Many of the properties of the well-known Kohonen map algorithm are not easily derivable from its discrete formulation. For instance, the “projection” implemented by the map from a high dimensional input space to a lower dimensional map space must be properly regarded as a projection from a smooth manifold to a lattice and, in this framework, some of its property are not easily identified. This ...

We introduce a method for deriving a metric, locally based on the Fisher information matrix, into the data space. A self-organizing map (SOM) is computed in the new metric to explore financial statements of enterprises. The metric measures local distances in terms of changes in the distribution of an auxiliary random variable that reflects what is important in the data. In this paper the variab...

In this paper we deal with the problem of designing preemptive patrolling itineraries at sea. As a case study we use real data provided by the Portuguese Navy, concerning search and rescue missions. This can be seen as a curve fitting problem in which we aim at predicting future occurrences based on previous reported ones. We propose a method for the design of itineraries based on the use of a ...

A recurrent oscillatory self-organizing map (ROSOM) introduced. This is an architecture that assumes oscillatory states, assigned to all units, indicating their "readiness-tofire" or "exhaustion", and constitutes an internal timing mechanism. The architecture feeds the vector of all these states back into the input layer, making the units recognize and adapt to not only input but also to the en...

The purpose is to analyse the quarterly financial performance of telecommunications companies with the help self-organising maps. In this report the three major actors on the telecommunications market is evaluated and benchmarked on the basis of seven key ratios, calculated for seven consecutive quarters between the first quarter of year 2000 to the third quarter of year 2001. To conduct benchm...

To see how an input is encoded by a limit cycle after training, we take the open-loop spatial map as an example. Limit cycles on the other maps are qualitatively similar. The spatial map is provided with a spatial location X∗ for 2 time steps as afferent input. The activation parameter γ is fixed at 0 after training, meaning each non-winner has an activation value of 0 (inactive) while each win...

The self-organizing map (SOM) converts statistical relationships between highdimensional data into geometric relationships on a low-dimensional grid. It can thus be regarded as a projection and a similarity graph of the primary data. As it preserves the most important topological relationships of the data elements on the display, it may be thought of as producing some form of abstraction. These...

Collaboration of growing self-organizing maps (GSOM) and adaptive resonance theory maps (ART) is considered through traveling sales-person problems (TSP).The ART is used to parallelize the GSOM: it divides the input space of city positions into subspaces automatically. One GSOM is allocated to each subspace and grows following the input data. After all the GSOMs grow sufficiently they are conne...

Image segmentation is a very crucial step in the field of image processing which helps us to simplify the representation of the image, to make it easier to analyze. This paper deals with the comparison of image segmentation techniques based on unsupervised artificial neural network technique, known as Kohonen’s Self Organizing Maps (SOM). We first present image segmentation using Kohonen’s Self...