Question

Assume, a two dimensional neural network with nine neurons is given. The coordinate vectors i j of the neurons in the lattice are i₁ = [ 0,2 ] ; i₂ = [1,2] ; i₃ = [2,2] ; i₄ = [0,3] ; i₅ = [2,3] ; i₆ = [0,4] ; i₇ = [1,3] ; i₈ = [1,4] ;i₉ = [2,4]. At a certain time step t the weight vectors wⱼ are : W₁ = [4,5] ; W₂ =[5,3] ; W₃= [4,6] ; W₄ =[1,1] ; W₅ = [0,0] ; W₆ =[6,4], W₇ =[2,2] ; W₈ = [3,5] ; W₉ = [5,4]. At time t we have an input vector v [2.5 , 3] What will be the value of the weights at time t+1 if we apply the Kohonen's SOM algorithmic adaptation rule?

Answer 1

The question involves updating weight vectors of a neural network using Kohonen's SOM algorithm, which requires determining the Best Matching Unit and applying the adaptation rule. However, the exact updated weight values cannot be computed without knowing the learning rate, neighborhood function, and BMU.

Step-by-step explanation:

The question involves applying Kohonen's Self-Organizing Map (SOM) algorithmic adaptation rule, which is a topic in neural networks, a subfield of computer science. In this case, a two-dimensional neural network with nine neurons is presented, and we are tasked with calculating the updated weight vectors at time t+1 after presenting the input vector v at time t.

To update the weight vectors using Kohonen's SOM algorithm, we typically identify the neuron with the weight vector closest to the input vector (called the Best Matching Unit, or BMU), and then adjust the weights of the BMU and its neighborhood neurons closer to the input vector. The adaptation rule is applied, which typically has the form: w_new = w_old + θ(L)*(v - w_old), where θ(L) is the learning rate that often decreases with time or distance from the BMU, and L denotes the actual iteration or step.

However, the exact updated values for the weight vectors at time t+1 cannot be determined without additional information about the learning rate, the neighborhood function, and which neuron is the BMU. Therefore, without specifying these parameters, the updated values for the weight vectors cannot be defined.