Enhancing SOM Efficiency through Data Order Adjustment

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 • Data order • 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 • 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