Proteins are a kind of macromolecules and the main component of a cell, and thus it is the most essential and versatile material of life. The research of protein functions is of great significance in decoding the secret of life. In recent years, researchers have introduced multi-label supervised topic model such as Labeled Latent Dirichlet Allocation (Labeled-LDA) into protein function prediction, which can obtain more accurate and explanatory prediction. However, the topic-label corresponding

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... ay of Labeled-LDA is associating each label (GO term) with a corresponding topic directly, which makes the latent topics to be completely degenerated, and ignores the differences between labels and latent topics. To achieve more accurate probabilistic modeling of function label, we propose a Partially Function-to-Topic Prediction (PFTP) model for introducing the local topics subset corresponding to each function label. Meanwhile, PFTP not only supports latent topics subset within a given function label but also a background topic corresponding to a 'fake' function label, which represents common semantic of protein function. Related definitions and the topic modeling process of PFTP are described in this paper. In a 5-fold cross validation experiment on yeast and human datasets, PFTP significantly outperforms five widely adopted methods for protein function prediction. Meanwhile, the impact of model parameters on prediction performance and the latent topics discovered by PFTP are also discussed in this paper. All of the experimental results provide evidence that PFTP is effective and have potential value for predicting protein function. Based on its ability of discovering more-refined latent sub-structure of function label, we can anticipate that PFTP is a potential method to reveal a deeper biological explanation for protein functions.