8/15/2019 Lecture 18 - Kohonen SOM

1/17

 Artificial Neural Networks

Dr. Abdul Basit Siddiqui Assistant Professor 

FURC

8/15/2019 Lecture 18 - Kohonen SOM

2/17

NEURAL NETWORKS BASEDON COMPETITION

Kohonen S! "#earnin$ Unsu%er&ised 'n&iron(ent)

8/15/2019 Lecture 18 - Kohonen SOM

3/17

Unsupervised LearningUnsu

pervised Learning

* +e can include additional structure in the network so

that the net is forced to (ake a decision as to which

one unit will res%ond.

* ,he (echanis( b- which it is achie&ed is called

competition.

* t can be used in unsu%er&ised learnin$.

*  A co((on use for unsu%er&ised learnin$ is clusterin$

based neural networks.

8/15/2019 Lecture 18 - Kohonen SOM

4/17

Unsupervised LearningUnsu

pervised Learning

* n a clusterin$ net/ there are as (an- units as the

in%ut &ector has co(%onents.

* '&er- out%ut unit re%resents a cluster and thenu(ber of out%ut units li(it the nu(ber of clusters.

* Durin$ the trainin$/ the network finds the best

(atchin$ out%ut unit to the in%ut &ector.

* ,he wei$ht &ector of the winner is then u%dated

accordin$ to learnin$ al$orith(.

8/15/2019 Lecture 18 - Kohonen SOM

5/17

Kohonen LearningKohonen Learnin

g

*  A &ariet- of nets use Kohonen #earnin$

 0 New wei$ht &ector is the linear co(bination of old

wei$ht &ector and the current in%ut &ector.

 0 ,he wei$ht u%date for cluster unit "out%ut unit) jcan be calculated as1

 

 0 the learnin$ rate al%ha decreases as the learnin$

%rocess %roceeds.

8/15/2019 Lecture 18 - Kohonen SOM

6/17

Kohonen SOM (Self Organizing Maps)Kohonen SOM

 (Self Organizing Maps)

* Since it is unsu%er&ised en&iron(ent/ so the na(e is

Self r$ani2in$ !a%s.

* Self r$ani2in$ NNs are also called ,o%olo$-Preser&in$ !a%s which leads to the idea of

nei$hborhood of the clusterin$ unit.

* Durin$ the self3or$ani2in$ %rocess/ the wei$ht&ectors of winnin$ unit and its nei$hbors are u%dated.

8/15/2019 Lecture 18 - Kohonen SOM

7/17

Kohonen SOM (Self Organizing Maps)Kohonen SOM (Self Organizing Maps)

* Nor(all-/ 'uclidean distance (easure is used to find

the cluster unit whose wei$ht &ector (atches (ost

closel- to the in%ut &ector.

* For a linear arra- of cluster units/ the nei$hborhood

of radius R  around cluster unit J  consists of all units j

such that1

8/15/2019 Lecture 18 - Kohonen SOM

8/17

Kohonen SOM (Self Organizing Maps)Kohonen SOM (Self Organizing Maps)

*  Architecture of S!

8/15/2019 Lecture 18 - Kohonen SOM

9/17

Kohonen SOM (Self Organizing Maps)Kohonen SOM (Self Organizing Maps)

* Structure of Nei$hborhoods

8/15/2019 Lecture 18 - Kohonen SOM

10/17

Kohonen SOM (Self Organizing Maps)Kohonen SOM (Self Organizing Maps)

* Structure of Nei$hborhoods

8/15/2019 Lecture 18 - Kohonen SOM

11/17

Kohonen SOM (Self Organizing Maps)Kohonen SOM (Self Organizing Maps)

* Structure of Nei$hborhoods

8/15/2019 Lecture 18 - Kohonen SOM

12/17

Kohonen SOM (Self Organizing Maps)Kohonen SOM (Self Organizing Maps)

 0 Nei$hborhoods do not wra% around fro( one sideof the $rid to other side which (eans (issin$ units

are si(%l- i$nored.

*  Al$orith(1

8/15/2019 Lecture 18 - Kohonen SOM

13/17

Kohonen SOM (Self Organizing Maps)Kohonen SOM (Self Organizing Maps)

*  Al$orith(1

 0 Radius and learnin$ rates (a- be decreased after

each e%och.

 0 #earnin$ rate decrease (a- be either linear or$eo(etric.

8/15/2019 Lecture 18 - Kohonen SOM

14/17

Winning neuron

wi 

neuron i 

Input vector X  X =[ x ! x "!# x n$ % 

n

wi = [w

i !wi "!#!win$ % n 

Kohonen la&erKohonen la&er

KO'O SL* O%+,I-I+ M,.SKO'O SL* O%+,I-I+ M,.S

 Architecture

8/15/2019 Lecture 18 - Kohonen SOM

15/17

Kohonen SOM (Self Organizing Maps)Kohonen SOM (Self Organizing Maps)

* '4a(%le

8/15/2019 Lecture 18 - Kohonen SOM

16/17

Kohonen SOM (Self Organizing Maps)Kohonen SOM (Self Organizing Maps)

8/15/2019 Lecture 18 - Kohonen SOM

17/17

Kohonen SOM (Self Organizing Maps)Kohonen SOM (Self Organizing Maps)