5,276 research outputs found
Self-Organizing Time Map: An Abstraction of Temporal Multivariate Patterns
This paper adopts and adapts Kohonen's standard Self-Organizing Map (SOM) for
exploratory temporal structure analysis. The Self-Organizing Time Map (SOTM)
implements SOM-type learning to one-dimensional arrays for individual time
units, preserves the orientation with short-term memory and arranges the arrays
in an ascending order of time. The two-dimensional representation of the SOTM
attempts thus twofold topology preservation, where the horizontal direction
preserves time topology and the vertical direction data topology. This enables
discovering the occurrence and exploring the properties of temporal structural
changes in data. For representing qualities and properties of SOTMs, we adapt
measures and visualizations from the standard SOM paradigm, as well as
introduce a measure of temporal structural changes. The functioning of the
SOTM, and its visualizations and quality and property measures, are illustrated
on artificial toy data. The usefulness of the SOTM in a real-world setting is
shown on poverty, welfare and development indicators
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
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
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
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
Evolutionary Neural Gas (ENG): A Model of Self Organizing Network from Input Categorization
Despite their claimed biological plausibility, most self organizing networks
have strict topological constraints and consequently they cannot take into
account a wide range of external stimuli. Furthermore their evolution is
conditioned by deterministic laws which often are not correlated with the
structural parameters and the global status of the network, as it should happen
in a real biological system. In nature the environmental inputs are noise
affected and fuzzy. Which thing sets the problem to investigate the possibility
of emergent behaviour in a not strictly constrained net and subjected to
different inputs. It is here presented a new model of Evolutionary Neural Gas
(ENG) with any topological constraints, trained by probabilistic laws depending
on the local distortion errors and the network dimension. The network is
considered as a population of nodes that coexist in an ecosystem sharing local
and global resources. Those particular features allow the network to quickly
adapt to the environment, according to its dimensions. The ENG model analysis
shows that the net evolves as a scale-free graph, and justifies in a deeply
physical sense- the term gas here used.Comment: 16 pages, 8 figure
Somoclu: An Efficient Parallel Library for Self-Organizing Maps
Somoclu is a massively parallel tool for training self-organizing maps on
large data sets written in C++. It builds on OpenMP for multicore execution,
and on MPI for distributing the workload across the nodes in a cluster. It is
also able to boost training by using CUDA if graphics processing units are
available. A sparse kernel is included, which is useful for high-dimensional
but sparse data, such as the vector spaces common in text mining workflows.
Python, R and MATLAB interfaces facilitate interactive use. Apart from fast
execution, memory use is highly optimized, enabling training large emergent
maps even on a single computer.Comment: 26 pages, 9 figures. The code is available at
https://peterwittek.github.io/somoclu
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