Kohonen Self Organizing Map




Introduction

Kohonen self organizing map is a unsupervised clustering algorithm

Clusters high dimensional input to easy to visualize 2D representations

Used to find patterns/ clusters

This is kind of constrained K-Means

Algorithm

Create Self Organizing Map

  • Define map width

  • Define map height

  • Define max epochs

  • Define no of colors, need to classify

  • Define inputs - pixels values in the range 0-256 with rgb values

  • Define initial weights - weight values in between 0-1 for all nodes

  • Define initial learning rate = 0.1

  • Define initial neighbourhood radius

  • Define time constant

  • Define node locations (x & y)

  • Iterate through the training loop & update weights

    • Select random input from the inputs of colors

    • Update weights

      • Find the winning neuron/Best Matching Unit - calculate Euclidean Distance  between the random input and nodes to find the node with minimum distance

        • Iterate through all nodes 

          • Find the euclidean distance between the current node and BMU

          • Find the influence 

                                              

    • Update the weight of the current node

  • Update the learning rate

                            

  • Update the neighborhood radius

            
            

  • Translate the weights of each node in the map to pixel data (image)

    • Image height = map height

    • Image width = map width

    • Each element has a vector with 3 values (rgb)

  • Plot the image


Source code

Click the following link 

Kohonen Self Organizing Map

Click open with google colaboratory

Go to Runtime -> Change Runtime Type

Set Hardware accelerator to GPU

Exercise 1 : Output


    width=10

    height=10

    no_of_colors=20

    Max_Epoch=100




Exercise 2 : Output

    width=10

    height=10

    no_of_colors=20

    Max_Epoch=200





Exercise 3: Output

     width=10

    height=10

    no_of_colors=20

    Max_Epoch=500





Exercise 4 : Output

    width=100

    height=100

    no_of_colors=20

    Max_Epoch=1000



Test Case 1

Inputs 

width = 10, height = 10, no_of_colors = 20, max_epoch = 100

Parameter,      Expected output

som.NO_OF_COLORS, 20

som.INPUT_DATA_SHAPE[0], 20  som.INPUT_DATA_SHAPE[1], 3

som.MAP_WIDTH, 10  som.MAP_HEIGHT, 10

som.SOM_SHAPE[0], 10  som.SOM_SHAPE[1], 10

Inputs values in range 0-256

Initial Weights values in range 0-1

som.MAX_EPOCH, 100

som.ALPHA_0, 0.1

som.SIGMA_0, 5

som.TIME_CONST, 143.0676558073393


Test Case 2


Inputs 

width = 10, height = 10, no_of_colors = 20, max_epoch = 100

input = [0.5,0.3,0.7]

nodes = [[5,13,20],[14,7,3],[2,12,30]]


Parameter,      Expected output

Node 1 Euclidean distance 23.5

Node 1 Euclidean distance 15.2

Node 1 Euclidean distance 31.6

Best Matching Unit, 1 (second node with weights of [14,7,3])



Test Case 3

Inputs 

width = 10, height = 10, no_of_colors = 20, max_epoch = 100

epoch =1, ALPHA_0 = 0.1, TIME_CONST, 143.0676558073393


Parameter,      Expected output

Decayed learning rate, 0.09930346710946143



Test Case 4

Inputs 

width = 10, height = 10, no_of_colors = 20, max_epoch = 100

epoch =1, SIGMA_0 = 5, TIME_CONST, 143.0676558073393


Parameter,      Expected output

Decayed neighbourhood radius, 4.9651733554730715







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