We propose a new type of Self-Organizing Map (SOM) that is based on discretizations of curved, non-euclidean spaces. As an introductory example, we brieey discuss \spherical SOMs" on tesselations of the sphere for the display of directional data. We then describe the construction of \hyperbolic SOMs", using regular tesselations of the hyperbolic plane, which is a non-euclidean space characteriz...

Various forms of the self-organizing map (SOM) have been proposed as models of cortical development [Choe Y., Miikkulainen R., (2004). Contour integration and segmentation with self-organized lateral connections. Biological Cybernetics, 90, 75-88; Kohonen T., (2001). Self-organizing maps (3rd ed.). Springer; Sirosh J., Miikkulainen R., (1997). Topographic receptive fields and patterned lateral ...

Thus far, the success of capturing and classifying temporal information with neural networks has been limited. Our methodology adds a spatio-temporal coupling to the Self-Organized Feature Map (SOFM) which creates temporally and spatially localized neighborhoods in the map. The spatio-temporal coupling is based on traveling waves of activity starting at each winning node which are naturally att...

This paper describes a method for identifying Ontology components by using Self-Organizing Maps. Our system represents the knowledge contained in a particular digital archive by assembling and displaying the ontologies components. This novel approach provides an alternative solution to the problem of classifying on-line information and retrieval, support mechanisms that explore domains, and all...

Kohonen's self-organizing map bears large potentials as a universal tool of nonlinear data analysis. From the practical point of view control parameters like the learning rate and the neighborhood width need special attention in order to exploit the possibilities of the approach. Our paper introduces second order learning methods which generalize the dynamics of Kohonen's learning algorithm in ...

The original Kohonen's Self-Organizing Map model has been extended by several authors to incorporate an underlying probability distribution. These proposals assume mixtures of Gaussian probability densities. Here we present a new self-organizing model which is based on a mixture of multivariate Student-t components. This improves the robustness of the map against outliers, while it includes the...

SFI WORKING PAPER: 1998-07-066 SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peer-reviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for papers by our external faculty, papers must be based on work done at ...

Clustering time series has become in recent years a topic of great interest in a wide range of fields. The several approaches differ mainly in their notion of similarity (for a review see Focardi, 2001). Most researches use the Euclidean distance or some variation of it because of its easy implementation, even if it is very sensitive to temporal axis alignment. Furthermore, there are many appli...

A major problem in connectionist phonetic acoustic decoding is the way to present acoustic signal to the network. Neurobiological data about the inner ear and the primary auditory cortex can be very helpful but are rare. On the other hand, other biological works have shown that structure and functioning of the visual cortex, which have been extensively studied, are very close to the structure a...