(Solved):   Kohonen self-organizing maps Write a computer program to implement a Kohonen self-organizi ...

 

Kohonen self-organizing maps Write a computer program to implement a Kohonen self-organizing neural network. Use 2 input units, 50 cluster units, and a linear topology (one-dimensional lattice) for the cluster units. Allow the winner and its topological neighbors to learn such that: the radius must be chosen as 4 initially, 3 between \( 1000-5000 \) epochs, 2 between 5000 10000 epochs, 1 between \( 10000-25000 \) epochs and 0 after 25000 epochs (In other words, if unit \( J \) is the winner, then nearest \( 2 r \) units located on the both sides of \( J \) also learn, unless \( J-r<1 \) or \( J+r>50 \).) Use an initial learning rate of \( 0.5 \), and gradually reduce it to \( 0.01 \) (over 20000 epochs). The learning rate should be kept constant at \( 0.01 \) after 20000 epochs. The initial weights on all cluster units are to be random numbers between 1 and \( +1 \) (for each component of the weight vector for each unit). Generate training data as follows: Choose two random numbers between \( -0.5 \) and \( 0.5 \), and call them \( x_{1} \) and \( x_{2} \). Put the point \( \left(x_{1}, x_{2}\right) \) in the training set if \( x_{1}^{2}+x_{2}^{2}<0.25 \) (i.e. \( \left.x_{2}<\sqrt{0.25-x_{1}^{2}}\right) \). The plot of the training data set is shown below. Repeat until you have a set of 50000 training points. After \( 1,100,1000 \) and then every 10000 epochs of training, graph the cluster units (by using their weight vector as a position in the two-dimensional Euclidean plane); draw a line connecting cluster units ( \( C_{1} \) to \( C_{2}, C_{2} \) to \( C_{3} \), etc.), to show their topological relationships. You should start with a real mess for the initial positions of the weights, which will gradually form the projection of the region from which the training point were chosen.