An Introduction to Kohonen Self Organizing · PDF fileKohonen Self Organizing Maps Utility...

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An Introduction to Kohonen Self Organizing Maps Rajarshi Guha Penn State University An Introduction to Kohonen Self Organizing Maps – p.1/12

Transcript of An Introduction to Kohonen Self Organizing · PDF fileKohonen Self Organizing Maps Utility...

An Introduction to Kohonen SelfOrganizing Maps

Rajarshi Guha

Penn State University

An Introduction to Kohonen Self Organizing Maps – p.1/12

Kohonen Self OrganizingMaps

What are SOM’s ?Competitive Learning ANNElastic net of points which is made to fit theinput vector

Mode of FunctioningEach unit of the map recieves identicalinputsThe units compete for selectionThe selected neuron and surroundingneighbours get modifiedResults in groups of units becomingsensitized to features of the input vectors

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Kohonen Self OrganizingMaps

UtilityVisualizing N dimensional data in 2DDetecing similarity and degree’s ofsimilarity

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Structure of the Map

Square grid

Each grid point is avector containing thedescriptor values

The grid wraps roundthe edges

The grid is initializedwith random vectors

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Training the Map

Each descriptor vector in the training set ispresented to all grid points.

Select the closest matching grid point basedon minimum Euclidean distance

dsj =

m∑

i=1

(ssi − wji)

Modify the selected grid point and itsneighbours.

Degree of modification reduces with eachtraining iteration

Once all the training vectors have beenpresented, repeat the cycle.

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Modification of GridPoints, aka Learning

Selected grid point and topologically closegridpoints are modified

Leads to smoothing which leads to globalordering

The general form of modification is

mi(t + 1) = mi(t) + hci(t)[x(t) − mi(t)]

hci(t) is termed as the neighborhood function

As t → ∞, hci(t) → 0

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The NeighborhoodFunction

The neighborhood function can be

of various forms.

Neighborhood Sethci(t) = α(t) ifi ∈ Nc

hci(t) = 0 if i /∈ Nc

The size of the setdetermines howlarge an area willbe affected by theselected neuronIf it is initially toosmall, globalordering will notemerge.

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The NeighborhoodFunction

Gaussian Neighborhood Function

hci(t) = α(t) exp(

−‖rc−ri‖2

2σ2(t)

)

σ is the width of the smootheningCorresponds to the radius of theneighborhood set

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The Learning Factor

α(t) is termed the learning factor. Someproperties of the function are:

0 < α < 1

Decreases monotonically with time

When α = 0, learning stops

α can be varied in several waysConstant decrementFunction of training iterationRecursive - αi(t + 1) = αi(t)/(1 + hciαi(t))

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Classification

Assign an arbitrary class to the first grid point

For each grid point calculate distances toeach nearest neighbor

If the distance to a neighbor is less than auser specified threshold then the neighbor isin the same class as the grid point

Finally, find the closest matching neuron inthe training set for the initial grid point.Correspondingly modify class assignments ofall the other grid points

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More to Come

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References[1] Lingran, C.; Gasteiger, J. J. Am. Chem. Soc. 1997, 119, 4033.

[2] Gasteiger, J.; Zupan, J. Angew. Chem. Intl. Ed. Engl. 1993, 32, 503.

[3] Kohonen, T. Self Organizing Maps; Springer Series in Information SciencesSpringer: Espoo, Finland, 1994.

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