CONTENTS• 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
What is a Neural Network? A neuron is a func?on, Y=f(X), with input X and output Y: X Y Y = f(X) Neurons are connected by synapses. A synapse mul?plies the output by a weigh?ng factor, W: 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:
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”.)