Learning from labeled and unlabeled data on a directed graph

Abstract

We propose a general framework for learning from labeled and unlabeled data on a directed graph in which the structure of the graph including the directionality of the edges is considered. The time complexity of the algorithm derived from this framework is nearly linear due to recently developed numerical techniques. In the absence of labeled instances, this framework can be utilized as a spectral clustering method for directed graphs, which generalizes the spectral clustering approach for undirected graphs. We have applied our framework to real-world web classification problems and obtained encouraging results.

Information Marginalization on Subgraphs

“…Before presenting our approach in detail, we briefly review related techniques for clustering and transductive learning in graphs involved with Markov chain properties of natural random walks [10]. A graph G = (V, E) can be associated with a Markov chain defined via a random walk on the graph.…”

“…can also be derived with respect to a normalized cut criterion that generalizes the standard spectral clustering criterion to directed graphs [10].…”

“…Moving beyond documents and terms, if one considers clustering Web pages, it is clear that the bipartite graph information between Web pages and terms ignores significant relevant information encoded in the hyperlink structure [7,6,10]. When clustering Web pages, it seems clear that both hyperlink structure and term co-occurrence are relevant sources of useful information that one would like to take account of in a unified way.…”

“…Two objects in the target subgraph that share a lot of common external information will be highly linked in the induced random walk, even if they share no direct links in the induced subgraph. Once a valid random walk model has been defined, one can derive algorithms for transductive classification, clustering and ranking, by performing random walks over a Markov Chain [10]. The idea of marginalization is a simple and elegant way of dealing with many types of complex scenarios uniformly.…”

Hypernode Graphs for Spectral Learning on Binary Relations over Sets

“…We define the kernel of a hypernode graph to be the MoorePenrose pseudoinverse [15] of its Laplacian. The spectral theory for hypernode graphs and its properties allow us to use spectral graph learning algorithms [16], [18], [20] for hypernode graphs.…”