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BASICS OF NEURAL NETWORK ANALYSIS
Multilayer Perceptron Neural Networks
Kohonen Neural Networks
• What is a Neural Network? • What can it do for me? • Advantages and Disadvantages • Two Common Types of Neural Networks
– Mul?layer Perceptron • A “black box” model predicts output values
– Kohonen Classifica?on • Experimental cases are classified into groups
• Training Neural Networks
CONTENTS
What is a Neural Network?
A neuron is a func?on, Y=f(X), with input X and output Y: Neurons are connected by synapses. A synapse mul?plies the output by a weigh?ng factor, W:
X Y Y = f(X)
X WY Z Y = f(X) Z = g(WY)
The func?on in a neuron can be linear or nonlinear. A typical nonlinear func?on is the Sigmoid func?on:
Neural networks are trained with cases
• What is a case? – A case is an experiment with one or more inputs (controlled variables) and one or more outputs (results or observa?ons)
– Example • Inputs: temp 298°K, ini?al concentra?on 1.0 g/l, ?me 7 days; Outputs: final concentra?on 0.9 g/l, degrada?on product 0.15 g/l
When a neural network is “trained” with different cases, the parameters of the neuronal func?ons and synap?c weigh?ng factors are adjusted for the best “fit”: The inputs are x1 thru xp. The outputs are y1 thru ym. The w-‐values are the synap?c weigh?ng factors. The u-‐values are sums of weigh?ng factors.
What can a neural network do for me?
• Analyze data with a large number of variables with complex rela?onships.
• Develop formula?ons or mul?-‐step processes.
• Compare performance characteris?cs of mul?ple formula?ons or processes.
• Analyze experimental data even when data points are missing or not in a balanced design.
Advantages
• No need to propose a model prior to data analysis.
• Can handle variables with very complex interac?ons.
• No assump?on that inputs and outputs are normally distributed.
• More robust to noise.
• No need to pre-‐determine important variables and interac?ons with a Design of Experiments
Disadvantages
• Need a lot of data. – (Number of Training Cases) ≈ 10 x (Number of Synapses)
• Output variables are not expressed as analy?c func?ons of input variables.
Training Kohonen Neural Networks and
Mul?layer Perceptron Neural Networks
• A por?on of the cases are randomly selected to be training cases – typically about 70%.
• A por?on of the cases are randomly selected to be verifica?on cases – typically about 20%.
• The remainder are test cases – typically about 10%.
Teaching the neural network with just the training cases will result in “over-‐fieng” the data:
So, the verifica?on cases are added:
Then the network is “retrained” with the verifica?on cases and the final model is the result:
Finally, the test cases are used to determine how well the “black box” model predicts the outputs.
The outputs of a Kohonen Neural Network will be the different “classes” into which the cases have been classified.
The outputs of a Mul?layer Perceptron Neural Network will be con?nuous variables represen?ng the performance characteris?cs of all the formula?ons or all the mul?-‐step processes. (Remember, each formula?on or process is a “case”.)