Neural Networks Representation

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Neural Networks Representation

1.3 Vectorizing Logistic Regression

All right, I already used the Vectorized approach and without any loops last exercise.

1.4 One-vs-all Classification

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initial_theta = zeros(n + 1, 1);
options = optimset('GradObj', 'on', 'MaxIter', 50);

for i = 1:num_labels
    [theta] = fmincg(@(t)(lrCostFunction(t, X, (y == i), lambda)), initial_theta, options);

all_theta(i,:) = [theta];

the key points here are:

  • for is needed here to loop from 1 to num_labels
  • all_theta should assigned with (i,:), otherwise it will be a one-dimensional vector.

1.4.1 One-vs-all Prediction

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A = sigmoid(X * all_theta');
[m, p] = max(A, [], 2);

the max function will return a two-dimensional vector, m is the value, and p is the max index in that row.

2 Neural Networks

Finally, I touched the Neural Networks with so many classes after. 😳

The are trained to predict.

Before this, I wondering what is the process of prediction with a trained model. Is it the same with the training process?

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a0x = ones(m, 1);

A1 = [a0x, X];
A2 = [a0x, sigmoid(A1 * Theta1')];
A3 = sigmoid(A2 * Theta2');

[v, p] =  max(A3, [], 2);

Amazing ha! 🤩

First I forgot to sigmoid the hidden layer and output layer. The Accuracy shows

Training Set Accuracy: 69.62

And it will get the same accuracy if the output layer has no sigmoid . It also happened in the previous One-vs-all Prediction.

Therefore I still have the question. 🧐

It’s time to keep on the training part. 💪