A joint optimization framework integrated with biological knowledge for clustering incomplete gene expression data

Clustering algorithms have been successfully applied to identify co-expressed gene groups from gene expression data. Missing values often occur in gene expression data, which presents a challenge for gene clustering. When partitioning incomplete gene expression data into co-expressed gene groups, missing value imputation and clustering are generally performed as two separate processes. These two-stage methods are likely to result in unsuitable imputation values for clustering task and unsatisfying clustering performance. This paper proposes a multi-objective joint optimization framework for clustering incomplete gene expression data that addresses this problem. The proposed framework can impute the missing expression values under the guidance of clustering, and therefore realize the synergistic improvement of imputation and clustering. In addition, gene expression similarity and gene semantic similarity extracted from the Gene Ontology are combined, as the form of functional neighbor interval for each missing expression value, to provide reasonable constraints for the joint optimization framework. The experiments are carried out on several benchmark data sets. In terms of the average improvement rate over the data sets and different missing rates, our framework can reduce the imputation error by 6.4-14.7% and increase the clustering accuracy by 4.0-10.1% compared with six popular and promising methods. Furthermore, biological significance of the identified gene clusters is reported to evaluate the effectiveness of the proposed framework.