An Exploratory Multivariate Statistical Analysis to Assess Urban Diversity

Abstract

Understanding diversity in complex urban systems is fundamental in facing current and future sustainability challenges. In this article, we apply an exploratory multivariate statistical analysis (i.e., Principal Component Analysis (PCA) and Multiple Factor Analysis (MFA)) to an urban system’s abstraction of the city’s functioning. Specifically, we relate the environmental, economical, and social characters of the city in a multivariate system of indicators by collecting measurements of those variables at the district scale. Statistical methods are applied to reduce the dimensionality of the multivariate dataset, such that, hidden relationships between the districts of the city are exposed. The methodology has been mainly designed to display diversity, being understood as differentiated attributes of the districts in their dimensionally-reduced description, and to measure it with Euclidean distances. Differentiated characters and distinctive functions of districts are identifiable in the exploratory analysis of a case study of Barcelona (Spain). The distances allow for the identification of clustered districts, as well as those that are separated, exemplifying dissimilarity. Moreover, the temporal dependency of the dataset reveals information about the district’s differentiation or homogenization trends between 2003 and 2015.

Visualization of the Strain-Rate State of a Data Cloud: Analysis of the Temporal Change of an Urban Multivariate Description

“…The time-dependent data cloud comes from the PCA output of a multivariate description of the city of Barcelona in [2]. Since 1987, the city has been divided into 10 administrative districts, which are the largest territorial units of the city and can be compared with neighborhoods in a common metropolitan area: Ciutat Vella, Eixample, Gràcia, Les Corts, Sarria, Sant Andreu, Sant Marti, Horta, Sants, and Nou Barris.…”

“…In the present article, we explore formal approaches to quantify the temporal change of discrete three-dimensional data. Specifically, we build a methodology to assess the transformation of a data cloud that is derived from a Principal Component Analysis (PCA): a 13-year multivariate description in [2] that provides a reduced description of an urban system given only by the first three principal components. Since the points represent an abstraction of an urban system, one main goal is to understand the temporal variation of the multivariate description of the districts in order to analyze the behavior of the overall city in the time-span.…”

Visualization of the Strain-rate State of a Data Cloud: Analysis of the Temporal Change of an Urban Multivariate Description

“…In the present article, we explore formal approaches to quantify the temporal change of discrete three-dimensional data. Specifically, we build a methodology to assess the transformation of a data cloud that is derived from a Principal Component Analysis(PCA): a 13-years span multivariate description in [2] that provides a reduced description of an urban system given only by the first three principal components. Since the points represent an abstraction of an urban system, one main goal is to understand the temporal variation of the multivariate description of the districts in order to analyze the behavior of the overall city in the time-span.…”