Metric learning to learn a good distance metric for distinguishing different people while being insensitive to intra-person variations is widely applied to person re-identification. In previous works, local histograms are densely sampled to extract spatially localized information of each person image. The extracted local histograms are then concatenated into one vector that is used as an input of metric learning. However, the dimensionality of such a concatenated vector often becomes large while the number of training samples is limited. This leads to an over fitting problem. In this work, we argue that such a problem of over-fitting comes from that it is each local histogram dimension (e.g. color brightness bin) in the same position is treated separately to examine which part of the image is more discriminative. To solve this problem, we propose a method that analyzes discriminative image positions shared by different local histogram dimensions. A common weight map shared by different dimensions and a distance metric which emphasizes discriminative dimensions in the local histogram are jointly learned with a unified discriminative criterion. Our experiments using four different public datasets confirmed the effectiveness of the proposed method.