Self Organizing Maps

Made ByDaksh Raj Chopra

(Trainee – Defence Research and Development Organization(DRDO), Delhi)

What is SOM

• A map which quantizes the high dimensional data items to two – dimensional image in an orderly fashion.

• A non linear projection in which data items having same attributes are present in a dense area.

• It represents input data by models, which are local averages of data.

Why do we need SOM

There existed a projection known as Sammon Projection which showed image of data items having same attributes closer to each other and different one having more distance. But it could not convert high dimensional to low dimensional image. For that we needed SOM which work on machine learning process from the neurons(attributes) provided at the input.

What does SOM do

• SOM is a neural model. In this models are developed that is the final value of model or weighted vectors are developed by learning.

• Similar models have nodes closer in the array and different models have farther nodes in the array.

SOM as DATA MINE

SOM used a data mining technique, that it works on the principle of pattern recognize. It uses the idea of adaptive networks that started the Artificial Intelligence research. This further helps in the data analysis. For example while studying 17 different elements, we used to differentiate of the basis of physical properties but SOM learned the values and made a pattern. After that it did a clustering of that 17 elements

Applications of SOM

• Statistical methods at large• Industrial analysis• Biomedical analysis• Financial application

Size selection of array• This is the first question that comes to our mind that what

should be the size of structure of data items. There is no particular size for the structure. It is purely a hit-and-trial error method and final answer can be obtained. Typical size of nodes can be from few dozens to hundreds.

• Also there are different shapes for the array having topology like cylinder, torus or sphere. Problem arises at the boundaries where there are distortion and discontinuities. Toroidal topology have solved the issue as it has no boundaries.

Batch computation of SOM

• This algorithm is usually preferred in practice because of 2 reasons. First is that it does not require time learning rate parameter which was needed in stepwise model making this algorithm faster.

• Secondly the algorithm gets over in fixed number of iterations if the training points are same at every iteration and neighborhood function is held constant.

Pictorial illustration ofSelf organizing map

Illustrations done using self organizing map technique

SOM of metallic elements

• Now first the physical attributes(density, fusion, boiling point, etc) of these metals were given. Then a SOM of these metals was created.

• Unexpectedly the ferromagnetic elements were placed in the first row even when the magnetic properties of these elements was not considered.

• Secondly the noble metal series was also unexpected as the chemical properties was not provided.

• This show that there is a strong correlation between physical and chemical properties of elements.

SOM of color vectors

• Another example in which a color matrix was given for the creation of SOM. Then again an unexpected result came in the SOM.

• An output of two dimensional color matrix came in which a three dimensional matrix was given. There was no black color in the matrix but only bright colors. Again the experiment was done and more bright colors were obtained.

Feature of SOM

U – MatrixU matrix helps in better visualization of map. Data items present close to each other are lightly colored and items at a far distance are darker in color.

Commands Used in MATLAB• min- this finds the minimum value in the vector/matrix.• max- this finds the minimum value in the vector/matrix.• som_lininit- this initializes the map after calculating the eigen

vectors• som_batchtrain- trains the given som with the given training

data.• som_cplane- this visualizes a 2D plane or u matrix• sum- adds all the array elements.• mod- gives the remainder.• floor- rounds off the number to the lower value.• text- creates text object at the axes.

Clustering of Data

Objective• A spectral data of 25 soils is given. • Adding some amount of noise to the

spectrum(0.4-2.5 nm) and see any change in the properties.

• Finally clustering the data with the help of SOM formed.

Experiment

Procedure• A range of spectral values was taken of any one

soil type(say Very dark grayish brown silty loam) at a time.

• A small amount of noise was added to the spectrum starting with the SNR 60 and further decreasing the SNR by 2(increasing the noise).

• A spectral table of 7 different spectrum having different noise level was clustered.

0 100 200 300 400 500 600 700 800 900 10000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

TOTAL PLOT

VISIBLE RANGE SPECTRUM (0.4-0.7 NM)

NEAR INFRARED RANGE (0.7 – 1.4 NM)

SHORT WAVELENGTH INFRARED(1.4 – 2.5 NM)

VISIBLE

NEAR INFRARED RANGE

SHORT

WAVELENGTH

INFERENCE

We can see from the above clustering that as the wavelength is increasing there is less effect on the properties of the material as when we see the clustering in visible range, the groups are little far and in near infrared region, they are little near but in short wavelength they are much near to each other.

THANK YOU