High-dimensional labeled data analysis with Gabriel graphs

We propose the use of the Gabriel graph for the exploratory analysis of potentially high dimensional labeled data. Gabriel graph is a subgraph of the Delaunay triangulation, which connects two data points vi and vj for which there is no other point v_k inside the open ball with diameter [vivj]. If all the Gabriel neighbors of a datum have a different class than its own, this datum is said to be”isolated”. While if some of its Gabriel neighbors have the same class as its own and some others have not, then this datum is said to be”border”. Isolated and border data together with Gabriel graph, allow to get informations about the topology of the different classes in the data space. It is complementary with “classical” and “neural” projection techniques.