Seriation, i.e., finding a suitable linear order for a set of objects given data and a loss or merit function, is a basic problem in data analysis. Caused by the problem's combinatorial nature, it is hard to solve for all but very small sets. Nevertheless, both exact solution methods and heuristics are available. In this paper we present the package seriation which provides an infrastructure for seriation with R. The infrastructure comprises data structures to represent linear orders as permutation vectors, a wide array of seriation methods using a consistent interface, a method to calculate the value of various loss and merit functions, and several visualization techniques which build on seriation. To illustrate how easily the package can be applied for a variety of applications, a comprehensive collection of examples is presented.

Seriation, i.e., finding a linear order for a set of objects given data and a loss or merit function, is a basic problem in data analysis. Caused by the problem's combinatorial nature, it is hard to solve for all but very small sets. Nevertheless, both exact solution methods and heuristics are available. In this paper we present the package seriation which provides the infrastructure for seriation with R. The infrastructure comprises data structures to represent linear orders as permutation vectors, a wide array of seriation methods using a consistent interface, a method to calculate the value of various loss and merit functions, and several visualization techniques which build on seriation. To illustrate how easily the package can be applied for a variety of applications, a comprehensive collection of examples is presented. / Series: Research Report Series / Department of Statistics and Mathematics

<p dir="ltr">The twenty-first century is a data-driven era where human activities and behavior, physical phenomena, scientific discoveries, technology advancements, and almost everything that happens in the world resulting in massive generation, collection, and utilization of data. </p><p dir="ltr">Connectivity in data is a crucial property. A straightforward example is the World Wide Web, where every webpage is connected to other web pages through hyperlinks, providing a form of directed connectivity. Combinatorial data refers to combinations of data items based on certain connectivity rules. Other forms of combinatorial data include social networks, meshes, community clusters, set systems, and molecules.</p><p dir="ltr">This Ph.D. dissertation focuses on learning and computing with combinatorial data. We study and examine topological and connectivity features within and across connected data to improve the performance of learning and achieve high algorithmic efficiency.</p>