Orthogonal projection correction for confounders in biological data classification

The existence of confounders such as population structure in genome-wide association study makes it difficult to apply machine learning methods directly to solve biological problems. It is still unclear how to effectively correct confounders. In this work, we propose an Orthogonal Projection Correction (OPC) method to correct confounders. This is achieved by orthogonally decomposing each feature to a confounding component and a non-confounding component, such that the original data can be best reconstructed by only the non-confounding components of features. The confounder space is built based on prior knowledge, and each feature is projected to its orthogonal complement space. This OPC procedure is shown to be kernelisable. We then propose a ProSVM method by integrating the OPC method and support vector machine for classification. In the experiments, our OPC method for confounder correction improves the tumour diagnosis based on samples from different labs and phenotype prediction in the presence of population structure.