Knowledge Discovery in a multi-mode network: a visualization approach to measure the interdependence between actors and social venues Dragos Calitoiu Zachary Jacobson Margaret Varga Ben Houston Health Canada, Exocortex, QinetiQ, Carleton Univ. Nov. 2008

Abstract: We propose: - separating the set of actors and their personal connections in a social network from the sets of superordinate and subordinate connections among them [e.g., places, organizations, events]. - building a structure that contains the network of actors, the network of other properties and the links between them. With this separation, we propose measures to describe how the network of actors affects the other networks, and also to describe how the network of places influences the structure of the network of actors.

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One-mode visualization [ We are very grateful to Dr. Ann Jolly who provided us the data.]

3D visualization (iteration 0) There are two persons (#’s 96 and 98), each linked with the same two places. We show a link between these two places in plane P2.

3D visualization (iteration 1) If two individuals, who are directly connected with two different palaces, are also connected in P1 (neighborhood of order 1, namely directly connected), we show a link in P2 between these two places.

3D visualization (iteration 2) If two individuals who are direct connected with two different places are also connected in P1 (neighborhood of order 2), we show a link in P2 between these two places.

New local measures k-Local Place Connectedness (k-LPC) k-Local Link Connectedness (k-LLC) k-Local Ratio of Connectedness (k-LRC k-Local Place Efficiency of order i (k-LPE of order i) k-Local Links Efficiency of order i: (k-LLE of order i) (Definitions in the paper)

New global measures Global Place Connectedness (GPC) Global Link Connectedness (GLC) Global Ratio of Connectedness (GRC) Global Place Efficiency of order i (GPE of order i) Global Links Efficiency of order i (GLE of order i) (Definitions published for 2 levels)

Generalization to multi-modes Rigorous generalized measures under development and study

Clustering coefficient – a new approach for N-mode network Classical definitions: The local clustering coefficient for an individual node i with deg i neighbors and  i edges between its neighbors is: an alternative and more widely used definition of the clustering coefficient This formula is basically not defined if the number of neighbors deg i becomes zero or one as the denominator becomes zero. These cases are usually treated as C i = 0 although some authors also set these values to one.

Clustering coefficient – a new approach for N-mode network Solving the definition: Marcus Kaiser (Newcastle University) looked at the effect of removing nodes with less than two neighbors corresponding to leafs and isolated nodes before averaging for the global clustering coefficient. The relation between the new coefficient C’ and the traditional measure C 1 can be derived from the fraction of nodes that have one or zero neighbors,  by A new computational problem for a N-mode network

Questions and Comments: - What next? - Now what?