multidimensional scaling and kohonen's self-organizing maps

56738874436511 22FIG. 2. The two-dimensional representations of the 8 points of the 3D cube obtained bySOM (left) with a 20 x 20 neuron map, a training of 10000 cycles, a nal quantization errorof 0.001 and stress 0.321, MDS (right) has the nal stress value 0.246 after 22 iterations.135 10 141613614129191 2154105124 31111328168 7 157 6FIG. 3. The two-dimensional representations of the 16 points of the 4D hypercube obtainedby SOM (left) with a 20 x 20 neurons map, a training of 10000 cycles, quantizationerror of 0.001, stress value 0.327, MDS (right) has the nal stress of 0.312 after 18 iterations.292526 3031 16 322826182231 2719233 7913101415 12112730101426151152118226 27 317 1 4 82419232029 25 17 211391 528321216242084FIG. 4. The two-dimensional representations of the 32 points of the 5D hypercube obtainedby SOM (left) with a 20 x 20 neurons map, a training of 10000 cycles, the stress valueof 0.353 and by MDS (right) with a nal stress of 0.333 after 18 iterations.In gures 2-4 all corners of the hypercube that are adjacent toeach other areconnected by lines. All these lines should be short but SOM tries to use all neurons