With the popularity of various social media applications, massive social images associated with high quality tags have been made available in many social media web sites nowadays. Mining social images on the web has become an emerging important research topic in web search and data mining. In this paper, we propose a machine learning framework for mining social images and investigate its application to automated image tagging. To effectively discover knowledge from social images that are often associated with multimodal contents (including visual images and textual tags), we propose a novel Unified Distance Metric Learning (UDML) scheme, which not only exploits both visual and textual contents of social images, but also effectively unifies both inductive and transductive metric learning techniques in a systematic learning framework. We further develop an efficient stochastic gradient descent algorithm for solving the UDML optimization task and prove the convergence of the algorithm. By applying the proposed technique to the automated image tagging task in our experiments, we demonstrate that our technique is empirically effective and promising for mining social images towards some real applications.