In the era of big data, it is often the rare categories that are of great interest in many high-impact applications, ranging from financial fraud detection in online transaction networks to emerging trend detection in social networks, from network intrusion detection in computer networks to fault detection in manufacturing. As a result, rare category characterization becomes a fundamental learning task, which aims to accurately characterize the rare categories given limited label information. The unique challenge of rare category characterization, i.e., the non-separability nature of the rare categories from the majority classes, together with the availability of the multi-modal representation of the examples, poses a new research question: how can we learn a salient rare category oriented embedding representation such that the rare examples are well separated from the majority class examples in the embedding space, which facilitates the follow-up rare category characterization? To address this question, inspired by the family of curriculum learning that simulates the cognitive mechanism of human beings, we propose a self-paced framework named SPARC that gradually learns the rare category oriented network representation and the characterization model in a mutually beneficial way by shifting from the 'easy' concept to the target 'difficult' one, in order to facilitate more reliable label propagation to the large number of unlabeled examples. The experimental results on various real data demonstrate that our proposed SPARC algorithm: (1) shows a significant improvement over state-of-the-art graph embedding methods on representing the rare categories that are non-separable from the majority classes; (2) outperforms the existing methods on rare category characterization tasks.