Show Reference: "The Self-Organizing Maps: Background, Theories, Extensions and Applications"

The Self-Organizing Maps: Background, Theories, Extensions and Applications Computational Intelligence: A Compendium In Computational Intelligence: A Compendium, Vol. 115 (2008), pp. 715-762, doi:10.1007/978-3-540-78293-3_17 by Hujun Yin edited by John Fulcher, Lakhmi C. Jain
@incollection{yin-2008,
    abstract = {For many years, artificial neural networks ({ANNs}) have been studied and used to model information processing systems based on or inspired by biological neural structures. They not only can provide solutions with improved performance when compared with traditional problem-solving methods, but also give a deeper understanding of human cognitive abilities. Among various existing neural network architectures and learning algorithms, Kohonen's selforganizing map ({SOM}) [46] is one of the most popular neural network models. Developed for an associative memory model, it is an unsupervised learning algorithm with a simple structure and computational form, and is motivated by the retina-cortex mapping. Self-organization in general is a fundamental pattern recognition process, in which intrinsic inter- and intra-pattern relationships among the stimuli and responses are learnt without the presence of a potentially biased or subjective external influence. The {SOM} can provide topologically preserved mapping from input to output spaces. Although the computational form of the {SOM} is very simple, numerous researchers have already examined the algorithm and many of its problems, nevertheless research in this area goes deeper and deeper — there are still many aspects to be exploited.
                            In this Chapter, we review the background, theories and statistical properties of this important learning model and present recent advances from various pattern recognition aspects through a number of case studies and applications. The {SOM} is optimal for vector quantization. Its topographical ordering provides the mapping with enhanced fault- and noise-tolerant abilities. It is also applicable to many other applications, such as dimensionality reduction, data visualization, clustering and classification. Various extensions of the {SOM} have been devised since its introduction to extend the mapping as effective solutions for a wide range of applications. Its connections with other learning paradigms and application aspects are also exploited. The Chapter is intended to serve as an updated, extended tutorial, a review, as well as a reference for advanced topics in the subject.},
    author = {Yin, Hujun},
    booktitle = {Computational Intelligence: A Compendium},
    doi = {10.1007/978-3-540-78293-3\_17},
    editor = {Fulcher, John and Jain, Lakhmi C.},
    journal = {Computational Intelligence: A Compendium},
    keywords = {ann, dimensionality-reduction, manifold, math, model, som},
    pages = {715--762},
    posted-at = {2013-01-14 09:20:51},
    priority = {2},
    publisher = {Springer Berlin Heidelberg},
    series = {Studies in Computational Intelligence},
    title = {The {Self-Organizing} Maps: Background, Theories, Extensions and Applications},
    url = {http://dx.doi.org/10.1007/978-3-540-78293-3\_17},
    volume = {115},
    year = {2008}
}

See the CiteULike entry for more info, PDF links, BibTex etc.

SOMs can be used as a means of learning principal manifolds.

The SOM has ancestors in von der Malsburg's "Self-Organization of Orientation Sensitive Cells in the Striate Cortex" and other early models of self-organization

The SOM is an abstraction of biologically-plausible ANN.

The SOM is an asymptotically optimal vector quantizer.

There is no cost function that the SOM algorithm follows exactly.

Quality of order in SOMs is a difficult issue because there is no unique definition of `order' in for the $n$-dimensional case if $n>2$.

Nevertheless, there have been a number of attempts.

There have been many extensions of the original SOM ANN, like

  • (Growing) Neural Gas
  • adaptive subspace SOM (ASSOM)
  • Parameterized SOM (PSOM)
  • Stochastic SOM
  • recursive and recurrent SOMs

Recursive and Recurrent SOMs have been used for mapping temporal data.

SOMs tend to have greater unit densities for points in data space with high data density. They do not follow the density strictly, however.

Manifold-mapping is important in visualization. (Think (world) map projection)