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

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

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

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

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

Some Further Evidence about Magnification and Shape in Neural Gas

Neural gas (NG) is a robust vector quantization algorithm with a well-known mathematical model. According to this, the neural gas samples the underlying data distribution following a power law with a magnification exponent that depends on data dimensionality only. The effects of shape in the input data distribution, however, are not entirely covered by the NG model above, due to the technical difficulties involved. The experimental work described here shows that shape is indeed relevant in determining the overall NG behavior; in particular, some experiments reveal richer and complex behaviors induced by shape that cannot be explained by the power law alone. Although a more comprehensive analytical model remains to be defined, the evidence collected in these experiments suggests that the NG algorithm has an interesting potential for detecting complex shapes in noisy datasets

Magnitude Sensitive Competitive Neural Networks

En esta Tesis se presentan un conjunto de redes neuronales llamadas Magnitude Sensitive Competitive Neural Networks (MSCNNs). Se trata de un conjunto de algoritmos de Competitive Learning que incluyen un término de magnitud como un factor de modulación de la distancia usada en la competición. Al igual que otros métodos competitivos, MSCNNs realizan la cuantización vectorial de los datos, pero el término de magnitud guía el entrenamiento de los centroides de modo que se representan con alto detalle las zonas deseadas, definidas por la magnitud. Estas redes se han comparado con otros algoritmos de cuantización vectorial en diversos ejemplos de interpolación, reducción de color, modelado de superficies, clasificación, y varios ejemplos sencillos de demostración. Además se introduce un nuevo algoritmo de compresión de imágenes, MSIC (Magnitude Sensitive Image Compression), que hace uso de los algoritmos mencionados previamente, y que consigue una compresión de la imagen variable según una magnitud definida por el usuario. Los resultados muestran que las nuevas redes neuronales MSCNNs son más versátiles que otros algoritmos de aprendizaje competitivo, y presentan una clara mejora en cuantización vectorial sobre ellos cuando el dato está sopesado por una magnitud que indica el ¿interés¿ de cada muestra

Integrated modulation of sympathetic tone in the microcirculation by oxygen, adenosine, and nitric oxide

Despite a profound reduction in hemodynamic shear stress, a sustained release of endothelium-derived nitric oxide (NO) limits arteriolar constriction during periods of increased sympathetic nerve activity in the rat small intestine. In this project, we sought to test the hypothesis that adenosine, formed in response to a flow-dependent fall in local PO2, serves as the stimulus to preserve endothelial NO release under these conditions. Sympathetic nerve stimulation induced frequency-dependent arteriolar constrictions and a flow-dependent fall in local PO2. The arteriolar responses to nerve stimulation were enhanced after inhibition of NO synthase with NG-monomethyl-L-arginine (L-NMMA). Under a high (20%) O2 superfusate, the fall in local PO2 during nerve stimulation was significantly attenuated, arteriolar constrictions were significantly increased, and these responses were no longer sensitive to L-NMMA. Treatment with adenosine deaminase (2.0 U/ml) or the selective A1 receptor antagonist 8-cyclopentyl-1,3-dipropylxanthine (4 x 10-4 M) completely blocked the enhancing effect of L-NMMA on sympathetic constriction. In the presence of the 5\u27-ectonucleotidase inhibitor alpha,beta-methyleneadenosine 5\u27-diphosphate (4.5 x 10-5 M), the enhancing effects of L-NMMA and the high-O2 superfusate on sympathetic constriction were preserved. None of these treatments had an effect on vascular smooth muscle responsiveness to NO (as judged by arteriolar responses to sodium nitroprusside). The high-O 2 superfusate also did not lead to the generation of reactive oxygen species in the arteriolar wall (as determined by the reduction of tetranitroblue tetrazolium dye). In conclusion, these results suggest that a flow-dependent fall in arteriolar wall and/or tissue PO2 leads to the release of intracellularly-formed adenosine, which, through its interaction with endothelial A1 receptors, stimulates NO release during neurogenic constriction in this vascular bed

Sensor fusion in distributed cortical circuits

The substantial motion of the nature is to balance, to survive, and to reach perfection. The evolution in biological systems is a key signature of this quintessence. Survival cannot be achieved without understanding the surrounding world. How can a fruit fly live without searching for food, and thereby with no form of perception that guides the behavior? The nervous system of fruit fly with hundred thousand of neurons can perform very complicated tasks that are beyond the power of an advanced supercomputer. Recently developed computing machines are made by billions of transistors and they are remarkably fast in precise calculations. But these machines are unable to perform a single task that an insect is able to do by means of thousands of neurons. The complexity of information processing and data compression in a single biological neuron and neural circuits are not comparable with that of developed today in transistors and integrated circuits. On the other hand, the style of information processing in neural systems is also very different from that of employed by microprocessors which is mostly centralized. Almost all cognitive functions are generated by a combined effort of multiple brain areas. In mammals, Cortical regions are organized hierarchically, and they are reciprocally interconnected, exchanging the information from multiple senses. This hierarchy in circuit level, also preserves the sensory world within different levels of complexity and within the scope of multiple modalities. The main behavioral advantage of that is to understand the real-world through multiple sensory systems, and thereby to provide a robust and coherent form of perception. When the quality of a sensory signal drops, the brain can alternatively employ other information pathways to handle cognitive tasks, or even to calibrate the error-prone sensory node. Mammalian brain also takes a good advantage of multimodal processing in learning and development; where one sensory system helps another sensory modality to develop. Multisensory integration is considered as one of the main factors that generates consciousness in human. Although, we still do not know where exactly the information is consolidated into a single percept, and what is the underpinning neural mechanism of this process? One straightforward hypothesis suggests that the uni-sensory signals are pooled in a ploy-sensory convergence zone, which creates a unified form of perception. But it is hard to believe that there is just one single dedicated region that realizes this functionality. Using a set of realistic neuro-computational principles, I have explored theoretically how multisensory integration can be performed within a distributed hierarchical circuit. I argued that the interaction of cortical populations can be interpreted as a specific form of relation satisfaction in which the information preserved in one neural ensemble must agree with incoming signals from connected populations according to a relation function. This relation function can be seen as a coherency function which is implicitly learnt through synaptic strength. Apart from the fact that the real world is composed of multisensory attributes, the sensory signals are subject to uncertainty. This requires a cortical mechanism to incorporate the statistical parameters of the sensory world in neural circuits and to deal with the issue of inaccuracy in perception. I argued in this thesis how the intrinsic stochasticity of neural activity enables a systematic mechanism to encode probabilistic quantities within neural circuits, e.g. reliability, prior probability. The systematic benefit of neural stochasticity is well paraphrased by the problem of Duns Scotus paradox: imagine a donkey with a deterministic brain that is exposed to two identical food rewards. This may make the animal suffer and die starving because of indecision. In this thesis, I have introduced an optimal encoding framework that can describe the probability function of a Gaussian-like random variable in a pool of Poisson neurons. Thereafter a distributed neural model is proposed that can optimally combine conditional probabilities over sensory signals, in order to compute Bayesian Multisensory Causal Inference. This process is known as a complex multisensory function in the cortex. Recently it is found that this process is performed within a distributed hierarchy in sensory cortex. Our work is amongst the first successful attempts that put a mechanistic spotlight on understanding the underlying neural mechanism of Multisensory Causal Perception in the brain, and in general the theory of decentralized multisensory integration in sensory cortex. Engineering information processing concepts in the brain and developing new computing technologies have been recently growing. Neuromorphic Engineering is a new branch that undertakes this mission. In a dedicated part of this thesis, I have proposed a Neuromorphic algorithm for event-based stereoscopic fusion. This algorithm is anchored in the idea of cooperative computing that dictates the defined epipolar and temporal constraints of the stereoscopic setup, to the neural dynamics. The performance of this algorithm is tested using a pair of silicon retinas