GESTs (gene expression similarity and taxonomy similarity), a gene functional prediction approach previously proposed by us, is based on gene expression similarity and concept similarity of functional classes defined in Gene Ontology (GO). In this paper, we extend this method to protein-protein interaction data by introducing several methods to filter the neighbors in protein interaction networks for a protein of unknown function(s). Unlike other conventional methods, the proposed approach automatically selects the most appropriate functional classes as specific as possible during the learning process, and calls on genes annotated to nearby classes to support the predictions to some small-sized specific classes in GO. Based on the yeast protein-protein interaction information from MIPS and a dataset of gene expression profiles, we assess the performances of our approach for predicting protein functions to "biology process" by three measures particularly designed for functional classes organized in GO. Results show that our method is powerful for widely predicting gene functions with very specific functional terms. Based on the GO database published in December 2004, we predict some proteins whose functions were unknown at that time, and some of the predictions have been confirmed by the new SGD annotation data published in April, 2006.