4 research outputs found
Generalized Optimization Framework for Graph-based Semi-supervised Learning
We develop a generalized optimization framework for graph-based
semi-supervised learning. The framework gives as particular cases the Standard
Laplacian, Normalized Laplacian and PageRank based methods. We have also
provided new probabilistic interpretation based on random walks and
characterized the limiting behaviour of the methods. The random walk based
interpretation allows us to explain di erences between the performances of
methods with di erent smoothing kernels. It appears that the PageRank based
method is robust with respect to the choice of the regularization parameter and
the labelled data. We illustrate our theoretical results with two realistic
datasets, characterizing di erent challenges: Les Miserables characters social
network and Wikipedia hyper-link graph. The graph-based semi-supervised
learning classi- es the Wikipedia articles with very good precision and perfect
recall employing only the information about the hyper-text links
Finding and visualizing graph clusters using pagerank optimization
Abstract. We give algorithms for finding graph clusters and drawing graphs, highlighting local community structure within the context of a larger network. For a given graph G, we use the personalized PageRank vectors to determine a set of clusters, by optimizing the jumping parameter α subject to several cluster variance measures in order to capture the graph structure according to PageRank. We then give a graph visualization algorithm for the clusters using PageRank-based coordinates. Several drawings of real-world data are given, illustrating the partition and local community structure.