Analysis and Visualization of Gene Expression Data via a Framework of Geometric Representation

To understand the gene function and complex regulatory mechanisms, it is expected to be an effective way by analyzing gene expression data using various computing approaches. However, intense nonlinearity of the expression data limits the application of traditional linear classifying and clustering methods. This paper proposed a novel geometric framework for the analysis and visualization of these expression data. Expression manifold and sample manifold are defined separately by using the conception and theory of manifold in modern differential geometry. Based on this new angle of view, algorithms of manifold learning are used to embed high-dimension expression data into a low-dimension Euclidean coordinate system. The embedding process reserves the intrinsic geometry structure locally, thus new features and function patterns can be characterized in an intuitional way. Our method is applied to analyze and interpret the cell-cycle data set of Saccharomyces cerevisiae. The results show that the geometric framework is useful for the analysis of gene expression data.