Distance metric has an important role in many machine learning algorithms. Recently, metric learning for semi-supervised algorithms has received much attention. For semi-supervised clustering, usually a set of pairwise similarity and dissimilarity constraints is provided as supervisory information. Until now, various metric learning methods utilizing pairwise constraints have been proposed. The existing methods that can consider both positive (must-link) and negative (cannot-link) constraints find linear transformations or equivalently global Mahalanobis metrics. Additionally, they find metrics only according to the data points appearing in constraints (without considering other data points). In this paper, we consider the topological structure of data along with both positive and negative constraints. We propose a kernel-based metric learning method that provides a non-linear transformation. Experimental results on synthetic and real-world data sets show the effectiveness of our metric learning method. 1