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Story clustering is a critical step for news retrieval, topic mining, and summarization. Nonetheless, the task remains highly challenging owing to the fact that news topics exhibit clusters of varying densities, shapes, and sizes. Traditional algorithms are found to be ineffective in mining these types of clusters. This paper offers a new perspective by exploring the pairwise visual cues deriving from near-duplicate keyframes (NDK) for constraint-based clustering. We propose a constraint-driven co-clustering algorithm (CCC), which utilizes the near-duplicate constraints built on top of text, to mine topic-related stories and the outliers. With CCC, the duality between stories and their underlying multimodal features is exploited to transform features in low-dimensional space with normalized cut. The visual constraints are added directly to this new space, while the traditional DBSCAN is revisited to capitalize on the availability of constraints and the reduced dimensional space. We modify DBSCAN with two new characteristics for story clustering: 1) constraint-based centroid selection and 2) adaptive radius. Experiments on TRECVID-2004 corpus demonstrate that CCC with visual constraints is more capable of mining news topics of varying densities, shapes and sizes, compared with traditional k-means, DBSCAN, and spectral co-clustering algorithms.