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The goal of clustering is to partition the data points into clusters, such that the data points in the same cluster are similar. Therefore, similarity measure is one of the most critical issues for clustering. In this paper, we present a novel similarity measure based on intrinsic dimension, where the local intrinsic dimension of each data point is considered as a new feature to describe the data points, leading to a new type of similarity measure combining the new feature and original features. The main idea is that the data points in the same cluster are expected to have the same intrinsic dimension while they have similar values of the traditional features. The proposed method is evaluated on some artificial data sets and the experiment results illustrate the effectiveness of the proposed similarity measure. Moreover, the segmentation results of natural images based on the proposed similarity measure show that the intrinsic dimension is worthy of being considered as a new feature of the data points in more applications.