Extracting directed information flow networks: An application to genetics and semantics

We introduce a general method to infer the directional information flow between populations whose elements are described by $n$-dimensional vectors of symbolic attributes. The method is based on the Jensen-Shannon divergence and on the Shannon entropy and has a wide range of application. We show here the results of two applications: first we extract the network of genetic flow between meadows of the seagrass Poseidonia oceanica, where the meadow elements are specified by sets of microsatellite markers, and then we extract the semantic flow network from a set of Wikipedia pages, showing the semantic channels between different areas of knowledge.

Figure 1

An example of two probability distributions $P(X)$ and $Q(X)$ defined in an attribute domain $X$ where a fraction $J$ of the domain is shared by the two distributions.

Figure 2

Following the notation of the example in Fig. 1, here we show the renormalized distribution of the shared elements ${\stackrel{̲}{P}}_J$ and ${\stackrel{̲}{Q}}_J$, in the joint domain $J$. In this particular example it is evident that ${\stackrel{̲}{P}}_J$ is a peaked distribution, while ${\stackrel{̲}{Q}}_J$ is uniformly distributed. Hence the distribution ${\stackrel{̲}{P}}_J$ results in being more segregated than ${\stackrel{̲}{Q}}_J$.

Figure 3

Directed genetic flow network of PO meadows in the Mediterranean Sea. The network is displayed via a classical algorithm of spring embedding at its percolation threshold, without additional geographical information. Nevertheless the genetic clusters efficiently reflect the geographic locations for the meadows and the directions of the genetic flows agree with standard evolutionary theories for the PO.

Figure 4

Semantic flow network between 78 Wikipedia pages selected within 14 different categories. The network is displayed at the percolation threshold via an automatic spring embedding technique. The clusters efficiently split the different semantic areas.