OK - here are few links to click on, read and to click on references:
General intro to the field:
See paragraph which starts:
Boltzmann machine The Quick Facts about: Boltzmann machine
Quick Summary not found for this subjectBoltzmann machine can be
thought of as a noisy Hopfield network. Invented by Geoff Hinton and
Quick Facts about: Terry Sejnowski
Quick Summary not found for this subjectTerry Sejnowski (1985), the
Boltzmann machine was important because it was one of the first neural
networks in which learning of latent variables (hidden units) was
demonstrated....
http://www.absoluteastronomy.com/encyclopedia/n/ne/neural_network.htm
Then read: (SEARCH TERMS tellu you what researcher entered to the engine
to get suggested links. It is often useful to get additional references by
entering those terms into Google or other SE).
SEARCH TERMS: Boltzmann machine algorithm
SEARCH TERMS: minimalization nonlinear
e.g.
A polynomial time algorithm for Boltzmann Machine learning
Boltzmann Machines (BMs) [1], are networks of binary neurons with a
stochastic neuron dynamics, known as Glauber dynamics. Assuming
symmetric connections between neurons, the probability distribution
over neuron states will become stationary and will be given by the
Boltzmann-Gibbs distribution .
http://www.mbfys.kun.nl/~bert/cambridge/
... and learning rules in general Boltzmann machines, and towards the design of
special-case algorithms. An attractive special case are networks, ...
http://www.doc.ic.ac.uk/~srueger/www-pub/dbmfd-imacs97.pdf
SEARCH TERMS (category) :Simulated annealing
See:
The original Metropolis scheme was that an initial state of a
thermodynamic system was chosen at energy E and temperature T, holding
T constant the initial configuration is perturbed and the change in
energy dE is computed. If the change in energy is negative the new
configuration is accepted. If the change in energy is positive it is
accepted with a probability given by the Boltzmann factor exp -(dE/T).
This processes is then repeated sufficient times to give good sampling
statistics for the current temperature, and then the temperature is
decremented and the entire process repeated until a frozen state is
achieved at T=0.
http://www.cs.sandia.gov/opt/survey/sa.html
demo:
http://www.taygeta.com/annealing/demo1.html
book:
Simulated Annealing and Boltzmann Machines: A Stochastic Approach to
Combinatorial Optimization and Neural Computing
Emile Aarts, Jan Korst
http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471921467.html
Potentially useful library
http://attrasoft.com/imagefinder60/polyapplet/
more references:
http://citeseer.ist.psu.edu/context/3330/0
://www.google.com/search?hl=en&ie=UTF-8&q=Simulated+annealing,+Boltzmann&spell=1
Free Unsolicitated Advice: do not be afraid to use the Search Engine
enjoy
Hedgie |