Issue No. 04 - April (2011 vol. 23)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TKDE.2010.142
Luh Yen , Universite catholique de Louvain, Belgium
Marco Saerens , Universite catholique de Louvain, Belgium
François Fouss , Facultés Universitaires Catholiques de Mons (FUCaM), Belgium
This work introduces a link analysis procedure for discovering relationships in a relational database or a graph, generalizing both simple and multiple correspondence analysis. It is based on a random walk model through the database defining a Markov chain having as many states as elements in the database. Suppose we are interested in analyzing the relationships between some elements (or records) contained in two different tables of the relational database. To this end, in a first step, a reduced, much smaller, Markov chain containing only the elements of interest and preserving the main characteristics of the initial chain, is extracted by stochastic complementation . This reduced chain is then analyzed by projecting jointly the elements of interest in the diffusion map subspace  and visualizing the results. This two-step procedure reduces to simple correspondence analysis when only two tables are defined, and to multiple correspondence analysis when the database takes the form of a simple star-schema. On the other hand, a kernel version of the diffusion map distance, generalizing the basic diffusion map distance to directed graphs, is also introduced and the links with spectral clustering are discussed. Several data sets are analyzed by using the proposed methodology, showing the usefulness of the technique for extracting relationships in relational databases or graphs.
Graph mining, link analysis, kernel on a graph, diffusion map, correspondence analysis, dimensionality reduction, statistical relational learning.
M. Saerens, F. Fouss and L. Yen, "A Link Analysis Extension of Correspondence Analysis for Mining Relational Databases," in IEEE Transactions on Knowledge & Data Engineering, vol. 23, no. , pp. 481-495, 2010.