Abstract  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.