Adopting a measure is essential in many multimedia applications. Recently, distance learning is becoming an active research problem. In fact, the distance is the natural measure for dissimilarity. Generally, a pairwise relationship between two objects in learning tasks includes two aspects: similarity and dissimilarity. The similarity measure provides different information for pairwise relationships. However, similarity learning has been paid less attention in learning problems. In this work, firstly, we propose a general framework for similarity measure learning (SML). Additionally, we define a generalized type of correlation as a similarity measure. By a set of parameters, generalized correlation provides flexibility for learning tasks. Based on this similarity measure, we present a specific algorithm under the SML framework, called correlation similarity measure learning (CSML), to learn a parameterized similarity measure over input space. A nonlinear extension version of CSML, kernel CSML, is also proposed. Particularly, we give a closed-form solution avoiding iterative search for a local optimal solution in the high-dimensional space as the previous work did. Finally, classification experiments have been performed on face databases and a handwritten digits database to demonstrate the efficiency and reliability of CSML and KCSML.