Constructing pathways of tumor progression and discovering the biomarkers associated with cancer is critical for understanding the molecular basis of the disease and for the establishment of novel chemotherapeutic approaches and in turn improving the clinical efficiency of the drugs. It has recently received a lot of attention from bioinformatics researchers. However, relatively few methods are available for constructing pathways. This article develops a novel entropy kernel based kernel clustering and fuzzy kernel clustering algorithms to construct the tumor progression pathways using CpG island methylation data. The methylation data which come from tumor tissues diagnosed at different stages can be used to distinguish epigenotype and phenotypes the describe the molecular events of different phases. Using kernel and fuzzy kernel kmeans, we built tumor progression trees to describe the pathways of tumor progression and find the possible biomarkers associated with cancer. Our results indicate that the proposed algorithms together with methylation profiles can predict the tumor progression stages and discover the biomarkers efficiently. Software is available upon request
