This is the NeuroDimension Newsletter, which you are receiving because you requested to stay informed about new developments at NeuroDimension. If you would like to stop receiving these newsletters, please see the bottom of this newsletter for instructions.
In this issue...
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Register Now for the Neural Network Course
The next neural network course has been scheduled for Nov 7 - Nov 11, 2005 at the Sheraton World Resort in Orlando, Florida. This course always fills up fast, so be sure to sign up today!
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Our course format allows both novice and advanced users to find a suitable course. Offered courses include: "Introduction to NeuroSolutions", "Fundamentals of Neural Networks and NeuroSolutions", and "Advanced NeuroSolutions". The courses include a copy of our interactive book, "Neural and Adaptive Systems: Fundamentals Through Simulations".
For details on this new offering, or to sign-up from the Internet, see: http://www.neurosolutions.com/products/course/fall.html
If you are not able to attend this specific course, but are interested in our neural network courses in general, please visit our course information page to take a quick survey and sign up for our course mailing list: http://www.neurosolutions.com/products/course/live.html
For more information and samples of the interactive book, see http://www.neurosolutions.com/products/nsbook/
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New Help for Product Selection
Need help determining which NeuroDimension products best meet your needs? Let the new NeuroDimension Product Advisor help you.
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Answer a few brief questions on our website about your application and the Advisor will point you to the product or set of products that best meet your needs.
If you’re considering neural networks for your application, try the NeuroDimension Product Advisor today: http://www.nd.com/advisor/
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NeuroDimension is Actively Seeking Resellers Worldwide!
We have designed the Authorized Reseller program to encourage easy participation and incremental sales. Our goals are to assist you in generating additional revenue through our product co-marketing within your customer environment.
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We currently sell to over 60 countries around the world, and are in the process of expanding our global distribution and reseller network.
If you are interested in becoming an Authorized Reseller for NeuroDimension software, please visit: http://www.nd.com/resellers.html
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NeuroSolutions Tip Box: Levenberg-Marquardt
Technical Details
One of the most significant enhancements made to NeuroSolutions for the 5.0 release is the addition of the Levenberg-Marquardt learning algorithm. Levenberg-Marquardt (LM) is one of the most efficient higher-order adaptive algorithms known for minimizing the MSE of a neural network.
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It is a member of a class of learning algorithms called "pseudo second order methods". Standard gradient descent algorithms use only the local approximation of the slope of the performance surface (error versus weights) to determine the best direction to move the weights in order to lower the error. Second order methods use the Hessian or the matrix of second derivatives (the curvature instead of just the slope) of the performance surface to determine the weight update, while pseudo-second order methods approximate the Hessian.
Example of Benefits
Each epoch of LM requires much more processing than standard backprop, so it will seem to run slower. However, LM usually trains in far fewer epochs, so the training time is usually less for small to medium sized networks. LM will almost always be able to reach a lower training error than standard backprop, and it often produces a lower cross validation and/or testing error as well. To illustrate this, we built a default MLP with the NeuralBuilder using two of the sample data files in the "Sample Data" directory. We set aside 20% for cross validation and 20% for testing and trained it first with the default Momentum learning and then changed the learning rule to LM and retrained. The lowest training error and the lowest cross validation error were recorded for each. The network was then tested using the best weights (based on the cross validation performance) and that error was also recorded. The results are summarized below:
In all cases LM performed better than Momentum. This won’t always be the case of course, but we generally recommend that you try LM for your current models trained with standard backprop to see if it improves the performance. To change the learning of a backprop network to LM, simply change the Gradient Search Plane within the Backpropagation Inspector.
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We appreciate your feedback! Please send us your comments or suggestions concerning this newsletter, our web site, or part of the NeuroDimension product line. Write to us at: newsletters@nd.com.
Have questions about NeuroDimension products? Send your questions to: info@nd.com
This issue and previous issues of this newsletter are available on the NeuroSolutions web site at: http://www.neurosolutions.com/newsletters.html
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Thank you again for your support of NeuroDimension products!
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