# lecture 18 - kohonen som

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• 8/15/2019 Lecture 18 - Kohonen SOM

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Artificial Neural Networks

Dr. Abdul Basit Siddiqui Assistant Professor

FURC

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NEURAL NETWORKS BASEDON COMPETITION

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

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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.

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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(.

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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.

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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.

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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

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

*  Architecture of S!

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

* Structure of Nei\$hborhoods

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

* Structure of Nei\$hborhoods

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

* Structure of Nei\$hborhoods

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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

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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.

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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

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

* '4a(%le

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

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