We are interested in tracking changes in large-scale data by periodically creating an agglomerative clustering and examining the evolution of clusters (communities) over time. We examine a large real-world data set: the NEC CiteSeer database, a linked network of >250,000 papers. Tracking changes over time requires a clustering algorithm that produces clusters stable under small perturbations of the input data. However, small perturbations of the CiteSeer data lead to significant changes to most of the clusters. One reason for this is that the order in which papers within communities are combined is somewhat arbitrary. However, certain subsets of papers, called natural communities, correspond to real structure in the CiteSeer database and thus appear in any clustering. By identifying the subset of clusters that remain stable under multiple clustering runs, we get the set of natural communities that we can track over time. We demonstrate that such natural communities allow us to identify emerging communities and track temporal changes in the underlying structure of our network data. E mergent properties of large linked networks have recently become the focus of intense study. This research is driven by the increasing complexity and importance of large networks, such as the World Wide Web, the electricity grid, and large social networks that capture relationships between individuals. Realworld networks generally exhibit properties that lie somewhere in-between those of highly structured networks and purely random ones (1-4). So far, most research has focused on using static properties, such as the connectivity of the nodes in the network and the average distance between two nodes, to explain the complex structure. However, these networks generally evolve over time and so temporal characteristics are a key source of interest. Our goal in this paper is to provide techniques for the study of the evolution of large linked networks. In our approach, we use agglomerative clusterings of the linked network. By clustering the network at different points in time, we study its temporal evolution. This approach places a new burden on the underlying clustering method. Clustering methods can be surprisingly sensitive to minor changes of the input data. For obtaining a static view of the higher-level structure of the data, such instabilities may be acceptable because the resulting hierarchy often already reveals interesting structure. However, in tracking changes over time, we need to be able to find corresponding communities in clusterings taken from the data at different points in time. If the clusterings are very sensitive to small perturbations of the input data, distinguishing between ''real'' changes versus ''accidental'' changes in the higher-level structure becomes difficult, if not impossible. In the clusterings of our linked network data, we found there are a large number of relatively random clusters that do not correspond to real community structures. These random clusters obscure the real temporal changes. Fortunately, we found that, when performing a series of agglomerative clustering runs, each run on slightly perturbed input data, one can identify a stable set of clusters that occur in a significant proportion of the clusterings. Moreover, these stable clusters appear to correspond to the true underlying community structure of the network. We refer to such stable clusters as natural communities. We use the notion of natural communities to show that we can track these natural communities effectively over time, and can therefore characterize the temporal evolution of the network.
The work of REF for example, detected natural communities that were stable to small perturbations of the input data.
Tracking evolving communities in large linked networks
Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America
Computer Science Medicine