Growing Neural Gas approach for obtaining homogeneous maps by restricting the insertion of new nodes

The Growing Neural Gas model is used widely in artificial neural networks. However, its application is limited in some contexts by the proliferation of nodes in dense areas of the input space. In this study, we introduce some modifications to address this problem by imposing three restrictions on the insertion of new nodes. Each restriction aims to maintain the homogeneous values of selected criteria. One criterion is related to the square error of classification and an alternative approach is proposed for avoiding additional computational costs. Three parameters are added that allow the regulation of the restriction criteria. The resulting algorithm allows models to be obtained that suit specific needs by specifying meaningful parameters.

A new betweenness centrality measure based on an algorithm for ranking the nodes of a network

We propose and discuss a new centrality index for urban street patterns represented as networks in geographical space. This centrality measure, that we call ranking-betweenness centrality, combines the idea behind the random-walk betweenness centrality measure and the idea of ranking the nodes of a network produced by an adapted PageRank algorithm. We initially use a PageRank algorithm in which we are able to transform some information of the network that we want to analyze into numerical values. Numerical values summarizing the information are associated to each of the nodes by means of a data matrix. After running the adapted PageRank algorithm, a ranking of the nodes is obtained, according to their importance in the network. This classification is the starting point for applying an algorithm based on the random-walk betweenness centrality. A detailed example of a real urban street network is discussed in order to understand the process to evaluate the ranking-betweenness centrality proposed, performing some comparisons with other classical centrality measures.

Analyzing the commercial activities of a street network by ranking their nodes: a case study in Murcia, Spain

Urban researchers and planners are often interested in understanding how economic activities are distributed in urban regions, what forces influence their special pattern and how urban structure and functions are mutually dependent. In this paper, we want to show how an algorithm for ranking the nodes in a network can be used to understand and visualize certain commercial activities of a city. The first part of the method consists of collecting real information about different types of commercial activities at each location in the urban network of the city of Murcia, Spain. Four clearly differentiated commercial activities are studied, such as restaurants and bars, shops, banks and supermarkets or department stores, but obviously we can study other. The information collected is then quantified by means of a data matrix, which is used as the basis for the implementation of a PageRank algorithm which produces a ranking of all the nodes in the network, according to their significance within it. Finally, we visualize the resulting classification using a colour scale that helps us to represent the business network.