Introduction

Biological progressions are increasingly being described by the temporal ordering of highly orchestrated activities of different genes, proteins, and other regulatory components (Mandel and Grosschedl, 2010). In the literature, time series experiments have been used to study biological progressions. For example, microarray experiments of different time points during the cell cycle produced gene expression time series data for the identification of cell-cycle regulated genes (Whitfield et al., 2002). Cells at different stages of normal B-cell differentiation were profiled by microarray to study the changes in gene expression during the B-cell differentiation process (Hystad et al., 2007). For such time series data, a variety of computational methods have been developed to identify which genes vary and how they vary across some or all the time points (Filkov et al., 2002; Storey et al., 2005; Zhu et al., 2005; Huang et al., 2007). However, fewer methods are available to handle data sets in which samples are from a certain biological process but their order is unknown.

Recovery of an ordering among unordered objects has been studied in the literature. In computer vision, the multiview matching problem deals with unordered images of the same scene taken from random viewpoints and angles. An appropriate ordering of the images enables three-dimensional navigation in the scene. This ordering can be derived on the basis of predefined features that are invariant to different viewpoints (Schaffalitzky and Zisserman, 2002).