Question

Give an example of neural network using matrices please and explain it

Answer 1

Really the use of matrices in representing the neural network and perform calculation will allow us to express the work we need to do concisely and easily.

Let us begin by visualising the simplest of all the network which consist of one input with two neurons and one output.

I think the above calculation we have done already and really doesn’t need matrices. Hmm… let try a bit more complex by making the output layer with two neuron.

Now instead of going through each node and multiply with the weights with input and passing to next layer, we can simply represent using the below matrix notation where:

A bit more with 3 layers with 3 neurons each and this time let’s use code to compute the output. Below is the network we are trying to solve:

Instead of assigning all the weights, let’s see in matrices form:

Input -> Hidden layer (W x I = H)

The Input layer is multiple with weight matrices which gives the output of the Hidden Layer.

Code:

// Define matrix I
double[,] I_Array = {{ 0.2},
{ 0.1},
{0.3}};

Matrix<double> I = Matrix<double>.Build.DenseOfArray(I_Array);


// Define weight matrics between Input and Hidden layer
double[,] W_IH_Array = {{ 0.6,0.4,0.1},
{ 0.5,0.3,0.1},
{0.2,0.9,0.7}};

Matrix<double> W_IH = Matrix<double>.Build.DenseOfArray(W_IH_Array);


//Multiple W x I to get output for the hidden layer
Matrix<double> H = W_IH * I;
H.Dump();

And below is the result of the Hidden layer:

Hidden -> Output Layer (W x H = Y)

Code:

// Define weight matrics between Input and Hidden layer
double[,] W_HY_Array = {{ 0.2,0.4,0.9},
{ 0.6,0.2,0.1},
{0.7,0.4,0.7}};

Matrix<double> W_HY = Matrix<double>.Build.DenseOfArray(W_HY_Array);
//Multiple W x H to get output for the final outout layer
Matrix<double> Y = W_HY * H;
Y.Dump();

Below is the result of the output layer

That it, so easy in just a few lines of code we simply calculated the output of the 3 layered neural networks.