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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$hborhood
of radius R around cluster unit J consists of all units j
such that1
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Kohonen SOM (Self Organizing Maps)Kohonen SOM (Self Organizing Maps)
* Architecture of S!
8/15/2019 Lecture 18 - Kohonen SOM
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Kohonen SOM (Self Organizing Maps)Kohonen SOM (Self Organizing Maps)
* Structure of Nei$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)