Scenic Routes in $R^d$

TL;DR

This paper introduces the scenic routes problem in high-dimensional spaces, proposing algorithms to generate visually interpretable trajectories that aid in understanding complex data layouts and their applications.

Contribution

It defines the scenic routes problem in Rd and develops algorithms for generating scenic routes with various criteria, enhancing data visualization and interpretation.

Findings

Algorithms successfully generate scenic routes in 2D, 3D, and higher dimensions.

Applications demonstrated in machine learning visualization and landscape design.

Provides a framework for visual trajectory generation in high-dimensional data.

Abstract

In this work, we introduce the problem of scenic routes among points in Rd. The key development is the nature of the problem in terms of both defining the concept of scenic points and scenic routes and then coming up with algorithms that meet different criteria for the generated scenic routes. The scenic routes problem provides a visual trajectory for a user to comprehend the layout of high-dimensional points. The nature of this trajectory and the visual layout of the points have applications in comprehending the results of machine learning supervised and unsupervised learning techniques. We study the problem in 2D and 3D (with two color points) before exploring the issues in Rd. The red/blue points in our examples could be to be in a class or not to be in a class. The applications could include landscape design to adhere to the scenic beauty of the artifacts on the ground. The generation of equally separated layouts for designing composite hardware where interference could be an issue.