What does spectral analysis tell us about the global structure of a network? Some case studies in linguistic networks

Monojit Choudhury, Microsoft Research Lab - Bangalore, India
09 avril 2010
One of the very important aspect of studying any complex network is to characterize and describe its global structure, which, by definition, is too complex to be described in terms of simple statistics. Traditionally aggregate statistics of certain local properties, such as degree distribution, assortatitivity, and clustering coefficient are used to characterize the topology of the network, but these statistics do not capture the global structure of a network. In this talk, I shall describe how the spectrum of a network (i.e., the eigenvalues and eigenvectors of the adjacency matrix of the network or its Laplacian) provides us with valuable insight into the global structure of the network and therefore, the underlying physical processes generating it. I will take the following three case studies from the domain of language to illustrate this: (a) the co-occurrence networks of words, (b) the networks of syntactic and semantic similarity of the distribution of words, and (c) the co-occurrence network of phonemes (PhoNet).
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