9,247 research outputs found
A combined measure for quantifying and qualifying the topology preservation of growing self-organizing maps
The Self-OrganizingMap (SOM) is a neural network model that performs an ordered projection of a high dimensional input space in a low-dimensional topological structure. The process in which such mapping is formed is defined by the SOM algorithm, which is a competitive, unsupervised and nonparametric method, since it does not make any assumption about the input data distribution. The feature maps provided by this algorithm have been successfully applied for vector quantization, clustering and high dimensional data visualization processes. However, the initialization of the network topology and the selection of the SOM training parameters are two difficult tasks caused by the unknown distribution of the input signals. A misconfiguration of these parameters can generate a feature map of low-quality, so it is necessary to have some measure of the degree of adaptation of the SOM network to the input data model. The topologypreservation is the most common concept used to implement this measure. Several qualitative and quantitative methods have been proposed for measuring the degree of SOM topologypreservation, particularly using Kohonen's model. In this work, two methods for measuring the topologypreservation of the Growing Cell Structures (GCSs) model are proposed: the topographic function and the topology preserving ma
On the Topological Characterization of Near Force-Free Magnetic Fields, and the work of late-onset visually-impaired Topologists
The Giroux correspondence and the notion of a near force-free magnetic field
are used to topologically characterize near force-free magnetic fields which
describe a variety of physical processes, including plasma equilibrium. As a
byproduct, the topological characterization of force-free magnetic fields
associated with current-carrying links, as conjectured by Crager and Kotiuga,
is shown to be necessary and conditions for sufficiency are given. Along the
way a paradox is exposed: The seemingly unintuitive mathematical tools, often
associated to higher dimensional topology, have their origins in three
dimensional contexts but in the hands of late-onset visually impaired
topologists. This paradox was previously exposed in the context of algorithms
for the visualization of three-dimensional magnetic fields. For this reason,
the paper concludes by developing connections between mathematics and cognitive
science in this specific context.Comment: 20 pages, no figures, a paper which was presented at a conference in
honor of the 60th birthdays of Alberto Valli and Paolo Secci. The current
preprint is from December 2014; it has been submitted to an AIMS journa
Fast training of self organizing maps for the visual exploration of molecular compounds
Visual exploration of scientific data in life science
area is a growing research field due to the large amount of
available data. The Kohonen’s Self Organizing Map (SOM) is
a widely used tool for visualization of multidimensional data.
In this paper we present a fast learning algorithm for SOMs
that uses a simulated annealing method to adapt the learning
parameters. The algorithm has been adopted in a data analysis
framework for the generation of similarity maps. Such maps
provide an effective tool for the visual exploration of large and
multi-dimensional input spaces. The approach has been applied
to data generated during the High Throughput Screening
of molecular compounds; the generated maps allow a visual
exploration of molecules with similar topological properties.
The experimental analysis on real world data from the
National Cancer Institute shows the speed up of the proposed
SOM training process in comparison to a traditional approach.
The resulting visual landscape groups molecules with similar
chemical properties in densely connected regions
Context-aware visual exploration of molecular databases
Facilitating the visual exploration of scientific data has
received increasing attention in the past decade or so. Especially
in life science related application areas the amount
of available data has grown at a breath taking pace. In this
paper we describe an approach that allows for visual inspection
of large collections of molecular compounds. In
contrast to classical visualizations of such spaces we incorporate
a specific focus of analysis, for example the outcome
of a biological experiment such as high throughout
screening results. The presented method uses this experimental
data to select molecular fragments of the underlying
molecules that have interesting properties and uses the
resulting space to generate a two dimensional map based
on a singular value decomposition algorithm and a self organizing
map. Experiments on real datasets show that
the resulting visual landscape groups molecules of similar
chemical properties in densely connected regions
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