Measuring an orienteer's performance: a method based on lower rank approximation of asymmetric matrices

Villers Gomez, Sofia (2015). Measuring an orienteer's performance: a method based on lower rank approximation of asymmetric matrices. PhD thesis The Open University.

DOI: https://doi.org/10.21954/ou.ro.0000f862

Abstract

The objective of this thesis is to develop a method that measures the performance of competitors in an orienteering course. The measures proposed will allow the comparison of the orienteer’s performance with other competitors running the same course, and with his/her performance in different courses.

This thesis presents two main contributions, the first one refers to an orienteer’s performance measure, and the second one relates to the lower rank approximation theory developed for this research. In the orienteering context, we developed a method that calculates a fitness measure and a navigational measure for each orienteer running a course. This differentiation between physical and navigational skills is an original approach to the orienteering performance analysis, and it allows a clear identification of areas that need improvement to achieve better times in an event. Based on the performance measures of orienteers participating in 100 events that took place in the UK between January 2013 and May 2014, we construct a course technical difficulty measure for green, blue and brown courses. This course difficulty allows the identification
of easy and hard courses.

On the statistical theory context, this thesis presents a robust and asymmetric lower rank approximation algorithm to reduce matrices with asymmetric outliers into two vectors. This algorithm was based on the robust lower rank approximation algorithm proposed by Maronna and Yohai (2008). This thesis presents two original modifications to this algorithm, which produces better estimates when the data has asymmetric outliers. Those modifications are the definition of an asymmetric objective function, and the use of a robust scale parameter that is updated at each iteration. The proposed modification to the scale parameter caused that the estimates do not depend anymore on initial values and the value reached by the loss function is most of the time better than the point reached without the modification. We also show that this methodology can be applied in contexts other than orienteering.