Circular Order Aggregation and Its Application to Cell-Cycle Genes Expressions

Abstract

Abstract-The aim of circular rank aggregation is to find a circular rank or order on a set of n items using angular values from p heterogeneous data sets. This problem is new in the literature and has been motivated by the biological question of finding the order among the peak expression of a group of cell cycle genes. In this paper, two very different approaches to solve the problem that use pairwise and triplewise information are proposed. Both approaches are analyzed and compared using theoretical developments and numerical studies, and applied to the cell cycle data that motivated the problem.

Recent advances in directional statistics

“…A review of such developments was provided by Rueda et al (2015). Subsequently, Rueda et al (2016) proposed a piecewise circular regression model for the relationship between the phase angles of cell-cycle genes in two species with differing periods, and Barragán et al (2017) considered the problem of aggregating different circular orders for the peak expressions of genes coming from heterogeneous datasets. Recently, Larriba et al (2020) proposed a circular signal plus error model for identifying components of systems displaying rhythmic temporal patterns.…”

Statistical methodology and software to analyse oscillatory signals with applications to biology

“…where can be read as is followed by". If φ ∈ C o , then φ is said to follow the circular order o, see Fernández et al (2012) or Barragán et al (2017) for details. Circular signals are equivalently formulated both in the Euclidean and in the circular space throughout the mapping T LU , see Figure 1.4.…”

“…Robertson and Wright (1980), Robertson et al (1988) and Menéndez and Salvador (1991) extended theories proposed in the early years providing new algorithms for making them accessible in practice. Moreover, Rueda et al (2009), Fernández et al (2012) and Barragán et al (2017) developed ORI procedures to the circular manifold.…”