64 research outputs found
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
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 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
Dendritic inhibition enhances neural coding properties.
The presence of a large number of inhibitory contacts at the soma and axon
initial segment of cortical pyramidal cells has inspired a large and influential
class of neural network model which use post-integration lateral inhibition as a
mechanism for competition between nodes. However, inhibitory synapses also
target the dendrites of pyramidal cells. The role of this dendritic inhibition
in competition between neurons has not previously been addressed. We
demonstrate, using a simple computational model, that such pre-integration
lateral inhibition provides networks of neurons with useful representational and
computational properties which are not provided by post-integration
inhibition
Principles for Shape Sonification
Hermann T. Principles for Shape Sonification. Empirical Musicology Review. 2013;8(2):88-91.This commentary starts with a critical reflection on Jensenius and Godøy’s sonomotiongrams as a sonification technique to represent movement shapes. Based on this we propose alternative mappings that require less information reduction. Furthermore, design criteria such as invariance, convergence, and stability are presented and applied to sonomotiongrams. Finally, we formulate necessary conditions for sonifications of movement shapes to support the perception and categorization of shapes, and we propose an experimental procedure to assess and compare movement shapes from auditory representations
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
Principal manifolds and graphs in practice: from molecular biology to dynamical systems
We present several applications of non-linear data modeling, using principal
manifolds and principal graphs constructed using the metaphor of elasticity
(elastic principal graph approach). These approaches are generalizations of the
Kohonen's self-organizing maps, a class of artificial neural networks. On
several examples we show advantages of using non-linear objects for data
approximation in comparison to the linear ones. We propose four numerical
criteria for comparing linear and non-linear mappings of datasets into the
spaces of lower dimension. The examples are taken from comparative political
science, from analysis of high-throughput data in molecular biology, from
analysis of dynamical systems.Comment: 12 pages, 9 figure
Pre-integration lateral inhibition enhances unsupervised learning
A large and influential class of neural network architectures use
post-integration lateral inhibition as a mechanism for competition. We argue
that these algorithms are computationally deficient in that they fail to
generate, or learn, appropriate perceptual representations under certain
circumstances. An alternative neural network architecture is presented in which
nodes compete for the right to receive inputs rather than for the right to
generate outputs. This form of competition, implemented through pre-integration
lateral inhibition, does provide appropriate coding properties and can be used
to efficiently learn such representations. Furthermore, this architecture is
consistent with both neuro-anatomical and neuro-physiological data. We thus
argue that pre-integration lateral inhibition has computational advantages over
conventional neural network architectures while remaining equally biologically
plausible
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