ABSTRACT:

This work introduces a link analysis procedure for locating relationships during a very relational database or a graph, generalizing every simple and multiple correspondence analysis. It relies on a random walk model through the database defining a Markov chain having as several states as components among the database. Suppose we are fascinated by analyzing the relationships between some parts (or records) contained in two utterly different tables of the relational database. To this finish, in a very initial step, a reduced, a heap of smaller, Markov chain containing solely the weather 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 weather of interest within the diffusion map subspace and visualizing the results. This 2-step procedure reduces to easy correspondence analysis when solely 2 tables are defined, and to multiple correspondence analysis when the database takes the form of a easy star-schema. On the other hand, a kernel version of the diffusion map distance, generalizing the basic diffusion map distance to directed graphs, is additionally introduced and thus the links with spectral clustering are mentioned. Several knowledge sets are analyzed by using the proposed methodology, showing the usefulness of the technique for extracting relationships in relational databases or graphs.