Relative Neighbourhood Graph Editing (RNG)

In RNG (Relative Neighbourhood Graph) two points, xi and xj, are neighbours if and only if there is no other point from set laying in a lune between xi, xj which is defined as the disjoint intersection between two hyperspheres centered at xi and xj and whose radius are equal to the distance between them.

The graph-based approach consists of a applying the general idea of Wilson's editing algorithm but using the RN of each prototype, instead of the classical nearest neighbourhood, in order to estimate mislabelled patterns. In a few words, the simplest graph editing can be summarised as follows: after computing the graph neighbourhood of each training prototype, discard those patterns that are misclassified by their graph neighbours (instead of their k-NN). In practice, a first approach to this general editing scheme can be written as follows:

• Construct the proximity graph corresponding to the original Training Set, say X.
• For each xi in X do:
• Discard xi if there is a majority of graph neighbours from a different class.

---

How to use this applet?

1. The top panel is Modes panel, the right panel is Controls panel and the central panel is Drawing panel.
2. To select the number of classes (label No classes) in the controls panel for the training set.
3. To do click over any radiobutton that identify a class (labels 1, 2, ..., 12) in the controls panel.
4. To do click over the drawing panel to insert prototypes in the training set (of the class selected in the step 4). These prototypes will have 2 characteristics whose values will remain defined for the axes x and y.
5. To select el radiobutton with label "2. Editing" in the modes panel to changing to the editing mode. Then you can see the resultant set of the editing.
6. The radiobutton with label Inspection in the controls panel allows to know the coordinates to the next prototype (o sample) to the cursor mouse.
7. The radiobutton with label Remove (only in design mode) in the controls panel allows delete the next prototype (o sample) to the cursor mouse.
8. The button Clear (only in design mode) in the controls panel allows delete all the training set.