Winner-relaxing and winner-enhancing Kohonen maps: Maximal mutual information from enhancing the winner

The magnification behaviour of a generalized family of self-organizing feature maps, the Winner Relaxing and Winner Enhancing Kohonen algorithms is analyzed by the magnification law in the one-dimensional case, which can be obtained analytically. The Winner-Enhancing case allows to acheive a magnification exponent of one and therefore provides optimal mapping in the sense of information theory. A numerical verification of the magnification law is included, and the ordering behaviour is analyzed. Compared to the original Self-Organizing Map and some other approaches, the generalized Winner Enforcing Algorithm requires minimal extra computations per learning step and is conveniently easy to implement.Comment: 6 pages, 5 figures. For an extended version refer to cond-mat/0208414 (Neural Computation 17, 996-1009

Winner-Relaxing Self-Organizing Maps

A new family of self-organizing maps, the Winner-Relaxing Kohonen Algorithm, is introduced as a generalization of a variant given by Kohonen in 1991. The magnification behaviour is calculated analytically. For the original variant a magnification exponent of 4/7 is derived; the generalized version allows to steer the magnification in the wide range from exponent 1/2 to 1 in the one-dimensional case, thus provides optimal mapping in the sense of information theory. The Winner Relaxing Algorithm requires minimal extra computations per learning step and is conveniently easy to implement.Comment: 14 pages (6 figs included). To appear in Neural Computatio

Magnification Control in Self-Organizing Maps and Neural Gas

We consider different ways to control the magnification in self-organizing maps (SOM) and neural gas (NG). Starting from early approaches of magnification control in vector quantization, we then concentrate on different approaches for SOM and NG. We show that three structurally similar approaches can be applied to both algorithms: localized learning, concave-convex learning, and winner relaxing learning. Thereby, the approach of concave-convex learning in SOM is extended to a more general description, whereas the concave-convex learning for NG is new. In general, the control mechanisms generate only slightly different behavior comparing both neural algorithms. However, we emphasize that the NG results are valid for any data dimension, whereas in the SOM case the results hold only for the one-dimensional case.Comment: 24 pages, 4 figure

Magnification Control in Winner Relaxing Neural Gas

An important goal in neural map learning, which can conveniently be accomplished by magnification control, is to achieve information optimal coding in the sense of information theory. In the present contribution we consider the winner relaxing approach for the neural gas network. Originally, winner relaxing learning is a slight modification of the self-organizing map learning rule that allows for adjustment of the magnification behavior by an a priori chosen control parameter. We transfer this approach to the neural gas algorithm. The magnification exponent can be calculated analytically for arbitrary dimension from a continuum theory, and the entropy of the resulting map is studied numerically conf irming the theoretical prediction. The influence of a diagonal term, which can be added without impacting the magnification, is studied numerically. This approach to maps of maximal mutual information is interesting for applications as the winner relaxing term only adds computational cost of same order and is easy to implement. In particular, it is not necessary to estimate the generally unknown data probability density as in other magnification control approaches.Comment: 14pages, 2 figure

Extranoematic artifacts: neural systems in space and topology

During the past several decades, the evolution in architecture and engineering went through several stages of exploration of form. While the procedures of generating the form have varied from using physical analogous form-finding computation to engaging the form with simulated dynamic forces in digital environment, the self-generation and organization of form has always been the goal. this thesis further intend to contribute to self-organizational capacity in Architecture. The subject of investigation is the rationalizing of geometry from an unorganized point cloud by using learning neural networks. Furthermore, the focus is oriented upon aspects of efficient construction of generated topology. Neural network is connected with constraining properties, which adjust the members of the topology into predefined number of sizes while minimizing the error of deviation from the original form. The resulted algorithm is applied in several different scenarios of construction, highlighting the possibilities and versatility of this method

Investigation of topographical stability of the concave and convex Self-Organizing Map variant

We investigate, by a systematic numerical study, the parameter dependence of the stability of the Kohonen Self-Organizing Map and the Zheng and Greenleaf concave and convex learning with respect to different input distributions, input and output dimensions

Unsupervised Understanding of Location and Illumination Changes in Egocentric Videos

Wearable cameras stand out as one of the most promising devices for the upcoming years, and as a consequence, the demand of computer algorithms to automatically understand the videos recorded with them is increasing quickly. An automatic understanding of these videos is not an easy task, and its mobile nature implies important challenges to be faced, such as the changing light conditions and the unrestricted locations recorded. This paper proposes an unsupervised strategy based on global features and manifold learning to endow wearable cameras with contextual information regarding the light conditions and the location captured. Results show that non-linear manifold methods can capture contextual patterns from global features without compromising large computational resources. The proposed strategy is used, as an application case, as a switching mechanism to improve the hand-detection problem in egocentric videos.Comment: Submitted for publicatio