Spectral estimation in unevenly sampled space of periodically expressed microarray time series data

Periodogram analysis of time-series is widespread in biology. A new challenge for analyzing the microarray time series data is to identify genes that are periodically expressed. Such challenge occurs due to the fact that the observed time series usually exhibit non-idealities, such as noise, short length, and unevenly sampled time points. Most methods used in the literature operate on evenly sampled time series and are not suitable for unevenly sampled time series.

For evenly sampled data, methods based on the classical Fourier periodogram are often used to detect periodically expressed gene. Recently, the Lomb-Scargle algorithm has been applied to unevenly sampled gene expression data for spectral estimation. However, since the Lomb-Scargle method assumes that there is a single stationary sinusoid wave with infinite support, it introduces spurious periodic components in the periodogram for data with a finite length. In this paper, we propose a new spectral estimation algorithm for unevenly sampled gene expression data. The new method is based on signal reconstruction in a shift-invariant signal space, where a direct spectral estimation procedure is developed using the B-spline basis. Experiments on simulated noisy gene expression profiles show that our algorithm is superior to the Lomb-Scargle algorithm and the classical Fourier periodogram based method in detecting periodically expressed genes. We have applied our algorithm to the Plasmodium falciparum and Yeast gene expression data and the results show that the algorithm is able to detect biologically meaningful periodically expressed genes.

We have proposed an effective method for identifying periodic genes in unevenly sampled space of microarray time series gene expression data. The method can also be used as an effective tool for gene expression time series interpolation or resampling.