Self-Organizing Maps (SOM) are a type of neural network that can be used for clustering and visualizing complex, high-dimensional data. SOM reduces dimensionality while preserving topological relationships. It arranges nodes on a grid such that similar input vectors are mapped to nearby nodes. During training, the best matching node and its neighbors are adjusted to better match the input. This results in a 2D map where similar data clusters together. For example, a SOM was used to cluster countries based on quality of life indicators, grouping those with similar living standards. SOM can be useful for applications like data mining, pattern recognition, and more.

1. Self Organizing Maps (SOM) Nguyen Van Chuc- chucnv@ud.edu.vn

2. Outline Motivation Introduction to SOM SOM’s Algorithm An Example Application: Using SOM to cluster data Kohonen’s Neural Network or Self Organizing Maps (SOM)

3. Motivation The problem is how to find out semantics relationship among lots of information without manual labor How do I know, where to put my new data in, if I know nothing about information‘s topology? When I have a topic, how can I get all the information about it, if I don‘t know the place to search them?

4. Self-Organizing Maps : Origins Teuvo Kohonen Ideas first introduced by C. von der Malsburg (1973), developed and refined by T. Kohonen ( Finland ) (1982) Neural network algorithm using unsupervised competitive learning Primarily used for organization and visualization of complex data Neurons are arranged on a flat grid (map, lattice, 2 dimensional array). There is no hidden layer . Only an input and output layer. Each neuron on the grid is an output neuron Topological relationships within the training set are maintained

5. Self-Organizing Maps : The Basic Idea Make a two dimensional array, or map, and randomize it. Present training data to the map and let the cells on the map compete to win in some way ( Euclidean distance is usually used ) Stimulate the winner and some friends in the “neighborhood”. (update weight matrix) Do this a bunch of times. The result is a 2 dimensional “weight” map .

6. Self-Organizing Maps : Introduction

7. Self-Organizing Maps : Introduction The neurons in the output layer are arranged on a map 2d array of neurons Set of input signals (connected to all neurons in lattice) Weighted synapses x 1 x 2 x 3 x n ... w j1 w j2 w j3 w jn j

8. Self-Organizing Maps : Introduction The figure shows a very small Kohonen network of 4 x 4 nodes connected to the input layer (shown in green) representing a two dimensional vector. Each node has a specific topological position (an x, y coordinate in the lattice) and contains a vector of weights 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 Kohonen Network Architecture

9. Example Self-Organizing Maps ‘ Poverty map’ based on 39 indicators from World Bank statistics (1992) World Poverty Map A SOM has been used to classify statistical data describing various quality-of-life factors such as state of health, nutrition, educational services etc. . Countries with similar quality-of-life factors end up clustered together . The countries with better quality-of-life are situated toward the upper left and the most poverty stricken countries are toward the lower right. SOM – Result Example

10. Self-Organizing Maps : Algorithm

11. Example To make the problem very simple, suppose that there are only two neurons in the output layer as shown below:

12. Example Consider a simple example in which there are only 4 input training patterns . Following the algorithm presented in the previous algorithm:

13. Example

14. Example For vector 0011 D(1) = 0.7056, D(2) = 2.724 Hence J = 1 For vector 0001 D(1) = 0.66, D(2) = 2.2768 Hence J = 1. For vector 1000 D(1) = 1.8656, D(2) = 0.6768 Hence J = 2 Likewise for remains training patterns

15. Example This matrix seems to converge to

16. Example TEST NETWORK Suppose the input pattern is 1100. Then Thus neuron 2 is the " winner ", and is the localized active region of the SOM. Notice that we may label this input pattern to belong to cluster 2. For all the other patterns, we find the clusters are as listed below. This matrix seems to converge to

17. Application Using SOM to cluster Data The IRIS dataset IRIS is a classical data set used by statisticians to check classification methods. It is composed by 150 samples of flowers divided into 3 classes (50 setosa, 50 versicolor, 50 virginica) and described by 4 variables (petal length, petal width, sepal length, sepal width

18. Application Using SOM to cluster Data Graphical Results we can look at the assignment of each neuron (i.e. each neuron will be coloured on the basis of the assigned class).

19. Application Using SOM to cluster Data Graphical Results we can look at the weights of a specific neuron and at the labels of the samples placed in that neuron

20. Conclusions SOM is Algorithm that projects high-dimensional data onto a two-dimensional map. The projection preserves the topology of the data so that similar data items will be mapped to nearby locations on the map. SOM still have many practical applications in pattern recognition, speech analysis, industrial and medical diagnostics, data mining Large quantity of good quality representative training data required

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