The notion of relative attributes as introduced by Parikh and Grauman (ICCV, 2011) provides an appealing way of comparing two images based on their visual properties (or attributes) such as "smiling" for face images, "naturalness" for outdoor images, etc. For learning such attributes, a Ranking SVM based formulation was proposed that uses globally represented pairs of annotated images. In this paper, we extend this idea towards learning relative attributes using local parts that are shared across categories. First, instead of using a global representation, we introduce a part-based representation combining a pair of images that specifically compares corresponding parts. Then, with each part we associate a locally adaptive "significance-coefficient" that represents its discriminative ability with respect to a particular attribute. For each attribute, the significance-coefficients are learned simultaneously with a max-margin ranking model in an iterative manner. Compared to the baseline method, the new method is shown to achieve significant improvement in relative attribute prediction accuracy. Additionally, it is also shown to improve relative feedback based interactive image search.