About SOMs:
 SOMs
at First Glance
At first glance a self-organizing map might look something like a flow
chart. Or a constellation diagram. Or perhaps a set of local voting district
boundaries.
What it probably won't resemble is a geographic map (although
there are exceptions). Unlike cartographers, who map existing geography,
SOMs do not replace an existing real geography (such as the planet viewed
from space) with a geographical representation (Mercator projection
covered with imagined political boundaries, elevation and climate data,
etc.) Rather, while processing data which is distributed temporally or
conceptually, SOMs create an imagined geography in which the data
is presented.[2]
Most SOMs currently tend to be two-dimensional. Unlike a Cartesian graph,
however, in which two-dimensional data relate in accordance with the variation
of only 2 variables (X and Y), positionality within the flat space of
the map may be representative of a wide variety variables synthesized
into a general statement of relationship - for example, the relative size
and distance map-objects rather than their absolute positions.
SOMs generally present a simplified, relational view of a highly complex
data set.
Once map objects or nodes are organized, all the data associated with
a given node may be made available via that node. However this does not
mean that all this data participated in the process of self-organization.
A data set of nations might self-organize by annual rainfall, and once
organized provide additional information such as color-coding by GNP.
SOMs
and the Internet
Merely representing rainfall data dynamically is not an SOM. The most
common current application of representing map-data is much simpler.
Data-driven maps (DDMs) are part of a general move on the Internet to
make all things data-driven. Rather than porting static data from one
machine to another across Internet lines, the servers on which the data
resides to take part - processing, presenting, and representing the data
dynamically. Something is "data-driven" precisely if its contents
are filled in by one of these server-side processes.
Hence a map of total annual rainfall in the United States is data-driven
if it is supplied from a database on the server, and changes dynamically
as the data is updated or revised. However while the contents of the DDM
are dynamic, the form is static - a fixed output map with a fixed data
structure behind it varies numbers and plugs them into unvarying slots.
SOMs is one in which the system of relation and presentation itself is
generated from the data encountered - data-driven form as well as data-driven
content. However it is not self-organizing unless its form also changes
as the contents change.
This project postulates that our information systems in general (with
the Internet as a whole the primary example) are leaving a static stage
and entering a data-driven stage, in which data-driven maps are emerging
as key infrastructure. While self-organizing systems remain limited in
both use and implementation, I'll anticipate my conclusions here by asserting
that we must move from this data-driven stage to an increasingly self-organizing
stage, during which self-organizing maps will be key to negotiating our
increasingly large and increasingly complex data structures.
SOMs
and Computer Science
As a topic of ongoing research in contemporary
computer science, it is important to position SOMs in the field, even
if that is not the main focus of this site.
Artificial Intelligence: Lying mostly
within the field of Computer / Information Science is the branch of Artificial
Intelligence (AI). Its goal is to develop electronic devices that can
operate with some of the characteristics of human intelligence. Among
these properties are logical deduction and inference, creativity, the
ability to make decisions based on past experience or insufficient or
conflicting information, and the ability to understand natural language.
One of the earliest goals of AI research
was machine translation of natural languages. Although this effort has
attracted a great deal of attention, it has never progressed beyond a
rudimentary and mostly unreliable stage, because few researchers have
been prepared to recognize the enormous complexity and subtlety of human
language. More recent work in the modeling and emulation of neural networks
and in speech recognition has shown more promise.
Although many of the early hopes of AI have yet to be fulfilled, this
fact in itself has helped to reveal how much still remains to be understood
about the processes of human thought and intelligence.
Compact American Dictionary of Computer Words. Copyright © 1995,
1998 by Houghton Mifflin Company. All rights reserved.
Neural Networks: A modeling technique
based on the observed behavior of biological neurons and used to mimic
the performance of a system. It consists of a set of elements that start
out connected in a random pattern, and, based upon operational feedback,
are molded into the pattern required to generate the required results.
It is used in applications such as robotics, diagnosing, forecasting,
image processing and pattern recognition.
Computer Desktop Encyclopedia. © 2001 Computer Language Company
Inc. All rights reserved.
(Full term is Artificial Neural Network (ANN), also neural net.)
[more]
Kohonen Network: One of the basic
examples of a Neural Network, named for its inventor Teuvo Kohonen. The
system adapts over a number of iterations using an operational feedback
process Kohonen termed Learned Vector Quantization.
Learned Vector Quantization: A type
of neural network consisting of a set of vectors, the positions of which
are optimized with respect to a given dataset. The network consists of
an input and output layer, with vectors storing the connection weights
leading from input to output neurons.
The learning method of learning vector quantization is also called "competition
learning." For each training pattern cycle an input neuron finds
the closest vector, and selects the corresponding output neuron as the
"winner neuron." The weights of the connection to the winner
is then adapted - either closer to or farther away from the training pattern,
based on the class of the neuron.
This movement is controlled by a learning rate parameter. It states
(as a fraction of the distance to the training pattern) how far the the
reference vector is moved. Usually the learning rate is decreased in the
course of time, so that initial changes are larger than changes made in
later epochs of the training process. Learning may be terminated when
the positions of the reference vectors hardly change anymore.
Adapted from: Learning Vector Quantization Visualization. ©
2000 Christian Borgelt. [More]
[diagrams]
Self-Organizing Systems (SOSs): Essentially
a synonym for Kohonen Networks, although applied more broadly to all subsequent
refinement on and variations of Kohonen Networks.
Self-Organizing Maps (SOMs): The visual
display of SOS results, the more widely used term for the entire process.
Sometimes called Kohonen feature maps. [intro]
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