1. 1
Autocorrelators
Dept. of Computer Science & Engineering
2013-2014
Presented By:
Ranjit R. Banshpal
Mtech 1st sem (CSE)
Roll NO.18
1
A
seminar on
G.H. Raisoni College of Engineering Nagpur
1

2. Autocorrelators
 Autocorrelators easily recognized by the title of Hopfield
Associative Memory (HAM).
 First order autocorrelators obtain their connection matrix by
multiplying a pattern’s element with every other pattern’s elements.
 A first order autocorrelator stores M bipolar pattern
A1,A2,………,Am by summing together m outer product as

3. Here,
is a (p × p) connection matrix and
p
 The autocorrelator’s recall equation is vector-matrix
multiplication,
 The recall equation is given by,
=f ( )
Where Ai=(a1,a2,…..,ap) and two parameter
bipolar threshold function is,
1, if α > 0
f(α , β )= β, if α = 0
-1, if α < 0

4. Working of an autocorrelator
Consider the following pattern,
A1=(-1,1,-1,1)
A2=(1,1,1,-1)
A3=(-1,-1,-1,1)
The connection matrix,
3 1 3 -3
4×1 1×4 1 3 1 -1
3 1 3 -3
-3 -1 -3 3

5. Recognition of stored patterns
 The autocorrelator is presented stored pattern
A2=(1,1,1,-1)
With the help of recall equation
= f ( 3 + 1 + 3 + 3, 1 ) = 1
= f ( 6, 1 ) = 1
= f ( 10, 1 ) = 1
= f ( -10, 1 ) = -1

6. Recognition of noisy patterns
 Consider a vector A’=(1,1,1,1) which is a
distorted presentation of one among the store pattern
 With the help of Hamming Distance measure we
can find noisy vector pattern
 The Hamming distance (HD) of vector X from Y,
given X=(x1,x2,….,xn) and Y=(y1,y2,….,yn) is given
by,
HD( x, y ) =

7. Heterocorrelators : Kosko’s discrete BAM
 Bidirectional associative memory (BAM) is two level
nonlinear neural network
 Kosko extended the unidirectional to bidirectional
processes.
 Noise does not affect performance
 There are N training pairs
{(A1,B1),(A2,B2),….,(Ai,Bi),……,(An, Bn)} where
Ai=(ai1,ai2,…….,ain)
Bi =(bi1,bi2,……,bip)

8. Here, aij or bij is either ON or OFF state
In binary mode, ON = 1 and OFF = 0 and
In bipolar mode, ON = 1 and OFF = -1
 Formula for correlation matrix is,
 Recall equations,
Starting with (α, β) as the initial condition, we determine the
finite sequence (α’, β’ ),(α’’, β’’),…….., until equilibrium
point (αF, β F ) is reached.
Here ,
β’ = ϕ (αM)
α’ = ϕ (β’ MT)

9. Φ(F) = G = g1, g2, …., gn
F = ( f1,f2,….,f n)
1 if fi > 0
0 (binary)
gi = , fi < 0
-1 (bipolar)
previous gi, fi = 0

10. Addition and Deletion of Pattern Pairs
If given set of pattern pairs (Xi, Yi) for i=1,2,….,n
 Then we can be added (X’,Y’) or can be deleted (Xj,Yj)
from the memory model.
 In the case of addition,
 In the case of deletion,

11. Energy function for BAM
 The value of the energy function for
particular pattern has to occupy a minimum
point in energy landscape,
 Adding new patterns do not destroy
previously stored patterns.

12.  Hopfield propose an energy function as,
E(A) = -AMAT
 Kosko propose an energy function as,
E(A,B)= - AMBT
 If energy function for any point (α, β) is given by
E = - αMβT
 If energy E evaluate using the coordinates of the pair
(Ai,Bi),

13.  Working of Kosko’s BAM
Step 1:
converting to bipolar forms
 Step 2:
The matrix M is calculated as,
 Step 3:
Retrieve the associative pair
β’ = ϕ (αM)
α’ = ϕ (β’ MT)

14. THANK YOU…!!!