Flow Graphs, their Fusion and Data Analysis

Summary

This paper concerns a new approach to data analysis based on information flow distribution study in flow graphs. The introduced flow graphs differ from that proposed by Ford and Fulkerson, for they do not describe material flow in the flow graph but information “flow” about the data structure.

Data analysis (mining) can be reduced to information flow analysis and the relationship between data can be boiled down to information flow distribution in a flow network. Moreover, it is revealed that information flow satisfies Bayes’ rule, which is in fact an information flow conservation equation. Hence information flow has probabilistic character, however Bayes’ rule in our case can be interpreted in an entirely deterministic way, without referring to prior and posterior probabilities, inherently associated with Bayesian philosophy.

Furthermore in this paper we study hierarchical structure of flow networks by allowing to substitute a subgraph determined by branches x and y by a single branch connecting x and y, called fusion of x and y. This “fusion” operation allows us to look at data with different accuracy and move from details to general picture of data structure.