Fitting lines to points in the plane

TL;DR

This paper investigates the problem of fitting lines to a finite set of points in the plane by minimizing the L^p-norm of the distances, providing a unified analysis for various distance definitions.

Contribution

It offers a unified framework for understanding optimal lines under different L^p-norm distance measures using elementary methods.

Findings

Properties of optimal lines are characterized for various L^p-norms.

A uniform language for different distance measures is developed.

Elementary considerations suffice to derive key properties.

Abstract

We seek for lines of minimal distance to finitely many points in the plane. The distance between a line and a set of points is defined by the L^p-norm, 1\leq p\leq \infty, of the vector of vertical or orthogonal distances from the single points to the line. The known properties of optimal lines are deduced by elementary considerations and represented using a uniform language for the different choices to define the distance from a line to a set of points.