Biomarker discovery aims to find small subsets of relevant variables in omics data that correlate with the clinical syndromes of interest. Despite the fact that clinical phenotypes are usually characterized by a complex set of clinical parameters, current computational approaches assume univariate targets, e.g. diagnostic classes, against which associations are sought for. We propose an approach based on asymmetrical sparse canonical correlation analysis (SCCA) that finds multivariate correlations between the omics measurements and the complex clinical phenotypes. We correlated plasma proteomics data to multivariate overlapping complex clinical phenotypes from tuberculosis and malaria datasets. We discovered relevant omic biomarkers that have a high correlation to profiles of clinical measurements and are remarkably sparse, containing 1.5-3% of all omic variables. We show that using clinical view projections we obtain remarkable improvements in diagnostic class prediction, up to 11% in tuberculosis and up to 5% in malaria. Our approach finds proteomic-biomarkers that correlate with complex combinations of clinical-biomarkers. Using the clinical-biomarkers improves the accuracy of diagnostic class prediction while not requiring the measurement plasma proteomic profiles of each subject. Our approach makes it feasible to use omics data to build accurate diagnostic algorithms that can be deployed to community health centres lacking the expensive omics measurement capabilities.