how do i sub-select and make a stack of fully connected layers into partially connected layers?

take the following example of a network architecture:

layers = [
    imageInputLayer([20 20 1],'Name','input')

    fullyConnectedLayer(100,'Name','fc1')  
    fullyConnectedLayer(50,'Name','fc2')
    fullyConnectedLayer(30,'Name','fc3')
    fullyConnectedLayer(10,'Name','fc4')
    softmaxLayer('Name','softmax')
    classificationLayer('Name','classOutput')];

I'd like to do the following

1. train such a network on some custom dataset
2. analyze all the weigths,
3. drop out some weights (make them zero) using some criterion (not important for now) and
4. design a new network with this new "connectivity pattern" - i.e. i want to completely remove the possibility of training these weights - i would like to remove these connections.p.s. these new layers would be "partially connected" and not fullyConnected.
5. train this novel network architecture from scratch but this time id have fewer weights to learn.

I would like help in trying to implement this. Thanks in advance

[Greg Heath]

Good Luck!