The workflow for PPIA + ellipsoidFN method. (A1) Gene expression data for cancer (rows are genes and columns are samples with multiple different types) and human protein-protein interaction network. (A2) Combining gene expression data with human PPI network by product approximation, where each protein-protein interaction affinity Ei can be computed based on the law of mass action. The rows are edges of PPI or gene nodes and the columns are samples. (A3) By the PPIA+ellipsoidFN method, different cancer types or normal and disease case can be represented by different ellipsoids, and the distances among these ellipsoids are maximized. (A4) PPIA network biomarkers are identified by the PPIA+ellipsoidFN method to classify different phenotypes.