KOHONEN SELF ORGANISING MAP

SEMINAR BYM.V.MAHENDRAN.,Reg no:200831328

III SEM,M.E., Control And Instrumentation Engg

Introduction to Neural networks

• Artificial Intelligence: -Automation of Intelligence of human behaviour

• Turing test: -output indistinguishable

• Hard computing: -computations using ones and zeros

• Soft computing: -computation as like as human brain does

Introduction to Neural networks.. cont

• Soft computing: -Neural network -Fuzzy logic -Genetic algorithm

• Feature of Neural networks -Highly massive parallel and distributed computation.

-Fault tolerant -Mapping , Generalization, Robustness

Neural networks

• ANN learning:-Training with known examples of problem-Supervised-as if teacher present-Unsupervised –as if no teacher present-Weight are updated…

how? Using rules. Whether continuous manner or discrete step Delta rule..

Weight update rule

• Delta rule:Input /output pair is known.

-Apply input to ANN.-Compute output. -Compute error

-Forming error function-Minimization of error

-Reach local minimum / global minimum

*** this delta Rule can be generalized for any number of layers

Kohonen self organising map

• SOM motivated by the feature of human brain.• The neurons organized in one or multi dimensional lattices.•The Neurons compete among themselves to be activated in according to a competition learning scheme. •The weight vector accosicated with winning neuron is only updated in the scheme ’WINNER TAKES ALL’.•The ‘soft max’ rule however not only winning neurons but also other neighbourhood neurons take path in the self organising process.

Kohonen self organising map (cont) • Kohonen introduced a novel neighbourhood

concept where the topology of input data space can be learnt through SOM.

•In this scheme , a neural lattice can be one or multi dimensional neighbourhood concept among individual neurons in a lattice is a priory embedded.

•As neurons updates their weights upon competition, a meaningful co-ordinated system for different input feature over the lattice is developed.

•2 D Kohonen Lattices

SOM LEARNING ALGORITHM

• Random weight initialization.

•There are three essential processes involved in the formation of SOM.

1. Competition. ( To find Winner)2. Co-operation ( Neighbourhood)3. Weight update

1. COMPETITION

• computing distance measure ƒ(lateral distance) for all neuron.

• The neuron for which ƒ(lateral distance) is minimum declared as Winner.

2. CO-OPERATION

• The winning neuron selects the neighbourhood according to a

pre-defined neighbourhood function.

• Let D(i) denotes the topological neighbourhood centered on

winning neuron i.

• di,j denotes the lateral distance between winning neuron I and

excited neuron j

• The amplitude of topological neighbourhood decreases

monotonically with increasing lateral distance and decaying

to zero. This is necessary condition for convergences.

3. WEIGHT UPDATE

• In beginning winning neuron, all other neurons are considered as neighbours. As learning progress neighbourhood shrinks

• Weight associated with winning neuron and its neighbours are updated as per neighbourhood index.

• Winning neuron allowed o be maximally benefited from the weight update while neurons farthest from the winner is minimally benefitted.

CLUSTERING

• How can we represent voluminous data using finite number of samples.

• Topology of input space preserved.

SOM Graphics

• Video demo how SOM formed

Architecture of KSOM

Kohonen SOM

problem

Problem soln:

Matlab SOM video

THAK YOU