Influence function of multiple kernel canonical analysis to identify outliers in imaging genetics data

Imaging genetic research has essentially focused on discovering unique and co-association effects, but typically ignoring to identify outliers or atypical objects in genetic as well as non-genetics variables. Identifying significant outliers is an essential and challenging issue for imaging genetics and multiple sources data analysis. Therefore, we need to examine for transcription errors of identified outliers. First, we address the influence function (IF) of kernel mean element, kernel covariance operator, kernel cross-covariance operator, kernel canonical correlation analysis (kernel CCA) and multiple kernel CCA. Second, we propose an IF of multiple kernel CCA, which can be applied for more than two datasets. Third, we propose a visualization method to detect influential observations of multiple sources of data based on the IF of kernel CCA and multiple kernel CCA. Finally, the proposed methods are capable of analyzing outliers of subjects usually found in biomedical applications, in which the number of dimension is large. To examine the outliers, we use the stem-and-leaf display. Experiments on both synthesized and imaging genetics data (e.g., SNP, fMRI, and DNA methylation) demonstrate that the proposed visualization can be applied effectively.