arXiv subjects

Zoe Shapcott

Publications and source records attributed to Zoe Shapcott.

2 recordsLinked to original sources

arXiv2024

An Investigation into Distance Measures in Cluster Analysis

This report provides an exploration of different distance measures that can be used with the $K$-means algorithm for cluster analysis. Specifically, we investigate the Mahalanobis distance, and critically assess any benefits it may have over the more traditional measures of the Euclidean, Manhattan and Maximum distances. We perform this by first defining the metrics, before considering their advantages and drawbacks as discussed in literature regarding this area. We apply these distances, first to some simulated data and then to subsets of the Dry Bean dataset [1], to explore if there is a better quality detectable for one metric over the others in these cases. One of the sections is devoted to analysing the information obtained from ChatGPT in response to prompts relating to this topic.

stat.OT↗

arXiv2023

Approximating the distribution of the $L_q$-norm of a random point in a $d$-dimensional cube

In this note, we assess the accuracy of CLT-based approximations for the volume of intersection of the $d$-dimensional cube $[-1,1]^d$ and an $L_q$-ball centred at the origin; this is clearly equivalent to approximating the distribution of the $L_q$-norm of a random point in a $d$-dimensional cube centered at 0. The approximations are CLT-based where to improve the normal approximation we use the first term in the Edgeworth expansion. We have included a section analysing the information obtained from ChatGPT in response to prompts regarding this theory; in our case, ChatGPT answers were not very helpful. Illustrations of the approximation formulae, as the radius of the ball increases, for different values of $d$ and $q$ are also given, alongside lines showing a Monte Carlo simulation of the intersection volume.

math.ST↗