PREDICTION OF CLUSTERING ANALYSIS TOOL FOR HIGHWAY TRAFFIC NETWORK

Abstract

This paper deals with highway traffic network (HTN) analysis which can be a worldwide problem as road network quality has direct impact in increasing citizen’s socio-economic welfare. It becomes more and more crucial due to the increasing number of users as well as the number of registered motor vehicles and road mileage per year. The main objective of this study is to develop a rigorous mathematical model for displaying HTN. From social network analysis point of view, HTN is a special network. If traditional social network is mathematically equivalent with a symmetric matrix, HTN is an asymmetric one. Furthermore, in terms of graph theory, the former is an undirected weighted graph while the latter is a directed weighted graph. We show that the matrix representing HTN can be uniquely decomposed into two orthogonal parts; a symmetric part and a skew-symmetric one. This implies that these parts can be analysed separately. We use sub-dominant ultrametric (SDU) matrix and the forest of all minimum spanning tress (MSTs) to analyze the first part and singular value decomposition (SVD) for the second one. As a result, we introduce a new method for analyzing HTN which combines the extended MST, the extended hierarchical clustering, and the result of SVD. The advantages of this method are illustrated using data about HTN in the Nigeria in 2023. To the knowledge of the authors, this is an unprecedented clustering method for HTN analysis.