The identification of co-regulated genes and their transcription-factor binding sites (TFBS) are the key steps toward understanding transcription regulation. In addition to effective laboratory assays, various bi-clustering algorithms for detection of the co-expressed genes have been developed. Bi-clustering methods are used to discover subgroups of genes with similar expression patterns under to-be-identified subsets of experimental conditions when applied to gene expression data. By building two fuzzy partition matrices of the gene expression data with the Axiomatic Fuzzy Set (AFS) theory, this paper proposes a novel fuzzy bi-clustering algorithm for identification of co-regulated genes. Specifically, the gene expression data is transformed into two fuzzy partition matrices via sub-preference relations theory of AFS at first. One of the matrices is considering the genes as the universe and the conditions as the concept, the other one is considering the genes as the concept and the conditions as the universe. The identification of the co-regulated genes (bi-clusters) is carried out on the two partition matrices at the same time. Then, a novel fuzzy-based similarity criterion is defined based on the partition matrixes, and a cyclic optimization algorithm is designed to discover the significant bi-clusters at expression level. The above procedures guarantee that the generated bi-clusters have more significant expression values than that of extracted by the traditional bi-clustering methods. Finally, the performance of the proposed method is evaluated with the performance of the three well-known bi-clustering algorithms on publicly available real microarray datasets. The experimental results are in agreement with the theoretical analysis and show that the proposed algorithm can effectively detect the co-regulated genes without any prior knowledge of the gene expression data.

翻译：共调控基因及其转录因子结合位点（TFBS）的识别是理解转录调控的关键步骤。除了有效的实验室检测方法外，目前已开发出多种用于检测共表达基因的双聚类算法。当应用于基因表达数据时，双聚类方法可用于发现实验条件待识别子集下具有相似表达模式的基因亚群。本文通过公理模糊集（AFS）理论构建基因表达数据的两个模糊划分矩阵，提出一种用于共调控基因识别的新型模糊双聚类算法。具体而言：首先利用AFS的子偏好关系理论将基因表达数据转换为两个模糊划分矩阵——其中一个矩阵以基因为论域、以条件为概念，另一个矩阵以基因为概念、以条件为论域。共调控基因（双聚类）的识别同时在这两个划分矩阵上进行。随后基于划分矩阵定义新型模糊相似准则，并设计循环优化算法以发现表达水平上的显著双聚类。上述流程保证了生成的双聚类比传统双聚类方法提取的结果具有更显著的表达值。最后，在公开真实微阵列数据集上将所提方法的性能与三种知名双聚类算法进行对比评估。实验结果与理论分析一致，表明所提算法无需基因表达数据的任何先验知识即可有效检测共调控基因。