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While looking for the BMU, m2 is found closer to xi. Changing the hypersphere's centroid from m(left) to m2(right) shrinks the radius.

While looking for the BMU, m2 is found closer to xi. Changing the hypersphere's centroid from m(left) to m2(right) shrinks the radius.

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Fig. 1. Prototype vector mi where i = {4, 5, 6} cannot be BMU for xi,...
Fig. 2. While looking for the BMU, m2 is found closer to xi. Changing...
SOM Training Optimization Using Triangle Inequality
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  • Jan 2016
Triangle inequality optimization is one of several strategies on the \(k\)-means algorithm that can reduce the search space in finding the nearest prototype vector. This optimization can also be applied towards Self-Organizing Maps training, particularly during finding the best matching unit in the batch training approach. This paper investigates v...
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Context 1
... . radius for the hyper-sphere can be shrunk as illustrated in Figure 2. A smaller radius means a smaller search space. ...
Context 2
... the hyper-sphere's radius become smaller, some of the prototype vec- tors may be checked twice. For example, m 1 in Figure 2 is checked twice when the centroid is m and m 2 . Furthermore, several prototype vectors that were not inside the previous hyper-sphere may be inside the smaller hyper-sphere, as shown by m 5 in Figure 2. ...
Context 3
... example, m 1 in Figure 2 is checked twice when the centroid is m and m 2 . Furthermore, several prototype vectors that were not inside the previous hyper-sphere may be inside the smaller hyper-sphere, as shown by m 5 in Figure 2. ...

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