Circular Object Arrangement using Spherical Embeddings

We consider the problem of recovering a circular arrangement of data instances with respect to some proximity measure, such that nearby instances are more similar. Applications of this problem, also referred to as circular seriation, can be found in various disciplines such as genome sequencing, data visualization and exploratory data analysis. Circular seriation can be expressed as a quadratic assignment problem, which is in general an intractable problem. Spectral-based approaches can be used to find approximate solutions, but are shown to perform well only for a specific class of data matrices. We propose a bilevel optimization framework where we employ a spherical embedding approach together with a spectral method for circular ordering in order to recover circular arrangements of the embedded data. Experiments on real and synthetic datasets demonstrate the competitive performance of the proposed method.