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Archive-name: ai-faq/neural-nets/part1
Last-modified: 2002-05-17
URL: ftp://ftp.sas.com/pub/neural/FAQ.html
Maintainer: saswss@unx.sas.com (Warren S. Sarle)

Copyright 1997, 1998, 1999, 2000, 2001, 2002 by Warren S. Sarle, Cary, NC,
USA. 

  ---------------------------------------------------------------
    Additions, corrections, or improvements are always welcome.
    Anybody who is willing to contribute any information,
    please email me; if it is relevant, I will incorporate it.

    The monthly posting departs around the 28th of every month.
  ---------------------------------------------------------------

This is the first of seven parts of a monthly posting to the Usenet
newsgroup comp.ai.neural-nets (as well as comp.answers and news.answers,
where it should be findable at any time). Its purpose is to provide basic
information for individuals who are new to the field of neural networks or
who are just beginning to read this group. It will help to avoid lengthy
discussion of questions that often arise for beginners. 

   SO, PLEASE, SEARCH THIS POSTING FIRST IF YOU HAVE A QUESTION
                           and
   DON'T POST ANSWERS TO FAQs: POINT THE ASKER TO THIS POSTING

The latest version of the FAQ is available as a hypertext document, readable
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All seven parts of the FAQ can be downloaded from either of the following
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   ftp://ftp.sas.com/pub/neural/FAQ.html.zip
   ftp://ftp.sas.com/pub/neural/FAQ.txt.zip

These postings are archived in the periodic posting archive on host
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can access the archives by mail server as well. Send an E-mail message to
mail-server@rtfm.mit.edu with "help" and "index" in the body on separate
lines for more information. 

For those of you who read this FAQ anywhere other than in Usenet: To read
comp.ai.neural-nets (or post articles to it) you need Usenet News access.
Try the commands, 'xrn', 'rn', 'nn', or 'trn' on your Unix machine, 'news'
on your VMS machine, or ask a local guru. WWW browsers are often set up for
Usenet access, too--try the URL news:comp.ai.neural-nets. 

The FAQ posting departs to comp.ai.neural-nets around the 28th of every
month. It is also sent to the groups comp.answers and news.answers where it
should be available at any time (ask your news manager). The FAQ posting,
like any other posting, may a take a few days to find its way over Usenet to
your site. Such delays are especially common outside of North America. 

All changes to the FAQ from the previous month are shown in another monthly
posting having the subject `changes to "comp.ai.neural-nets FAQ" -- monthly
posting', which immediately follows the FAQ posting. The `changes' post
contains the full text of all changes and can also be found at
ftp://ftp.sas.com/pub/neural/changes.txt . There is also a weekly post with
the subject "comp.ai.neural-nets FAQ: weekly reminder" that briefly
describes any major changes to the FAQ. 

This FAQ is not meant to discuss any topic exhaustively. It is neither a
tutorial nor a textbook, but should be viewed as a supplement to the many
excellent books and online resources described in Part 4: Books, data, etc..

Disclaimer: 

   This posting is provided 'as is'. No warranty whatsoever is expressed or
   implied, in particular, no warranty that the information contained herein
   is correct or useful in any way, although both are intended. 

To find the answer of question "x", search for the string "Subject: x"

========== Questions ========== 
********************************

Part 1: Introduction

   What is this newsgroup for? How shall it be used?
   Where is comp.ai.neural-nets archived?
   What if my question is not answered in the FAQ?
   May I copy this FAQ?
   What is a neural network (NN)?
   Where can I find a simple introduction to NNs?
   Are there any online books about NNs?
   What can you do with an NN and what not?
   Who is concerned with NNs?
   How many kinds of NNs exist?
   How many kinds of Kohonen networks exist? (And what is k-means?)
      VQ: Vector Quantization and k-means
      SOM: Self-Organizing Map
      LVQ: Learning Vector Quantization
      Other Kohonen networks and references
   How are layers counted?
   What are cases and variables?
   What are the population, sample, training set, design set, validation
   set, and test set?
   How are NNs related to statistical methods?

Part 2: Learning

   What are combination, activation, error, and objective functions?
   What are batch, incremental, on-line, off-line, deterministic,
   stochastic, adaptive, instantaneous, pattern, epoch, constructive, and
   sequential learning?
   What is backprop?
   What learning rate should be used for backprop?
   What are conjugate gradients, Levenberg-Marquardt, etc.?
   How does ill-conditioning affect NN training?
   How should categories be encoded?
   Why not code binary inputs as 0 and 1?
   Why use a bias/threshold?
   Why use activation functions?
   How to avoid overflow in the logistic function?
   What is a softmax activation function?
   What is the curse of dimensionality?
   How do MLPs compare with RBFs?
   What are OLS and subset/stepwise regression?
   Should I normalize/standardize/rescale the data?
   Should I nonlinearly transform the data?
   How to measure importance of inputs?
   What is ART?
   What is PNN?
   What is GRNN?
   What does unsupervised learning learn?
   Help! My NN won't learn! What should I do?

Part 3: Generalization

   How is generalization possible?
   How does noise affect generalization?
   What is overfitting and how can I avoid it?
   What is jitter? (Training with noise)
   What is early stopping?
   What is weight decay?
   What is Bayesian learning?
   How to combine networks?
   How many hidden layers should I use?
   How many hidden units should I use?
   How can generalization error be estimated?
   What are cross-validation and bootstrapping?
   How to compute prediction and confidence intervals (error bars)?

Part 4: Books, data, etc.

   Books and articles about Neural Networks?
   Journals and magazines about Neural Networks?
   Conferences and Workshops on Neural Networks?
   Neural Network Associations?
   Mailing lists, BBS, CD-ROM?
   How to benchmark learning methods?
   Databases for experimentation with NNs?

Part 5: Free software

   Source code on the web?
   Freeware and shareware packages for NN simulation?

Part 6: Commercial software

   Commercial software packages for NN simulation?

Part 7: Hardware and miscellaneous

   Neural Network hardware?
   What are some applications of NNs?
      General
      Agriculture
      Chemistry
      Face recognition
      Finance and economics
      Games, sports, gambling
      Industry
      Materials science
      Medicine
      Music
      Robotics
      Weather forecasting
      Weird
   What to do with missing/incomplete data?
   How to forecast time series (temporal sequences)?
   How to learn an inverse of a function?
   How to get invariant recognition of images under translation, rotation,
   etc.?
   How to recognize handwritten characters?
   What about pulsed or spiking NNs?
   What about Genetic Algorithms and Evolutionary Computation?
   What about Fuzzy Logic?
   Unanswered FAQs
   Other NN links?

------------------------------------------------------------------------

Subject: What is this newsgroup for? How shall it be
====================================================
used?
=====

The newsgroup comp.ai.neural-nets is intended as a forum for people who want
to use or explore the capabilities of Artificial Neural Networks or
Neural-Network-like structures.

Posts should be in plain-text format, not postscript, html, rtf, TEX, MIME,
or any word-processor format. 

Do not use vcards or other excessively long signatures. 

Please do not post homework or take-home exam questions. Please do not post
a long source-code listing and ask readers to debug it. And note that chain
letters and other get-rich-quick pyramid schemes are illegal in the USA; for
example, see http://www.usps.gov/websites/depart/inspect/chainlet.htm

There should be the following types of articles in this newsgroup:

1. Requests
+++++++++++

   Requests are articles of the form "I am looking for X", where X
   is something public like a book, an article, a piece of software. The
   most important about such a request is to be as specific as possible!

   If multiple different answers can be expected, the person making the
   request should prepare to make a summary of the answers he/she got and
   announce to do so with a phrase like "Please reply by email,
   I'll summarize to the group" at the end of the posting.

   The Subject line of the posting should then be something like 
   "Request: X" 

2. Questions
++++++++++++

   As opposed to requests, questions ask for a larger piece of information
   or a more or less detailed explanation of something. To avoid lots of
   redundant traffic it is important that the poster provides with the
   question all information s/he already has about the subject asked and
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   should prepare to make a summary of the answers s/he got and announce to
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   The Subject line of the posting should be something like "Question:
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   Students: please do not ask comp.ai.neural-net readers to do your
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3. Answers
++++++++++

   These are reactions to questions or requests. If an answer is too
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   Most news-reader software automatically provides a subject line beginning
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4. Summaries
++++++++++++

   In all cases of requests or questions the answers for which can be
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   question shall summarize the answers he/she received. Such a summary
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   summarize"

   In such a case, people who answer to a question should NOT post their
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   Some care should be invested into a summary: 
    o simple concatenation of all the answers is not enough: instead,
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    o the answers should be separated clearly 
    o the contributors of the individual answers should be identifiable
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    o the summary should start with the "quintessence" of the answers, as
      seen by the original poster 
    o A summary should, when posted, clearly be indicated to be one by
      giving it a Subject line starting with "SUMMARY:" 
   Note that a good summary is pure gold for the rest of the newsgroup
   community, so summary work will be most appreciated by all of us. Good
   summaries are more valuable than any moderator ! :-) 

5. Announcements
++++++++++++++++

   Some articles never need any public reaction. These are called
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   availability of some technical report or software system).

   Announcements should be clearly indicated to be such by giving them a
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6. Reports
++++++++++

   Sometimes people spontaneously want to report something to the newsgroup.
   This might be special experiences with some software, results of own
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   Reports should be clearly indicated to be such by giving them a subject
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7. Discussions
++++++++++++++

   An especially valuable possibility of Usenet is of course that of
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   If somebody explicitly wants to start a discussion, he/she can do so by
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   It is quite difficult to keep a discussion from drifting into chaos, but,
   unfortunately, as many many other newsgroups show there seems to be no
   secure way to avoid this. On the other hand, comp.ai.neural-nets has not
   had many problems with this effect in the past, so let's just go and
   hope... 

8. Jobs Ads
+++++++++++

   Advertisements for jobs requiring expertise in artificial neural networks
   are appropriate in comp.ai.neural-nets. Job ads should be clearly
   indicated to be such by giving them a subject line of the form "Job:
   this-and-that". It is also useful to include the
   country-state-city abbreviations that are conventional in
   misc.jobs.offered, such as: "Job: US-NY-NYC Neural network
   engineer". If an employer has more than one job opening, all such
   openings should be listed in a single post, not multiple posts. Job ads
   should not be reposted more than once per month. 

------------------------------------------------------------------------

Subject: Where is comp.ai.neural-nets archived? 
================================================

The following archives are available for comp.ai.neural-nets: 

 o http://groups.google.com, formerly Deja News. Does not work very well
   yet. 
 o 94-09-14 through 97-08-16 
   ftp://ftp.cs.cmu.edu/user/ai/pubs/news/comp.ai.neural-nets 

For more information on newsgroup archives, see 
http://starbase.neosoft.com/~claird/news.lists/newsgroup_archives.html 
or http://www.pitt.edu/~grouprev/Usenet/Archive-List/newsgroup_archives.html

------------------------------------------------------------------------

Subject: What if my question is not answered in the FAQ?
========================================================

If your question is not answered in the FAQ, you can try a web search. The
following search engines are especially useful:
http://www.google.com/
http://search.yahoo.com/
http://www.altavista.com/
http://citeseer.nj.nec.com/cs

Another excellent web site on NNs is Donald Tveter's Backpropagator's Review
at http://www.dontveter.com/bpr/bpr.html or 
http://gannoo.uce.ac.uk/bpr/bpr.html. 

For feedforward NNs, the best reference book is: 

   Bishop, C.M. (1995), Neural Networks for Pattern Recognition, Oxford:
   Oxford University Press. 

If the answer isn't in Bishop, then for more theoretical questions try: 

   Ripley, B.D. (1996) Pattern Recognition and Neural Networks, Cambridge:
   Cambridge University Press. 

For more practical questions about MLP training, try: 

   Masters, T. (1993). Practical Neural Network Recipes in C++, San Diego:
   Academic Press. 

   Reed, R.D., and Marks, R.J, II (1999), Neural Smithing: Supervised
   Learning in Feedforward Artificial Neural Networks, Cambridge, MA: The
   MIT Press.

There are many more excellent books and web sites listed in the Neural
Network FAQ, Part 4: Books, data, etc. 

------------------------------------------------------------------------

Subject: May I copy this FAQ?
=============================

The intent in providing a FAQ is to make the information freely available to
whoever needs it. You may copy all or part of the FAQ, but please be sure to
include a reference to the URL of the master copy,
ftp://ftp.sas.com/pub/neural/FAQ.html, and do not sell copies of the FAQ. If
you want to include information from the FAQ in your own web site, it is
better to include links to the master copy rather than to copy text from the
FAQ to your web pages, because various answers in the FAQ are updated at
unpredictable times. To cite the FAQ in an academic-style bibliography, use
something along the lines of: 

   Sarle, W.S., ed. (1997), Neural Network FAQ, part 1 of 7: Introduction,
   periodic posting to the Usenet newsgroup comp.ai.neural-nets, URL:
   ftp://ftp.sas.com/pub/neural/FAQ.html 

------------------------------------------------------------------------

Subject: What is a neural network (NN)?
=======================================

   The question 'What is a neural network?' is ill-posed.
            
            
            
            
            
             - Pinkus
   (1999) 

First of all, when we are talking about a neural network, we should more
properly say "artificial neural network" (ANN), because that is what we mean
most of the time in comp.ai.neural-nets. Biological neural networks are much
more complicated than the mathematical models we use for ANNs. But it is
customary to be lazy and drop the "A" or the "artificial". 

There is no universally accepted definition of an NN. But perhaps most
people in the field would agree that an NN is a network of many simple
processors ("units"), each possibly having a small amount of local memory.
The units are connected by communication channels ("connections") which
usually carry numeric (as opposed to symbolic) data, encoded by any of
various means. The units operate only on their local data and on the inputs
they receive via the connections. The restriction to local operations is
often relaxed during training. 

Some NNs are models of biological neural networks and some are not, but
historically, much of the inspiration for the field of NNs came from the
desire to produce artificial systems capable of sophisticated, perhaps
"intelligent", computations similar to those that the human brain routinely
performs, and thereby possibly to enhance our understanding of the human
brain. 

Most NNs have some sort of "training" rule whereby the weights of
connections are adjusted on the basis of data. In other words, NNs "learn"
from examples, as children learn to distinguish dogs from cats based on
examples of dogs and cats. If trained carefully, NNs may exhibit some
capability for generalization beyond the training data, that is, to produce
approximately correct results for new cases that were not used for training.

NNs normally have great potential for parallelism, since the computations of
the components are largely independent of each other. Some people regard
massive parallelism and high connectivity to be defining characteristics of
NNs, but such requirements rule out various simple models, such as simple
linear regression (a minimal feedforward net with only two units plus bias),
which are usefully regarded as special cases of NNs. 

Here is a sampling of definitions from the books on the FAQ maintainer's
shelf. None will please everyone. Perhaps for that reason many NN textbooks
do not explicitly define neural networks. 

According to the DARPA Neural Network Study (1988, AFCEA International
Press, p. 60): 

   ... a neural network is a system composed of many simple processing
   elements operating in parallel whose function is determined by
   network structure, connection strengths, and the processing performed
   at computing elements or nodes. 

According to Haykin (1994), p. 2: 

   A neural network is a massively parallel distributed processor that
   has a natural propensity for storing experiential knowledge and
   making it available for use. It resembles the brain in two respects: 

   1. Knowledge is acquired by the network through a learning process. 
   2. Interneuron connection strengths known as synaptic weights are
      used to store the knowledge. 

According to Nigrin (1993), p. 11: 

   A neural network is a circuit composed of a very large number of
   simple processing elements that are neurally based. Each element
   operates only on local information. Furthermore each element operates
   asynchronously; thus there is no overall system clock. 

According to Zurada (1992), p. xv: 

   Artificial neural systems, or neural networks, are physical cellular
   systems which can acquire, store, and utilize experiential knowledge.

References: 

   Pinkus, A. (1999), "Approximation theory of the MLP model in neural
   networks," Acta Numerica, 8, 143-196. 

   Haykin, S. (1994), Neural Networks: A Comprehensive Foundation, NY:
   Macmillan. 

   Nigrin, A. (1993), Neural Networks for Pattern Recognition, Cambridge,
   MA: The MIT Press. 

   Zurada, J.M. (1992), Introduction To Artificial Neural Systems, Boston:
   PWS Publishing Company. 

------------------------------------------------------------------------

Subject: Where can I find a simple introduction to NNs?
=======================================================

Several excellent introductory books on NNs are listed in part 4 of the FAQ
under "Books and articles about Neural Networks?" If you want a book with
minimal math, see "The best introductory book for business executives." 

Dr. Leslie Smith has a brief on-line introduction to NNs with examples and
diagrams at http://www.cs.stir.ac.uk/~lss/NNIntro/InvSlides.html. 

If you are a Java enthusiast, see Jochen Fröhlich's diploma at 
http://rfhs8012.fh-regensburg.de/~saj39122/jfroehl/diplom/e-index.html

For a more detailed introduction, see Donald Tveter's excellent
Backpropagator's Review at http://www.dontveter.com/bpr/bpr.html or 
http://gannoo.uce.ac.uk/bpr/bpr.html, which contains both answers to
additional FAQs and an annotated neural net bibliography emphasizing on-line
articles. 

StatSoft Inc. has an on-line Electronic Statistics Textbook, at 
http://www.statsoft.com/textbook/stathome.html that includes a chapter on
neural nets as well as many statistical topics relevant to neural nets. 

------------------------------------------------------------------------

Subject: Are there any online books about NNs?
==============================================

Kevin Gurney has on-line a preliminary draft of his book, An Introduction to
Neural Networks, at 
http://www.shef.ac.uk/psychology/gurney/notes/index.html The book is now in
print and is one of the better general-purpose introductory textbooks on
NNs. Here is the table of contents from the on-line version: 

1. Computers and Symbols versus Nets and Neurons 
2. TLUs and vectors - simple learning rules 
3. The delta rule 
4. Multilayer nets and backpropagation 
5. Associative memories - the Hopfield net 
6. Hopfield nets (contd.) 
7. Kohonen nets 
8. Alternative node types 
9. Cubic nodes (contd.) and Reward Penalty training 
10. Drawing things together - some perspectives 

Another on-line book by Ben Kröse and Patrick van der Smagt, also called An
Introduction to Neural Networks, can be found at 
ftp://ftp.wins.uva.nl/pub/computer-systems/aut-sys/reports/neuro-intro/neuro-intro.ps.gz
or http://www.robotic.dlr.de/Smagt/books/neuro-intro.ps.gz. or 
http://www.supelec-rennes.fr/acth/net/neuro-intro.ps.gz 
Here is the table of contents: 

1. Introduction 
2. Fundamantals 
3. Perceptron and Adaline 
4. Back-Propagation 
5. Recurrent Networks 
6. Self-Organising Networks 
7. Reinforcement Learning 
8. Robot Control 
9. Vision 
10. General Purpose Hardware 
11. Dedicated Neuro-Hardware 

------------------------------------------------------------------------

Subject: What can you do with an NN and what not?
=================================================

In principle, NNs can compute any computable function, i.e., they can do
everything a normal digital computer can do (Valiant, 1988; Siegelmann and
Sontag, 1999; Orponen, 2000; Sima and Orponen, 2001), or perhaps even more,
under some assumptions of doubtful practicality (see Siegelmann, 1998, but
also Hadley, 1999). 

Practical applications of NNs most often employ supervised learning. For
supervised learning, you must provide training data that includes both the
input and the desired result (the target value). After successful training,
you can present input data alone to the NN (that is, input data without the
desired result), and the NN will compute an output value that approximates
the desired result. However, for training to be successful, you may need
lots of training data and lots of computer time to do the training. In many
applications, such as image and text processing, you will have to do a lot
of work to select appropriate input data and to code the data as numeric
values. 

In practice, NNs are especially useful for classification and function
approximation/mapping problems which are tolerant of some imprecision, which
have lots of training data available, but to which hard and fast rules (such
as those that might be used in an expert system) cannot easily be applied.
Almost any finite-dimensional vector function on a compact set can be
approximated to arbitrary precision by feedforward NNs (which are the type
most often used in practical applications) if you have enough data and
enough computing resources. 

To be somewhat more precise, feedforward networks with a single hidden layer
and trained by least-squares are statistically consistent estimators of
arbitrary square-integrable regression functions under certain
practically-satisfiable assumptions regarding sampling, target noise, number
of hidden units, size of weights, and form of hidden-unit activation
function (White, 1990). Such networks can also be trained as statistically
consistent estimators of derivatives of regression functions (White and
Gallant, 1992) and quantiles of the conditional noise distribution (White,
1992a). Feedforward networks with a single hidden layer using threshold or
sigmoid activation functions are universally consistent estimators of binary
classifications (Faragó and Lugosi, 1993; Lugosi and Zeger 1995; Devroye,
Györfi, and Lugosi, 1996) under similar assumptions. Note that these results
are stronger than the universal approximation theorems that merely show the
existence of weights for arbitrarily accurate approximations, without
demonstrating that such weights can be obtained by learning. 

Unfortunately, the above consistency results depend on one impractical
assumption: that the networks are trained by an error (L_p error or
misclassification rate) minimization technique that comes arbitrarily close
to the global minimum. Such minimization is computationally intractable
except in small or simple problems (Blum and Rivest, 1989; Judd, 1990). In
practice, however, you can usually get good results without doing a
full-blown global optimization; e.g., using multiple (say, 10 to 1000)
random weight initializations is usually sufficient. 

One example of a function that a typical neural net cannot learn is Y=1/X
on the open interval (0,1). An open interval is not a compact set. With any
bounded output activation function, the error will get arbitrarily large as
the input approaches zero. Of course, you could make the output activation
function a reciprocal function and easily get a perfect fit, but neural
networks are most often used in situations where you do not have enough
prior knowledge to set the activation function in such a clever way. There
are also many other important problems that are so difficult that a neural
network will be unable to learn them without memorizing the entire training
set, such as: 

 o Predicting random or pseudo-random numbers. 
 o Factoring large integers. 
 o Determing whether a large integer is prime or composite. 
 o Decrypting anything encrypted by a good algorithm. 

And it is important to understand that there are no methods for training NNs
that can magically create information that is not contained in the training
data. 

Feedforward NNs are restricted to finite-dimensional input and output
spaces. Recurrent NNs can in theory process arbitrarily long strings of
numbers or symbols. But training recurrent NNs has posed much more serious
practical difficulties than training feedforward networks. NNs are, at least
today, difficult to apply successfully to problems that concern manipulation
of symbols and rules, but much research is being done. 

There have been attempts to pack recursive structures into
finite-dimensional real vectors (Blair, 1997; Pollack, 1990; Chalmers, 1990;
Chrisman, 1991; Plate, 1994; Hammerton, 1998). Obviously, finite precision
limits how far the recursion can go (Hadley, 1999). The practicality of such
methods is open to debate. 

As for simulating human consciousness and emotion, that's still in the realm
of science fiction. Consciousness is still one of the world's great
mysteries. Artificial NNs may be useful for modeling some aspects of or
prerequisites for consciousness, such as perception and cognition, but ANNs
provide no insight so far into what Chalmers (1996, p. xi) calls the "hard
problem": 

   Many books and articles on consciousness have appeared in the past
   few years, and one might think we are making progress. But on a
   closer look, most of this work leaves the hardest problems about
   consciousness untouched. Often, such work addresses what might be
   called the "easy problems" of consciousness: How does the brain
   process environmental stimulation? How does it integrate information?

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