Homework  #4 Neural Networks

Visual Perception Modeling and Its Applications

CIS 4930/5930, Spring 2001

Department of Computer Science, Florida State University

¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾

Due:  Week 11, Monday, March 19, 2001 Points: 100

 

  1. Answer the following questions related to the McCulloch-Pitts neuron model.

a)      Describe the functionality of a single McCulloch-Pitts neuron. In other words, the operations that a McCulloch-Pitts neuron performs.

b)      Prove that a properly connected network of McCulloch-Pitts neurons can simulate any digital computer. In other words, the corresponding “McCulloch-Pitts” computer of any digital computer can perform any computation which can be performed by the given digital computer.

  1. Answer the following questions related to simple perceptrons, that is, a network with no hidden layer and the activation function is a step function (g(x) = 1 if x ³ 0 and g(x) = 0 otherwise).

a)      State and explain the learning algorithm for a simple perceptron network.

b)      For a two-category classification problem, show that the decision boundary is a hyper-plane, which is a line in 2-D space and a planar surface in 3-D space and so on.

c)      Show that a simple perceptron network cannot solve the following problem perfectly.

X1

X2

XOR

0

0

0

1

0

1

0

1

1

1

1

0

 

  1. Show that a multi-layer linear feed-forward network is exactly equivalent to a one-layer linear network, i.e., a network with no hidden layer.
  2. Describe and explain the steps of the back-propagation algorithm.
  3. Describe the major steps for using a neural network with back-propagation to classify salmon and sea bass for our fish-packing plant. Name some other applications where neural network can be useful.