(DROP) Data Reduction Algorithm - How it works?

Question

I am studing a PHD framework which the propose is to reduce the dataset with the most representative samples for training a classifier. Maybe I am loosing something, but I could not undestand a specific part.

Basic this is the algoritm 1 proposed:

Question 1: line 7 says it will union 'edge (s,t)'. What it means? It means that Z'2 (output) will be a set of edges with s and t from different cluster-id's?

And I am asking it because the second algorithm in thesis is the following:

I am not sure if I understood how it L list is generated because some edgs did not make sense by the figure below:

Question 2 Why 6 and 7 has the same element (triangles)? It not should be different, once the edges (from algorithm 1) are from different cluster-ids?

This is the link for thesis: http://repositorio.unicamp.br/handle/REPOSIP/275528?locale=en (page 21-22)

Answer 1

Algorithm 1 takes non-annotated data as input, so it is agnostic to the labels (shapes). In line 1, algorithm 1 computes clusters on the non-annotated data. The cluster assignments do not necessarily correspond exactly to the labels. The output of algorithm 1 will be a set of edges between data in different clusters, but the data need not have different labels. So the reason edges 6 and 7 can connect between triangles is because the triangles have been assigned to different clusters.