
The Use of Fuzzy Classification Techniques for World City Network Analysis
Funded by University of Ghent and HEFCE (dual support system) (2002)
Researchers: B. Derudder (University of Ghent), F. Witlox (University of Ghent) and P.J. Taylor
[Results]
Research objective: To explore the use of fuzzy classification techniques as a tool for world city network analysis
Rationale: Classifications of world cities using standard techniques (e.g. a crisp clustering algorithm), where classifications are conceived as disjoint gatherings of the data set, is hampered by various problems (see RB 75).
 The Network of World Cities exhibits a distinctively nonhierarchical urban structure. As a consequence, World Cities constitute a complex network system rather than a simple hierarchy. Although the upper ranks may stand out (London, New York), this urban system is not characterized by some kind of primacy, nor does it conform to a classical Zipfdistribution. This has been highlighted in various RB’s.
 Scrambling hierarchical and functional patterns complement this inherent complexity. There may or may not be hierarchical patterns within the spatial organisation of individual firms at the global scale (depending on their particular strategies), but when aggregated, the result is a complex network exhibiting multiple patterns.
 The lower rungs of the hierarchy are classified on sparse data, yielding vagueness in any classification: minor shifts in the sparse data may yield completely different outcomes, and therefore, mutually exclusive clusters are unlikely to be unbiased by the sparsity of the data.
To summarize, (i) it unlikely that clearcut patterns can be found, while (ii) sparse data hamper classifications at the lower rungs of the World City Network.
As a consequence, research designs resting on the application of standard data techniques may reveal some basic patterns in the large and complex data matrices on world cities, but they cannot take into account the full scope of complex patterns and sparse data. Therefore, in order to represent the real data structures more accurately, we propose to replace the crisp separation of clusters, defined by for all i=1,…n and c=1,…,C, by a fuzzy notion, defined by , where
 C = number of clusters;
 n = number of World Cities that will be classified;
 is the membership of city i in a cluster c.
A fuzzy classification scheme hence computes grades of membership in different clusters rather than assessing mere membership. It can reduce the previously identified problems, since…
 … the expected complexity of multiple and intertwined profiles in any classification is reflected by hybrid membership in different clusters.
 … previous results (see RB 75) have indicated that the second problem (scrambling functional and hierarchical tendencies) can be tackled by the use of this algorithm.
 … a minor shift in the data will be reflected by a minor shift in the resulting classification, which reduces the overall problem of sparse data to a problem of some bias in the data construction.
The results of the fuzzy clustering algorithm should be interpreted as follows:
 Clusters can be designated based on some instances with very high memberships (i.e. belonging unambiguously to a cluster). For the time being, the designations we propose are based on ideas issued in other RB’s (e.g. RB 5’s ‘Alpha World Cities’ and RB 50’s ‘Outer Wannabes’) or spatial patterns (e.g. Pacific AsiaWorld Cities).
 Apart from the designations of the clusters in and by themselves, we will be looking for patterns of hybrid memberships. As a result, a classification may yield more groups than formal clusters. For instance, drawing on hybrid membership patterns, eight clusters may yield 12 distinct groups, in addition to some World Cities that cannot be unambiguously classified.
Methods: A large data matrix of 100 advanced service firms and 316 cities has been created by project 10. Because of the data sparsity problem, existing analyses of this data (RBs 43, 50, 55, 57, 58, 61) has been restricted to just the 123 cities with highest network connectivity. In the new analyses we will focus upon all cities in which at least 20 of the 100 firms are located. This produces a set of 234 cities thus enabling the analysis to penetrate further into the body of numerous cities that have some world city functions but are never thought of as world cities.
For results of this project, see GaWC Research Bulletins 75, 88 and 97.

