Support vector clustering (SVC) is an important boundary-based clustering algorithm in multiple applications for its capability of handling arbitrary cluster shapes.However,SVC’s popularity is degraded by its highly intensive time complexity and poor label performance.To overcome such problems,we present a novel efficient and robust convex decomposition based cluster labeling (CDCL) method based on the topological property of dataset.The CDCL decomposes the implicit cluster into convex hulls and each one is comprised by a subset of support vectors (SVs).According to a robust algorithm applied in the nearest neighboring convex hulls,the adjacency matrix of convex hulls is built up for finding the connected components;and the remaining data points would be assigned the label of the nearest convex hull appropriately.The approach’s validation is guaranteed by geometric proofs.Time complexity analysis and comparative experiments suggest that CDCL improves both the efficiency and clustering quality significantly. Support vector clustering (SVC) is an important boundary-based clustering algorithm in multiple applications for its capability of handling arbitrary cluster shapes.However, SVC’s popularity is degraded by its highly intensive time complexity and poor label performance. To overcome such problems, we present a novel efficient and robust convex decomposition based cluster labeling (CDCL) method based on the topological property of dataset. The CDCL decomposes the implicit cluster into convex hulls and each one is comprised by a subset of support vectors (SVs) .According to to robust algorithm applied in the nearest neighbor convex hulls, the adjacency matrix of convex hulls is built up for finding the connected components; and the remaining data points would be assigned the label of the nearest convex hull appropriately.The approach’s validation is guaranteed by geometric proofs. Time complexity analysis and comparative experiments suggest that CDCL improves both the efficiency and clustering quality significantly.