By Barbara Hammer, Andrej Gisbrecht, Alexander Schulz (auth.), Pablo A. Estévez, José C. Príncipe, Pablo Zegers (eds.)
Self-organizing maps (SOMs) have been built by way of Teuvo Kohonen within the early eighties. when you consider that then greater than 10,000 works were in accordance with SOMs. SOMs are unsupervised neural networks helpful for clustering and visualization reasons. Many SOM functions were built in engineering and technology, and different fields.
This ebook comprises 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 publication chapters there are very good examples of using SOMs in agriculture, laptop technological know-how, facts visualization, healthiness platforms, economics, engineering, social sciences, textual content and snapshot research, and time sequence research. different chapters current the most recent theoretical paintings on SOMs in addition to studying Vector Quantization (LVQ) equipment.
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Additional info for Advances in Self-Organizing Maps: 9th International Workshop, WSOM 2012 Santiago, Chile, December 12-14, 2012 Proceedings
Here, we apply it to the chain-link problem  considered to be notoriously difficult, and to the problem of the separation of stacked random number planes . 1 The Comparison of the Results Obtained with the XOM Method and the Spherical SOM for a Benchmark Problem The benchmark problem consists of two rings (links) (Fig. 1(a)) with a distance d from each other and intersecting vertically in the three-dimensional space. A. Estévez et al. ): Advances in Self-Organizing Maps, AISC 198, pp. 35–44.
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.  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. The technique largely overcomes LabelSOM’s unlabeled neuron problem.
The mapping Φ is called feature map and H the feature space of V . Without further restrictions on the kernel κΦ , both, H and Φ are not unique. Positive kernels are of special interest because they uniquely correspond to a reproducing kernel Hilbert spaces (RKHS) H in a canonical manner [1,14]. The kernel κΦ is said to be positive deﬁnite if for all ﬁnite subsets Vm ⊆ V with cardinality #Vm = m, the Gram-Matrix Gm = [κ (vi , vj ) : i, j = 1 . . m] (16) is positive semi-deﬁnite . The norm Φ(v) RKHS induces a metric dH (Φ(v), Φ(w)) = H = κΦ (Φ(v), Φ(v)) of this κΦ (v, v) − 2κΦ (v, w) + κΦ (w, w) (17) based on the kernel κΦ .