predicting crossproduct and magnitude of a vector

I do programming exercises and need to answer if it’s possible to predict the magnitude of a vector in using neural networks. Here we assume that any element of a vector is a real number between -10 and 10. For this exo I'm supposed to use feedforwardnet function.Here is my attempt to code it:

arr = {};
vals = [];
for c = 1:10
    arr{c} = -10 + (10+10)*rand(3,1);
    vals(c) = norm(arr{c});
end
A = cell2mat(arr);
net = feedforwardnet([3 2]);
net.layers{1}.transferFcn = 'tansig';
net.layers{2}.transferFcn = 'purelin';
net = train(net, A,vals);
view(net)

arr2 = {};
vals2 = [];
for c = 1:10
    arr2{c} = -10 + (10+10)*rand(3,1);
    vals2(c) = norm(arr2{c});
end
A2 = cell2mat(arr2);

y2 = cell2mat(net(arr2));
err = immse(y2, vals2);

Probably I messed up with number of layers and functions. Also I don't have enough base in machine learning to answer if this task is possible for NN, so all ideas about it are welcome. And I wonder if it would be possible to predict a cross product of 2 vectors in ?

Answer 1

[Chunru]

Multiple-layer feedforward network is a universal approximater (with some nonlinear transfer functions). So you can predict the vector norm.

ntrain = 100000;        % need more train data
Xtrain = rand(3, ntrain)*20-10;     % Train input
Ttrain = sqrt(sum(Xtrain.^2));      % Train target

net = feedforwardnet([3 2]);
net.layers{1}.transferFcn = 'tansig';
net.layers{2}.transferFcn = 'purelin';
net = train(net, Xtrain, Ttrain);


ntest = 1000;        % test data
Xtest = rand(3, ntest)*20-10;     % test input
Ttest= sqrt(sum(Xtest.^2));      % test target
Ytest = net(Xtest);

err = std(Ytest-Ttest)

[d]

Thank you!

And for prediction of a cross product of 2 vectors is it possible? I'm not sure what input data should be in this case. An array of cells of 2 vectors?

[Chunru]

As universal approximator, it is also possible to predict the cross duct.

ntrain = 100000;        % need more train data

% inputs: 1-3 for vector1 and 4-6 for vector2 
Xtrain = rand(6, ntrain)*20-10;     % Train input for vector1 and vector 2

Ttrain = cross(Xtrain(1:3, :), Xtrain(4:6, :));      % Train target (output size is 3)
net = feedforwardnet([3 2]);

net.layers{1}.transferFcn = 'tansig';
net.layers{2}.transferFcn = 'purelin';