Time-series alignment by non-negative multiple generalized canonical correlation analysis

For a quantitative analysis of differential protein expression, one has to overcome the problem of aligning time series of measurements from liquid chromatography coupled to mass spectrometry. When repeating experiments one typically observes that the time axis is deformed in a non-linear way. In this paper we propose a technique to align the time series based on generalized canonical correlation analysis (GCCA) for multiple datasets. The monotonicity constraint in time series alignment is incorporated in the GCCA algorithm. The alignment function is learned both in a supervised and a semi-supervised fashion. We compare our approach with previously published methods for aligning mass spectrometry data on a large proteomics dataset.