Automated Alignment of Mass Spectrometry Data Using Functional Geometry

A principled approach for automated alignment of LC-MS chromatograms is critical for reconciling observations across settings and devices, and for annotating large databases of chromatograms. While current algorithms rely on certain pre-processing steps, such as peak detection and matching, tasks that are often subjective and require human intervention, we present a simple and yet fully automated, computational technique for alignment of peaks/nulls in chromatograms. The basic idea is to view chromatograms as real-valued functions on a fixed interval, and derive a geometric, template-based alignment approach. The template is constructed as the sample mean of the given functions under an extended Fisher-Rao metric, and the individual functions are aligned to this mean using time-warping under the same metric. While the original form of the metric is complicated, a square-root slope function representation simplifies it to the \(\mathbb{L}^{2}\) metric, and makes the overall algorithm very efficient. We demonstrate these ideas using a number of alignment experiments, both pairwise and groupwise, and highlight the effectiveness of this automated procedure in spectral alignment.