Fusion of Kohonen Maps Ranked by Cluster Validity Indexes

Aggregating Self-Organizing Maps with Topology Preservation

“…Another approach to preserve the topology property of the map is to align the different maps on one of them, which serves as a reference for the topology: in [12], the map is chosen arbitrarily, and the other maps are fused sequentially to this first one, averaging the prototypes (p b u ) u of the current map to the closest prototypes of the current fused map (p * u ) u . To leverage the problem of the choice of the map that is used to align the other maps, [9] proposes to choose a reference map that is the best one according to a given clustering quality criterion. However, this method makes the result strongly dependent on the choice of the first map because only its topology is used, whereas the topologies of the next maps are not utilized as such.…”

“…In the method described in the previous section, all maps are fused in an arbitrary order. However, as pointed out in [9], the maps may have very different qualities and may also be very different: merging a very peculiar map with a poor quality might lead to deterioration of the the results instead of improving them. In this section, two strategies are presented to leverage this problem.…”

“…1. the similarity strategy: following an idea similar to [9], the maps are merged by similarity: the merging process is initialized with the best map: M * ,1 ← M (1) . Then, this map is merged only with the maps that resemble this reference map.…”

“…This paper addresses the issue of aggregating several results of the SOM algorithm, all obtained on the same data set. Several attempts to combine SOMs while preserving their topological properties have been proposed in the literature [5][6][7][8][9]. In this paper, we present a novel method to combine several SOMs while preserving their topology.…”