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As recommendation systems continue to evolve, researchers are using trust data to improve the accuracy of recommendation prediction and help users find relevant information. However, large recommendation systems with trust data suffer from the sparse trust problem , which leads to grade inflation and severely affects the reliability of trust propagation. This paper presents a novel research on sparse trust data mining, which includes the new concept of sparse trust, a sparse trust model, and a trust mining framework. It lays a foundation for the trust-related research in large recommended systems. The new trust mining framework is based on customized normalization functions and a novel transitive gossip trust model, which discovers potential trust information between entities in a large-scale user network and applies it to a recommendation system. We conducts a comprehensive performance evaluation on both real-world and synthetic datasets. The results confirm that our framework mines new trust and effectively ameliorates sparse trust problem.