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Neural Networks and Applications

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Alex (Oleksiy) Varfolomiyev
Alex (Oleksiy) Varfolomiyev
ScienceTechnology
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Neural Networks & Applications Oleksiy Varfolomiyev NJIT, 2011
Why Neural Networks? State-of-the-art solutions for the diversity of applications
What do Neural Networks do? • Clustering, classification, categorization • Function approximation • Prediction • Optimization • Associative memory • Control
What Applications? Manufacturing process control Credit application Manipulator controllers evaluation Image/data compression Autopilot Breast cancer cell analysis Vehicle scheduling Special Effects
What Industries? Manufacturing Robotics Banking Telecommunications Aerospace Medical Transportation Entertainment
Simple Neuron Simple Neuron Model !"# $%&'()#&*(+ ,%-+'-&. ,+/01 $/2 &#%2(+ &#*3/214 -4 *"# 4-&. &#%2/&7 4%0" (4 *"-4 #8()6+#9 !"#2# (2# *"2## '-4*-&0* $%&0*-/&(+ /6#2(*-/&4 *"(* *(1# 6+(0# -& • &#%2/&9 input*"# 40(+(2 -&6%* ! -4 )%+*-6+-#' ,; *"# 40(+(2 3#-. p - :-24*7 • w - weight *"# 62/'%0* "!7 (.(-& ( 40(+(29 <#0/&'7 *"# 3#-."*#' -&6%* "! - *"# 40(+(2 ,-(4 # */ $/2) *"# &#* -&6%* $9 =>& *"-4 0(4#7 ;/% 0(& ? • b - bias (4 4"-$*-&. *"# $%&0*-/& % */ *"# +#$* ,; (& ()/%&* #9 !"# ,-(4 -4 • n - net input ( 3#-."*7 #80#6* *"(* -* "(4 ( 0/&4*(&* -&6%* /$ @9A :-&(++;7 *"# & 6(44#' *"2/%." *"# *2(&4$#2 $%&0*-/& %7 3"-0" 62/'%0#4 *"# 40(+( • !"# f - transfer */ *"#4# *"2## 62/0#44#4 (2#B *"# 3#-."* $%&0*- &()#4 .-?#& function • a - output -&6%* $%&0*-/& (&' *"# *2(&4$#2 $%&0*-/&9 :/2 )(&; *;6#4 /$ &#%2(+ &#*3/2147 *"# 3#-."* $%&0*-/& -4 ( 62/
Neuron with Vector Input
One Layer of Neurons
Multiple Layers of Neurons
Neural networks Static Dynamic The output is calculated The output depends also on directly form the input the previous inputs, outputs, through feedforward or states of the network connections
Neural networks Static Dynamic The output is calculated The output depends also on directly form the input the previous inputs, outputs, through feedforward or states of the network connections
Applications of Dynamic Networks • Financial Markets • Control Systems • Fault Detection • Speech recognition • Filtering
The work flow for the NN design process 1. Collect Data 2. Create the network 3. Configure the network 4. Initialize the weights and biases 5. Train the network 6. Validate the network 7. Use the network
Train the Network Tuning weights and biases of the NN to optimize NN performance function,e.g. Mean Square Error N N 1 2 1 2 F = (ei ) = (ti − ai ) N i=1 N i=1
Optimization methods • Use GRADIENT of the network performance w.r.t. the network weights • Use JACOBIAN of the network errors w.r.t. the network weights
What tools? MATLAB Neural Network Toolbox Simulink
Control Systems Example Neural Predictive Control for the Aiming and Stabilizing System
NN Training Error using Levenberg Marquardt algorithm
Control System Works Out the Harmonic Input
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Neural Networks and Applications

  • 1. Neural Networks & Applications Oleksiy Varfolomiyev NJIT, 2011
  • 2. Why Neural Networks? State-of-the-art solutions for the diversity of applications
  • 3. What do Neural Networks do? • Clustering, classification, categorization • Function approximation • Prediction • Optimization • Associative memory • Control
  • 4. What Applications? Manufacturing process control Credit application Manipulator controllers evaluation Image/data compression Autopilot Breast cancer cell analysis Vehicle scheduling Special Effects
  • 5. What Industries? Manufacturing Robotics Banking Telecommunications Aerospace Medical Transportation Entertainment
  • 6. Simple Neuron Simple Neuron Model !"# $%&'()#&*(+ ,%-+'-&. ,+/01 $/2 &#%2(+ &#*3/214 -4 *"# 4-&. &#%2/&7 4%0" (4 *"-4 #8()6+#9 !"#2# (2# *"2## '-4*-&0* $%&0*-/&(+ /6#2(*-/&4 *"(* *(1# 6+(0# -& • &#%2/&9 input*"# 40(+(2 -&6%* ! -4 )%+*-6+-#' ,; *"# 40(+(2 3#-. p - :-24*7 • w - weight *"# 62/'%0* "!7 (.(-& ( 40(+(29 <#0/&'7 *"# 3#-."*#' -&6%* "! - *"# 40(+(2 ,-(4 # */ $/2) *"# &#* -&6%* $9 =>& *"-4 0(4#7 ;/% 0(& ? • b - bias (4 4"-$*-&. *"# $%&0*-/& % */ *"# +#$* ,; (& ()/%&* #9 !"# ,-(4 -4 • n - net input ( 3#-."*7 #80#6* *"(* -* "(4 ( 0/&4*(&* -&6%* /$ @9A :-&(++;7 *"# & 6(44#' *"2/%." *"# *2(&4$#2 $%&0*-/& %7 3"-0" 62/'%0#4 *"# 40(+( • !"# f - transfer */ *"#4# *"2## 62/0#44#4 (2#B *"# 3#-."* $%&0*- &()#4 .-?#& function • a - output -&6%* $%&0*-/& (&' *"# *2(&4$#2 $%&0*-/&9 :/2 )(&; *;6#4 /$ &#%2(+ &#*3/2147 *"# 3#-."* $%&0*-/& -4 ( 62/
  • 8. One Layer of Neurons
  • 10. Neural networks Static Dynamic The output is calculated The output depends also on directly form the input the previous inputs, outputs, through feedforward or states of the network connections
  • 11. Neural networks Static Dynamic The output is calculated The output depends also on directly form the input the previous inputs, outputs, through feedforward or states of the network connections
  • 12. Applications of Dynamic Networks • Financial Markets • Control Systems • Fault Detection • Speech recognition • Filtering
  • 13. The work flow for the NN design process 1. Collect Data 2. Create the network 3. Configure the network 4. Initialize the weights and biases 5. Train the network 6. Validate the network 7. Use the network
  • 14. Train the Network Tuning weights and biases of the NN to optimize NN performance function,e.g. Mean Square Error N N 1 2 1 2 F = (ei ) = (ti − ai ) N i=1 N i=1
  • 15. Optimization methods • Use GRADIENT of the network performance w.r.t. the network weights • Use JACOBIAN of the network errors w.r.t. the network weights
  • 16. What tools? MATLAB Neural Network Toolbox Simulink
  • 17. Control Systems Example Neural Predictive Control for the Aiming and Stabilizing System
  • 18. NN Training Error using Levenberg Marquardt algorithm
  • 19. Control System Works Out the Harmonic Input

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