Kohonen self-organizing maps (SOMs) are a type of neural network that performs unsupervised learning to produce a low-dimensional representation of input patterns. SOMs were developed in the 1980s by Professor Tuevo Kohonen and work by mapping multi-dimensional input onto a two-dimensional grid. The algorithm finds groups in the data by finding similarities between input vectors and weight vectors in the nodes. It adjusts the weights to better match the input through competitive learning without supervision. SOMs have been used for applications like document organization, poverty classification, and text-to-speech.

1. KOHONEN SELF ORGANIZING MAPS

2. History of kohonen som
 Developed in 1982 by Tuevo Kohonen, a professor
emeritus of the Academy of Finland
 Professor Kohonen worked on auto-associative
memory during the 70s and 80s and in 1982 he
presented his self-organizing map algorithm

3. History of Kohonen SOMs
 His idea on Kohonen SOM only became famous much
later in 1988 when he presented a paper on “The Neural
Phonetic Typewriter” on IEEE computer that his work
became widely known
 Since then many excellent papers and books have been
made on SOM

4. What are self organizing maps?
•Are aptly named “Self-Organizing” because no
supervision is required.
•SOMs learn on their own through unsupervised
competitive learning.
•They attempt to map their weights to conform to
the given input data.

5. What are self organizing maps?
•Thus SOMs are neural networks that employ unsupervised
learning methods, mapping their weights to conform to the
given input data with a goal of representing
multidimensional data in an easier and understandable
form for the human eye. (pragmatic value of representing
complex data)

6. What are self organizing maps?
•Training a SOM requires no target vector. A SOM
learns to classify the training data without any
external supervision.

7. The Architecture
•Made up of an input nodes and computational
nodes.
•Each computational node is connected to each input
node to form a lattice.

8. The Architecture
•There are no interconnections among the
computational nodes.
•The number of input nodes is determined by the
dimensions of the input vector.

9. Representing Data
•Weight vectors are of the same dimension as the
input vectors. If the training data consists of
vectors, V, of n dimensions:
V1,V2,V3...Vn
•Then each node will contain a corresponding
weight vector W, of n dimensions:
W1,W2,W3...Wn

10. A sample SOM

11. Terms used in SOMs
•vector quantization -This is a data compression
technique. SOMs provide a way of representing
multidimensional data in a much lower
dimensional space; typically one or two
dimensions

12. Terms used in SOMs…
•Neighbourhood
•Output space
•Input space

13. EXPLANATION: How Kohonen SOMs work
The SOM Algorithm
•The Self-Organizing Map algorithm can be broken up
into 6 steps
•1). Each node's weights are initialized.
•2). A vector is chosen at random from the set of
training data and presented to the network.

14. EXPLANATION: The SOM Algorithm…
3). Every node in the network is examined to calculate
which ones' weights are most like the input vector.The
winning node is commonly known as the Best Matching
Unit (BMU).

15. EXPLANATION: The SOM Algorithm…
•4).The radius of the neighbourhood of the BMU is
calculated.This value starts large.Typically it is set to
be the radius of the network, diminishing each time-
step.

16. EXPLANATION: The SOM Algorithm…
•5). Any nodes found within the radius of the BMU,
calculated in 4), are adjusted to make them more like
the input vector (Equation 3a, 3b).The closer a node is
to the BMU, the more its' weights are altered
•6). Repeat 2) for N iterations.

17. Computation of scores
•The Function for calculating the score inclusion for
an output node is known as : 𝑖 𝑛𝑖 − 𝑤𝑖𝑗 2
•Thus to calculate the score for inclusion with
output node i:

18. Computation of scores…
•To calculate the score for inclusion with output
node j:
(0.4 − 0.3)2 + (0.7 − 0.6)2 = 0.141

19. The Winning Node
•Node j becomes the winning node since it has the
lowest score.
•This implies that its weight vector values are similar
to the input values of the presented instance.
•i.e.The value of node j is closest to the input vector.
•As a result, the weight vectors associated with the
winning node are adjusted so as to reward the node
for winning the instance.

20. Concluding the tests
• Both of these are decreased linearly over the span of several iterations and
terminates after instance classifications do not vary from one iteration to
the next
• Finally the clusters formed by the training or test data are analysed in order
to determine what has been discovered

21. NEIGHBORHOOD ADJUSMENTS
• After adjusting the weights of the winning node, the neighbourhood nodes
also have their weights adjusted using the same formula
• A neighbourhood is typified by a square grid with the centre of the grid
containing the winning node.
• The size of the neighbourhood as well as the learning rate r is specified when
training begins

22. ILLUSTRATION: A Color Classifier
•Problem: Group and represent the primary colors and
their corresponding shades on a two dimensional plane.

23. A Color classifier: Sample Data
•The colors are represented in their RGB values to
form 3-dimensional vectors.

24. A Color classifier: Node Weighting
•Each node is characterized by:
•Data of the same dimensions as the sample
vectors
•An X,Y position

25. A Color Classifier: The algorithm
Initialize Map
Radius = d
Learning rate = r
For 1 to N iterations
Randomly select a sample
Get best matching unit
Scale neighbors
Adjust d, r appropriately
End for

26. A Color classifier:The Layout

27. A Color classifier: Getting a winner
•Go through all the weight vectors and calculate the
Euclidean distance from each weight to the chosen
sample vector
•Assume the RGB values are represented by the
values 0 – 6 depending on their intensity.
•i.e. Red = (6, 0, 0); Green = (0, 6, 0); Blue = (0, 0, 6)

28. A Color classifier: Getting a winner…
•If we have colour green as the sample input instance, a
probable node representing the colour light green (3,6,3)
will be closer to green than red.
• Light green = Sqrt((3-0)^2+(6-6)^2+(3-0)^2) = 4.24
Red = Sqrt((6-0)^2+(0-6)^2+(0-0)^2) = 8.49

29. A COLOR CLASSIFIER: DETERMINING THE
NEIGHBORHOOD
• Since a node has an X – Y position,
it’s neighbors can be easily
determined based on their radial
distance from the BMU
coordinates.

30. A COLOR CLASSIFIER: DETERMINING THE
NEIGHBORHOOD…
• The area of the neighbourhood shrinks over time with
each iteration.

31. A Color classifier: Learning
•Every node within the BMU's neighbourhood (including
the BMU) has its weight vector adjusted according to a
pre-determined equation
•The learning rate is decayed over time.

32. A Color classifier: Learning
•The effect of learning should be proportional to the
distance a node is from the BMU.
•A Gaussian function can be used to achieve this, whereby
the closest neighbors are adjusted the most to be more
like the input vector.

33. A Color classifier: Sample output
• Classification on a 40 x 40 SOM

34. Current Applications
• WEBSOM: Organization of a Massive Document
Collection

35. Current Applications…
•Classifying World Poverty

36. Current Applications…
•PhoneticTypewriter