Although Tripartite Graph can reduce complexity among the relationships of social tagging system, it loses some information among the three elements, and it is also difficult to process the sparse data with missing values. In this paper, we present a Tripartite Tensor Decomposition (TTD) Algorithm to deal with these problems. We first analyzes the information may be lost in the Tripartite Graph, then propose a lower order tensor model based on tripartite graph to deal with the missing information and high-index sparse data. Comparing with tripartite graph model, TTD model reveals comprehensive relations in social tagging system, not only obtains the information between elements, but also gets the relation among three elements. The model is also applied in social tagging system for tagging recommendation by dealing with the missing value. The results of the model comparison experiment and social tagging predication experiment show that TTD model reveals the relations in social tagging system more comprehensive and the results show significant improvements in terms of effective measured through recall/precision when it is used for social tagging recommendation.%三部图作为社会标签系统的表示方法,虽然可以简化标签系统元素间关系的表达,但也丢失了部分元素间的相关信息,而且不能有效处理标签系统中具有大量稀疏值和缺失值的数据.基于以上问题,文中提出了基于三部图的三维张量分解推荐算法(TTD算法).首先分析三部图元素间可能丢失的信息,通过定义以三部图为基础的低阶张量分解模型,对高阶稀疏数据进行分析.该模型不仅包含三部图所表达的系统信息,同时还表达了三部图所丢失的元素间相互信息；在此基础上,利用缺失值处理,进行社会标签系统中的标签推荐预测.通过模型对比实验以及标签预测实验,表明TTD模型所揭示的社会标签系统中元素间的相互关系更加全面,同时在进行标签预测时,所得到的预测结果召回率和精确率得到了显著改善.
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