-Artificial Neural Network- Hopfield Neural Network(HNN)

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-Artificial Neural Network- Hopfield Neural
Network(HNN)

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Assoicative Memory (AM) -1

• Def Associative memory (AM) is any device that
  associates a set of predefined output patterns
  with specific input patterns.
• Two types of AM
• Auto-associative Memory Converts a corrupted
  input pattern into the most resembled input.
• Hetro-associative Memory Produces an output
  pattern that was stored corresponding to the most
  similar input pattern.

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Assoicative Memory (AM) - 2

• Models It is the associative mapping of an input
  vector X
• into the output vector V.
• EX Hopfield Neural Network (HNN)
• EX Bidirectional Associative Memory
  (BAM)

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Introduction

• Hopfield Neural Network(HNN) was proposed by
  Hopfield in 1982.
• HNN is an auto-associative memory network.
• It is a one layer, fully connected network.

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HNN Architecture

• Input? Xi ??-1, 1?
• Outputsame as input(?single layer network)
• Transfer functionXi new
• Weights
• Connections

(Xi?????X?)
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HNN Learning Process

• Learning Process
• a. Setup the network, i.e., design the input
  nodes connections.
• b. Calculate and derived the weight matrix
• C. Store the weight matrix. The learning process
  is done when the weight matrix is derived.

We shall obtain a nxn weight matrix, Wnxn.
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HNN Recall Process

• Recall
• a. Read the nxn weight matrix, Wnxn.
• b. Input the test pattern X for recalling.
• c. Compute new input (i.e. output)
• d. Repeat process c. until the network converge
• (i.e. the net value is not changed or the
  error is very small)

1 net j gt 0 Xj old if net j
0 1 net j lt 0
X j
X new
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Example Use HNN to memorize patterns (1)

• Use HNN to memorize the following patterns. Let
  the Green color is represented by 1 and white
  color is represented by -1. The input data is
  as shown in the table

X3
X4
X2
X1


P X1 X2 X3 X4 X5 X6
X1 1 -1 1 -1 1 -1
X2 -1 1 -1 1 -1 1
X3 1 1 1 1 1 1
X4 -1 -1 -1 -1 -1 -1
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Example Use HNN to memorize patterns (2)

• Wii0

P X1 X2 X3 X4 X5 X6
X1 1 -1 1 -1 1 -1
X2 -1 1 -1 1 -1 1
X3 1 1 1 1 1 1
X4 -1 -1 -1 -1 -1 -1

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Example Use HNN to memorize patterns (3)


Recall


The pattern is recalled as
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-Artificial Neural Network- Bidirectional
Associative Memory (BAM)

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Introduction

• Bidirectional Associative Memory (BAM) was
  proposed by Bart Kosko in 1985.
• It is a hetro-associative memory network.
• It allows the network to memorize from a set of
  pattern Xp to recall another set of pattern Yp

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Assoicative Memory (AM) 1

• Def Associative memory (AM) is any device that
  associates a set of predefined output patterns
  with specific input patterns.
• Two types of AM
• Auto-associative Memory Converts a corrupted
  input pattern into the most resembled input.
• Hetro-associative Memory Produces an output
  pattern that was stored corresponding to the most
  similar input pattern.

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Assoicative Memory (AM) 2

• Models It is the associative mapping of an input
  vector X
• into the output vector V.
• EX Hopfield Neural Network (HNN)
• EX Bidirectional Associative Memory
  (BAM)

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BAM Architecture

1. Input layer
2. Output layer
3. Weights
4. Connection

Its a 2-layer, fully connected, feed forward
feed back network.
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BAM Architecture (cont.)

1. Transfer function

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BAM Example(1/4)


? ?? ?? ?
??????
? ?? ? ??
? ?? ? ??
Y1 Y 2 Y3 Y4
1 -1 1 -1 1 -1 1 -1 1 -1
-1 1 -1 1 -1 1 -1 1 -1 1
1 1 1 1 1 1 -1 -1 -1 1-1
-1 -1 -1 -1 -1 -1 1 1 1 1

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Test pattern
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BAM Example(2/4)
Y1 Y 2 Y3 Y4
1 -1 1 -1 1 -1 1 -1 1 -1
-1 1 -1 1 -1 1 -1 1 -1 1
1 1 1 1 1 1 -1 -1 -1 1-1
-1 -1 -1 -1 -1 -1 1 1 1 1

• 1. Learning
• Set up network
• Setup weights

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BAM Example(3/4)

• 2. Recall
• Read network weights
• Read test pattern
• Compute Y

1. Compute X
2. Repeat (3) (4) until converge

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BAM Example(4/4)

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test pattern (1 1 1 -1 1 -1)16
(1)
(2)
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