吴恩达机器学习IV
于2020年11月15日2020年11月15日由Sukuna发布
这一周只需要对两个函数进行更改就行了
第一题:实现神经网络的前后传播
代码语言：javascript复制function [J grad] = nnCostFunction(nn_params, ...
input_layer_size, ...
hidden_layer_size, ...
num_labels, ...
X, y, lambda)
%NNCOSTFUNCTION Implements the neural network cost function for a two layer
%neural network which performs classification
% [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
% X, y, lambda) computes the cost and gradient of the neural network. The
% parameters for the neural network are "unrolled" into the vector
% nn_params and need to be converted back into the weight matrices.
%
% The returned parameter grad should be a "unrolled" vector of the
% partial derivatives of the neural network.
%
% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
% for our 2 layer neural network
Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size 1)), ...
hidden_layer_size, (input_layer_size 1));
Theta2 = reshape(nn_params((1 (hidden_layer_size * (input_layer_size 1))):end), ...
num_labels, (hidden_layer_size 1));
% Setup some useful variables
m = size(X, 1);
% You need to return the following variables correctly
J = 0;
Theta1_grad = zeros(size(Theta1));
Theta2_grad = zeros(size(Theta2));
% ====================== YOUR CODE HERE ======================
% Instructions: You should complete the code by working through the
% following parts.
%
% Part 1: Feedforward the neural network and return the cost in the
% variable J. After implementing Part 1, you can verify that your
% cost function computation is correct by verifying the cost
% computed in ex4.m
%
% Part 2: Implement the backpropagation algorithm to compute the gradients
% Theta1_grad and Theta2_grad. You should return the partial derivatives of
% the cost function with respect to Theta1 and Theta2 in Theta1_grad and
% Theta2_grad, respectively. After implementing Part 2, you can check
% that your implementation is correct by running checkNNGradients
%
% Note: The vector y passed into the function is a vector of labels
% containing values from 1..K. You need to map this vector into a
% binary vector of 1's and 0's to be used with the neural network
% cost function.
%
% Hint: We recommend implementing backpropagation using a for-loop
% over the training examples if you are implementing it for the
% first time.
%
% Part 3: Implement regularization with the cost function and gradients.
%
% Hint: You can implement this around the code for
% backpropagation. That is, you can compute the gradients for
% the regularization separately and then add them to Theta1_grad
% and Theta2_grad from Part 2.
%
%数据集X:5000*400
%y:1*m的向量
yNum = zeros(m,num_labels);
for i=1:m
yNum(i,y(i))=1;
end
%开始训练
a1=X
P00*25
%第一层开始训练了
%Theta1 25*401
z2=(Theta1 * [ones(m,1) a1]')';
a2=sigmoid(z2);
P00*10
%第二层开始训练
z3 = (Theta2 * [ones(m, 1) a2]')';
a3 = sigmoid(z3);
%计算代价函数
for i = 1:m
J = J (-yNum(i, :) * log(a3(i, :))' - (1.- yNum(i, :)) * log(1.- a3(i, :))');
end
%取第i行与a3(算出来的最后结果)的第i列做点积即可
J = J / m
%正则化
t1 = Theta1(:, 2:end);
t2 = Theta2(:, 2:end);
regularization = lambda / (2 * m) * (sum(sum(t1 .^ 2)) sum(sum(t2 .^ 2)));
J = J regularization;
%取非1的元素,平方求和
% 5000 x 10
d3 = a3-yNum;
% 5000 x 25
%sigmoidGradient是之前写好的求导函数
%不包含第1列:全部为1
d2 = (d3 * Theta2(:, 2:end)) .* sigmoidGradient(z2);
% 10 x 26 Theta2_grad
%这里是求最后的梯度下降值
%偏差乘以原来的元素就是梯度下降值
a2_with_a0 = [ones(m, 1) a2];
D2 = d3' * a2_with_a0;
Theta2_grad = D2 / m;
%正则化,不对第一行处理,因为是bias量
regularization = lambda / m * [zeros(size(Theta2, 1), 1) Theta2(:, 2:end)];
Theta2_grad = Theta2_grad regularization;
% 25 x 401 Theta1_grad
a1_with_a0 = [ones(m, 1) a1];
D1 = d2' * a1_with_a0;
Theta1_grad = D1 / m;
regularization = lambda / m * [zeros(size(Theta1, 1), 1) Theta1(:, 2:end)];
Theta1_grad = Theta1_grad regularization;
% -------------------------------------------------------------
% =========================================================================
% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];
end解释一下后传播
D是Delta,d是delta,
第二题 求sigmoid函数导数
代码语言：javascript复制function g = sigmoidGradient(z)
%SIGMOIDGRADIENT returns the gradient of the sigmoid function
%evaluated at z
% g = SIGMOIDGRADIENT(z) computes the gradient of the sigmoid function
% evaluated at z. This should work regardless if z is a matrix or a
% vector. In particular, if z is a vector or matrix, you should return
% the gradient for each element.
g = zeros(size(z));
% ====================== YOUR CODE HERE ======================
% Instructions: Compute the gradient of the sigmoid function evaluated at
% each value of z (z can be a matrix, vector or scalar).
%直接计算导函数,每一个元素的导函数值都存进去,所以说之间加了个.
g = sigmoid(z) .* (1.- sigmoid(z));
% =============================================================
end
