Multiple Peak Alignment in Sequential Data Analysis: A Scale-Space-Based Approach

Abstract

In this paper, we address the multiple peak alignment problem in sequential data analysis with an approach based on the Gaussian scale-space theory. We assume that multiple sets of detected peaks are the observed samples of a set of common peaks. We also assume that the locations of the observed peaks follow unimodal distributions (e.g., normal distribution) with their means equal to the corresponding locations of the common peaks and variances reflecting the extension of their variations. Under these assumptions, we convert the problem of estimating locations of the unknown number of common peaks from multiple sets of detected peaks into a much simpler problem of searching for local maxima in the scale-space representation. The optimization of the scale parameter is achieved using an energy minimization approach. We compare our approach with a hierarchical clustering method using both simulated data and real mass spectrometry data. We also demonstrate the merit of extending the binary peak detection method (i.e., a candidate is considered either as a peak or as a nonpeak) with a quantitative scoring measure-based approach (i.e., we assign to each candidate a possibility of being a peak).