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Topology-oriented self-organizing maps: a survey

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Abstract

The self-organizing map (SOM) is a prominent neural network model that has found wide application in a spectrum of domains. Accordingly, it has received widespread attention both from the communities of researchers and practitioners. As a result, several variations of the basic architecture have been devised, specifically in the early years of the SOM’s evolution, which were introduced so as to address various architectural shortcomings or to explore other structures of the basic model. The overall goal of this survey is to present a comprehensive comparison of these networks, in terms of their primitive components and properties. We dichotomize these schemes as being either tree based or non-tree based. We have embarked on this venture with the hope that since the survey is comprehensive and the bibliography extensive, it will be an asset and resource for future researchers.

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Notes

  1. The paper contains, without a detailed explanation, a list of some of the applications of the SOM.

  2. During the doctoral research of the first author, we tried, in vain, to locate a single comprehensive refereed survey of the families of topology-based SOMs. This motivated the present work, and we hope that it is appreciated by the research community.

  3. When we first introduced the principles of the SOM, we had mentioned the fact that different norms can be used for its training phase. The reader should note, however, that this must also be reflected in the calculation of the quantization error at the unit level. Indeed, one cannot use a specific norm for calculating the activation of the neurons and for determining the BMU, and subsequently utilize a different one for measuring the quantization characteristics of the map.

  4. Boundary neurons are described in Sect. 3.4.

  5. Other topological structures have been also reported for the SOM, such as the spherical topology reported in [52, 66].

  6. Even though in the GHTSOM each neuron is represented by hyper-tetrahedrons, we have decided to classify it as being SOM layered to stress that each neuron of the tree is a layer, as explained above.

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Acknowledgments

We record our gratitude to the Associate Editor and anonymous referees of the original version of this paper for their painstaking reviews. The changes that they requested certainly improved the quality of this paper. The work of César A. Astudillo was partially supported by the FONDECYT Grant 11121350, Chile. The work of B. John Oommen was partially supported by NSERC, the Natural Sciences and Engineering Research Council of Canada.

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Correspondence to César A. Astudillo.

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Chancellor's Professor; Fellow: IEEE and Fellow: IAPR. B. John Oommen also an Adjunct Professor with the University of Agder in Grimstad, Norway.

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Astudillo, C.A., Oommen, B.J. Topology-oriented self-organizing maps: a survey. Pattern Anal Applic 17, 223–248 (2014). https://doi.org/10.1007/s10044-014-0367-9

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