An ultrametric interpretation of building related event data

Abstract

The long-term behaviour of the built environment is relevant to practising architects and engineers as well as to investors and policy makers. In contrast to this, the size, structure and dynamics of that important capital of society are not well established. As a first step towards assessing the dynamics of new constructions, refurbishments, demolitions and other building related event variables in urban building stocks in Southwest Germany, a first random sample of event data is examined using the more efficient ultrametric hierarchical classification in order to compare their dynamics. To this end, different ways of binary encodings of the multivariate data are carried out, and their ultrametric classification results compared. It turns out that municipalities of comparable sizes show similar behaviour in contrast to those of differing sizes, which corresponds to previous findings. Consequently, ultrametric methods can be applied to the study of building stock dynamics by revealing inherent hierarchical structure in data.Building stock dynamics, hierarchical classification, ultrametric methods,

Heavy-tailed distributions for building stock data

“…The random sample is taken from the files corresponding to addresses whose buildings were not insured under that address in 1994, the reasons being demolition or property splitting. This same sample was studied in Bradley (2010) in order to classify the towns in which the buildings were located. The reason why a random sample was taken is that the data are all archived in analog records.…”

On p-adic classification

“…The a posteriori choice of centers turns out useful for constructing classifiers. A first application of some of the methods described here to event history data of building stocks is described in [3]. There, the classification algorithm is performed on different p-adic encodings of the data in order to compare the dynamics of some sampled municipal building stocks.…”