1. Associative Learning Memories -SOLAR_A
Matlab code presentation

2. Introduction Associating SOLAR (SOLAR_A)
SOLAR_A structures are hierarchically organized and have ability to classify patterns in a network of sparsely connected neurons. 

3. Association
Training
Neurons learn associations between pattern and its code. Once the training is completed, a network is capable to make necessary associations.
Testing
When the network is presented with the pattern only, it drives the associated input signals to these code values that represent the observed pattern.

4. Signal definition
The inner signals in the network range from 0 to 1. A signal is a determinate low or determinate high if its value is 0 or 1.
weak low
weak high
0.5 “inactive”, or “high impedance”

5. Neurons’ definitions
If a neuron is able to observe any type of statistical correlations of its input connections, it will function as an associative neuron.
Otherwise it will be a transmitting neuron.

6. Associative neuron
A neuron is called an associative neuron when its inputs I1 and I2 are associated
Inputs I1 and I2 are associated if and only if I2 can be implied from I1 and I1 can be implied from I2 simultaneously.

7. associative neuron
Low I1 is associated with low I2, and high I1 is associated with high I2.
I1 and I2 are inputs an associative neuron has received in training.
It is quite clear that I1 and I2 are most likely to be simultaneously low or high although there is some noise.
This can be verified using P(I2 | I1) and P(I1 | I2), and implying values I2 from I1 and I1 from I2.

8. Network Structure Hierarchical structure
In horizontal direction, the neurons on one layer can only connect to the neurons on the previous layer.

9. Network Structure The connection in vertical direction obeys
80% Gaussian distribution with standard deviation 2
+ 20% uniform distribution

10. Network Structure
The network uses feedback signals to pass information backwards to the associated inputs.

11. Testing
During testing, the missing parts of the data need to be recovered from the existing data through association.
For example, in a pattern recognition problem, the associated code inputs are unknown and therefore set to 0.5.

12. Neuron Feedback Scheme

13. Iris Plants Database The Iris database has:
3 classes (Iris Setosa, Iris Versicolour and Iris Virginica)
4 numeric attributes (petal length, petal width , sepal length , sepal width )
150 instances of 50 instances for each class, where each class refers to a type of iris plant.
The classification objective
Identify the class ID based on the input feature (attribute) values

14. Coding of the database
The 4 features were scaled linearly and coded using a sliding bar code .
Input bits from (V-Min)+1 to (V-Min)+L will be set high and remaining bits will be low
N-L=Max-Min

15. Coding of the database
We scaled the 4 features of Iris database between 0-30, and
Set the length of L equal to 12
The total length of each feature is 42
The feature input requires 168 bits

16. Coding of the database
In order to increase the probability that each feature is associated with sample class code, we merged the 4 features.

17. Coding of the database

18. Coding of the database There are 3 classes total
We use 3M bits to code the class ID maximizing their code Hamming distance
The white part is filled by 2M-bit 0 string, while the grey part is filled by M-bit 1 string.

19. Iris database simulation
Rows class ID
Rows Features

20. Iris database simulation

21. Glass identification database

22. Simulation of mixed features and class ID code

23. Simulation of mixed features and class ID code
Iris database

24. Image recovery Examples of training patterns
Testing results and recovered images of letter B and J

25. Coding example Samples from Iris database
5.1,3.5,1.4,0.2,Iris-setosa(class 1)
7.0,3.2,4.7,1.4,Iris-versicolor (class 2)
6.3,3.3,6.0,2.5,Iris-virginica (class 3)

26. Coding example Pre-preparing: 51,35,14,2,1
Coding:5.1,3.5,1.4,0.2,Iris-setosa (class 1)
Pre-preparing: 51,35,14,2,1
Scaling the features (51,35,14,2) from 0 to 30
After scaling: 7,19,2,2,1

27. Coding example Features 7 000000011111111111100000000000000000000000
7 bits
12 bits
Features
Class ID
… … …000
56 bits
112 bits

28. Coded data Matrix- Input
Features
Class ID code
Input matrix
M Training data
N Testing data

29. Matlab user interface main.m – main function
training2.m – training function
testing2.m – testing function
catchassociating.m– actively associative neurons
generate_input– coding the database

30. parameters columns- depth of layers rows- length of an input pattern
stdr- standard deviation in vertical
stdc- standard deviation in horizontal
n_tests- test numbers

31. training.m r_distribution(meanr,stdr,rows,columns,width)
--defines distribution in vertical direction
normrnd(meanr,stdc,rows,columns)
--defines distribution in horizontal direction