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)