Project Description: In this project, you need to complete the following tasks:
1.) First, generate the double half-moon pattern following the example code shown during the computer experiment video. The radius of the moon is 10, width is 6, and distance between two half-moons is 0.5. The total sample number is 2500.
2.) Construct your neural network with 2 inputs (coordinates), 1 extra input (bias), 1 neuron, 1 activation function, and 1 output (-1 or 1).
3.) Initialize the weights vector using a random number generator.
4.) Choose 500 training data and 2000 testing data.
5.) Train your neural network with the Gauss-Newton method. Details can be found from slides P30~P31.
6.) Compare your results with the training data using the initial weight vector and the well-trained weight vector.
7.) Compare your results with the testing data using the initial weight vector and the well-trained weight vector.
8.) Plot the MSE (Mean Squared Error) with respect to training iterations.