Periodicity detection method for small-sample time series datasets

Time series of gene expression often exhibit periodic behavior under the influence of multiple signal pathways, and are represented by a model that incorporates multiple harmonics and noise. Most of these data, which are observed using DNA microarrays, consist of few sampling points in time, but most periodicity detection methods require a relatively large number of sampling points. We have previously developed a detection algorithm based on the discrete Fourier transform and Akaike's information criterion. Here we demonstrate the performance of the algorithm for small-sample time series data through a comparison with conventional and newly proposed periodicity detection methods based on a statistical analysis of the power of harmonics.We show that this method has higher sensitivity for data consisting of multiple harmonics, and is more robust against noise than other methods. Although "combinatorial explosion" occurs for large datasets, the computational time is not a problem for small-sample datasets. The MATLAB/GNU Octave script of the algorithm is available on the author's web site: http://www.cbrc.jp/%7Etominaga/piccolo/.