Recursive Node Similarity in Networked Information Spaces
The link structure of a networked information space can be used to estimate similarity between nodes. A recursive definition of similarity arises naturally: two nodes are judged to be similar if they have similar neighbours. Quantifying similarity defined in this manner is challenging due to the tendency of the system to converge to a single point (i.e. all pairs of nodes are completely similar).
We present an embedding of undirected graphs into R n based on recursive node similarity which solves this problem by defining an iterative procedure that converges to a non-singular embedding. We use the spectral decomposition of the normalized adjacency matrix to find an explicit expression for this embedding, then show how to compute the embedding efficiently by solving a sparse system of linear equations.
Unable to display preview. Download preview PDF.
- 1.Chung, F.R.K.: Spectral Graph Theory. In: CBMS Lecture Notes, Regional Conference Series in Mathematics, vol. 92, p. 207. American Mathematical Society, Providence (1995)Google Scholar
- 2.Fasulo, D.: An Analysis of Recent Work on Clustering Algorithms, Technical Report #01-03-02, Department of Computer Science and Engineering, University of Washington, Seattle, WA, April 26 (1999)Google Scholar
- 4.Lee Giles, C., Bollacker, K.D., Lawrence, S.: Citeseer: An Automatic Citation Indexing System. In: Digital Libraries 1998 - Third ACM Conference on Digital Libraries 1998, pp. 89–98 (1998)Google Scholar
- 5.Lu, W., Janssen, J., Milios, E., Japkowicz, N.: Node Similarity in Networked Information Spaces. In: Proc. CASCON 2001, Toronto, Ontario, November 5-7 (2001)Google Scholar
- 7.Richards Jr., W.D., Seary, A.J.: Convergence Analysis of Communication Networks, pp. 36 (1999), http://www.sfu.ca/~richards/Pages/converge.pdf