effectiveness of the proposed framework and probe the working of its key components.