Download Advances in Self-Organizing Maps: 9th International by Barbara Hammer, Andrej Gisbrecht, Alexander Schulz (auth.), PDF

By Barbara Hammer, Andrej Gisbrecht, Alexander Schulz (auth.), Pablo A. Estévez, José C. Príncipe, Pablo Zegers (eds.)

Self-organizing maps (SOMs) have been constructed via Teuvo Kohonen within the early eighties. considering then greater than 10,000 works were in line with SOMs. SOMs are unsupervised neural networks helpful for clustering and visualization reasons. Many SOM functions were built in engineering and technological know-how, and different fields.

This booklet includes refereed papers provided on the 9th Workshop on Self-Organizing Maps (WSOM 2012) held on the Universidad de Chile, Santiago, Chile, on December 12-14, 2012. The workshop introduced jointly researchers and practitioners within the box of self-organizing platforms. one of the ebook chapters there are very good examples of using SOMs in agriculture, laptop technology, facts visualization, overall healthiness structures, economics, engineering, social sciences, textual content and photo research, and time sequence research. different chapters current the most recent theoretical paintings on SOMs in addition to studying Vector Quantization (LVQ) tools.

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Additional info for Advances in Self-Organizing Maps: 9th International Workshop, WSOM 2012 Santiago, Chile, December 12-14, 2012 Proceedings

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Fig. 3. (a) Each of the coordinates (Fig. 2) of the A ring are on the spherical surface, and the arrow starts and ends in A(0,1,z). (b) each of the coordinates (Fig. 2) on the B ring are on the spherical surface, and the arrow starts and ends in B(x,0,0). 38 M. Ohkita et al. Fig. 4. (a) the starting (blue) and (b) the end (black) position in Fig. 3 (a) (b) Fig. 5. Representation obtained when Fig. 4 is stretched to one dimension. In panels (a) and (b), the labels A and B, are the corresponding positions of start (left blue circled) and end (right black circled).

LabelSOM [19] maps each example in a labeling set to the example’s closest matching neuron. Based on each neuron’s mapped examples, attributes are chosen and combined with the attribute’s mean value over the mapped examples, to form sub-labels. Neurons with no mapped examples are not labeled, which becomes problematic when labeling sets are sparse and maps are large. Azcarraga et al. [4] propose a method similar to LabelSOM, but label clusters of neurons uniformly using attribute-value pairs selected from labeling examples that map to these clusters.

We show that for differentiable kernel this approach can be formulated as an online learning scheme. Hence, PCA can be explicitly carried out in the data space but now equipped with a non-Euclidean metric. Moreover, the theoretical framework can be extended to principal component learning in Banach spaces based on semi-inner products. This becomes particularly important when learning in lp -norm spaces with p =2 is considered. In this contribution we focus on the mathematics and theoretical justification of the approach.

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