1. Efficient SOM Learning by Data Order Adjustment
Authors: Miyoshi et al.
Advisor: Dr. Hsu
Graduate :Yu-Wei Su

2. Outline Motivation Objective SOM Data order and learning convergence
Ending point of convergence
Experiments
Conclusion
opinion

3. Motivation
In SOM, there are many factors to aggravate computational load and competition

4. Objective
Reducing the competition load and increasing the speed of SOM

5. SOM
SOM is a algorithm that map dimension from high to low, always two dimension
Step 1: finding BMU of each datum
Step 2: modifying the value of BMU and neighborhood nodes

6. Data order and learning convergence
The SOM spends lots of time to learn because of large map size, large quantity of input data and many dimensions in data et al.
In the beginning stage of learning process, SOM map is dynamically and widely and that is depended on the distance of each input data

7. Data order and learning convergence( cont.)
Adjusting data order based on the distance between data classes to reduce the competition load

8. Data order
To change order of input data, using class distance that is calculated by class center
First select typical data as class center in each class
And calculate Euclidian distance between all class centers as class distance

9. Data order( cont.) Order 1: random order
Order 2: the largest distance order based on previous data class
scli : selected data class i
ucli : still unselected data class i
cd(A,B) :class distance between A and B

10. Data order( cont.)
Order 3: the smallest distance order based on previous data class
Order 4: the smallest distance order based on all classes
scli : selected data class i
ucli : still unselected data class i
cd(A,B) :class distance between A and B

11. Data order( cont.)
Order 5: the largest distance order based on all classes
Order 6: average distance order based on all classes
scli : selected data class i
ucli : still unselected data class i
cd(A,B) :class distance between A and B

12. Ending point of convergence
Definition of converging point of learning
Keep maximum Euclidian distance for all nodes in each step of learning
Test the difference between (|xdn-xdn-1|) whether (|xdn-xdn-1|) is smaller than Th1
If it is, test how long the distance are continued smaller
If it continues long enough than Th2 it is determined as the ending point of learning

13. Ending point of convergence (cont.)
Th1 : threshold of difference
Th2 : threshold of period
xdn : n-th max distance through all input data and output nodes
ed(A,B) : Euclidian distance between A and B
dti : input data I
onj: output node j
dmax : total of input data
nmax : total of output nodes

14. Experiments Experiment data Parameters
Synthetic data, 5 dim, 7 classes each 49 data
Parameters
Size of map 8x8, initial neighborhood from 3 to 5, initial learning rate from 0.2 to 0.8, 300 maps that initialized at random

15. Experiments ( cont.)
Learning rate function
Neighborhood function

16. Experiments ( cont.)

17. Experiments ( cont.)

18. Conclusion
The data stream of small distance makes maximum 9% improvement
The data stream of large distance still similar with conventional SOM
All order make no remarkable difference in result map

19. Opinion No experiments of comparison with others
The terminal condition is a good idea