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Despite years of research, the name ambiguity problem remains largely unresolved. Outstanding issues include how to capture all information for name disambiguation in a unified approach, and how to determine the number of people K in the disambiguation process. In this paper, we formalize the problem in a unified probabilistic framework, which incorporates both attributes and relationships. Specifically, we define a disambiguation objective function for the problem and propose a two-step parameter estimation algorithm. We also investigate a dynamic approach for estimating the number of people K. Experiments show that our proposed framework significantly outperforms four baseline methods of using clustering algorithms and two other previous methods. Experiments also indicate that the number K automatically found by our method is close to the actual number.