264 J. Gosliga et al. The same matching can be performed for joints. In this case, the joint to examine in each graph is determined by examining the edges in the subgraph. which are adjacent in the subgraph. This gives a set of nodes which are connected by the edge in the original graphs. From this, the edge attributes can be extracted. The joint type is compared, and if the joint is kinematic, the restricted degrees of freedom can also be compared. If all elements and joints in two graphs are identical (all of the hierarchical attributes are available and match) then these two graphs form a homogeneous population. If all elements and joint in the subgraph of two graphs are identical, then they share a subcomponent and transfer is possible within this subcomponent [6]. The more likely case is that only partial matches are seen, and in this case the level of match determines the appropriate transfer learning approach. 26.4 Communities It is possible to determine a similarity score (Jaccard similarity coefficient) based purely on the size of this maximum common subgraph G . This is calculated using the following equation, Jv(G,H) = | V(G ) | | V(G) | + | V(H) | − | V(G ) | (26.1) where Jv(G,H) is the Jaccard index for the node sets. Similarly, it is possible to find the Jaccard index for the edge sets, Je(G,H) = | E(G ) | | E(G) | + | E(H) | − | E(G ) | (26.2) Multiplying Jv(G,H) and Je(G,H) by 100 gives a percentage similarity score. This was calculated for several representative structures and the results are shown in Fig. 26.10. Structures tend to match more with similar structures, for example aeroplanes match strongly with aeroplanes, and bridges match strongly with bridges. However, some bridge graphs match more with the aeroplane and turbine structures. This could be caused by there being a higher chance of finding large subgraphs when the two graphs Gand Hare larger. Fig. 26.10 Figures showing the percentage topology match between structures. The percentage score is based on the Jaccard indexJv(G,H) and Je(G,H) for nodes and edges respectively
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