The self-organizing map (SOM) method is a new, powerful software tool for the visualization of high-dimensional data. It converts complex, nonlinear statistical relationships between high-dimensional data into simple geometric relationships on a low-dimensional display. As it thereby compresses information while preserving the most important topological and metric relationships of the primary data elements on the display, it may also be thought to produce some kind of abstractions. The term self-organizing map signifies a class of mappings defined by error-theoretic considerations. In practice they result in certain unsupervised, competitive learning processes, computed by simple-looking SOM algorithms. Many industries have found the SOM-based software tools useful. The most important property of the SOM, orderliness of the input-output mapping, can be utilized for many tasks: reduction of the amount of training data, speeding up learning nonlinear interpolation and extrapolation, generalization, and effective compression of information for its transmission.

Engineering applications of the self-organizing map

The Self-Organizing Map (SOM) algorithm has attracted an ever increasing amount of interest among researches and practitioners in a wide variety of elds The SOM and a variant of it, the LVQ, have been analyzed extensively, a number of variants of them have been developed and, perhaps most notably, they have been applied extensively within elds ranging from engineering sciences to medicine, biology, and economics We have collected a comprehensive list of 3343 scienti c papers that use the algorithms, have bene ted from them, or contain analyses of them The list is intended to serve as a source for literature surveys We have provided both a thematic and a keyword index to help nding articles of interest

Bibliography of Self-Organizing Map (SOM) Papers: 1981-1997

We present a modification of Kohonens SOFMin order to simulate cortical plasticity induced by coactivation patterns. This is accomplished by introducing a probabilistic mode of stimulus presentation and by substituting the winner-takes- all mechanism by selecting the winner from a set of best matching neurons.

Modification of Kohonen's SOFM to Simulate Cortical Plasticity Induced by Coactivation Input Patterns

Developments and applications of the self-organizing map and related algorithms

The self-organizing Kohonen map is a reliable and efficient way to achieve vector quantization. Typical application of such algorithm is image compression. Moreover, Kohonen networks realize a mapping between an input and an output space that preserves topology. This feature can be used to build new compression schemes which allow to obtain better compression rate than with classical method as JPEG without reducing the image quality. Compared to JPEG, our lossy compression scheme shows better performances (in terms of PSNR) for compression rates higher than 30 [C. Amerijckx, M. Verleysen, P. Thissen and J.-D. Legat (1998). Image compression by self-organized Kohonen map. IEEE Transactions on Neural Networks, 9(3), 503-507.]. For lossless compression, this rate is about 2.7 for standard images.

/pdf/image-compression-using-self-organizing-maps-1u85e3e8te.pdf

Image compression using self-organizing maps

The implicit ordering in scalar quantization is used to substantiate the need for explicit ordering in vector quantization and the ordering of Kohonen's neural net vector quantizer is shown to provide a multidimensional analog to this scalar quantization ordering. Ordered vector quantization, using Kohonen's neural net, was successfully applied to image coding and was then shown to be advantageous for progressive transmission. In particular, the intermediate images had a signal-to-noise ratio that was quite close to a standard tree-structured vector quantizer, while the final full-fidelity image from the neural net vector quantizer was superior to the tree-structured vector quantizer. Subsidiary results include a new definition of index of disorder which was empirically found to correlate strongly with the progressive reduction of image signal-to-noise ratio and a hybrid neural net-generalized Lloyd training algorithm which has a high final image signal-to-noise ratio while still maintaining ordering. >

http://ieeexplore.ieee.org/iel2/574/6142/00239487.pdf

Ordered neural maps and their applications to data compression

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Ordered neural maps and their applications to data compression