1. Ch10 : Self-Organizing Feature Maps
。 Cortex:
。Ordered Feature Map
e.g. Auditory cortex
-- tonotopic maps
Hippocampal cortex
-- geographic maps
Somatosensory cortex
-- somatic maps
Visual cortex
-- retinotectal maps
i) 6 layers of neurons
ii) Size:
iii) Thick:

2. 。 Macroscopic scale: Consistently uniform structure.
Microscopic scale: Located consistently relative to
one another logical ordering of functionality
Tissue level – inherence
Mental level – learning

3. ◎ Architecture of SOFM Neural Networks
Primary mechanisms:
(1) Lateral feedback
(2) Clustering
(3) Topology preserving projection

4. Objective : formation of localized responses
○ Lateral Feedback
Objective : formation of localized responses
Lateral interaction
function
: input,
: output

5. Lateral interaction function
＋: excitation
－: inhibition
。Output:
primary input lateral input
a: transfer function

6. ○ Clustering e.g., Clustering of activity in a 1-D array:
input signal
Clustering of
activity in a
1-D array:
Clustering of
activity in a
2-D array:

7. 。 Nonsmooth input signalor
Nonlinear transfer function a
Arbitrary lateral feedback function
Irregular activity bubbles

8. ○ Topology Preserving Projection 。 3-D
Physical space Weight space
。 2-D

9. 。 1-D

10. Mathematical treatment of self – organization
○ 1-D case
: a scalar input signal to a neuron
neurons : 1, 2, …. , l
weights :

11. 。 The best match
。 Neighborhood neurons (first-order neighbors)

12. 。 Weight update
: learning step,
g : Gaussian
○ 2-D System
Input scalar signals:
Output response:
: weight

13. Find the best match between x and
2 ways
。 Topological neighborhood
-- To be engaged in
learning but with
different degrees
(approximated by
Gaussian that is
reduced with time)

14. ◎ Applications – Geometrical Modeling
S. W. Chen, G. C. Stockman, and K. E. Change,
“SO Dynamic Deformation for Building of 3D
Models,” IEEE Trans. on Neural Networks, Vol.
7, No. 2, pp , 1996.

16. ○ Data
Acquisition