Coursera Machine Learning-fourth week-neural network Forwardpropagation

The origin of Neural network

Considering a nonlinear classification, when the number of features is very small, the logical regression can be completed, but when the feature number becomes larger, the higher order term will be exponential growth, the complexity is conceivable. The following figure: a high low-grade classification of housing, when the eigenvalues only x1,x2,x3 x_1,x_2,x_3, we can handle it, classification. But when the feature number increases to x1,x2....x100 x_1,x_2....x_100, the efficiency of the classifier is very low.
Here's G (z) =1/(1+e−z) g (z) =1/(1+e^{-z})

Symbol Description: A (j) I a_i^{(j)} represents the first neuron of the J-layer network, for example, the following figure A (2) 1 a_1^{(2)} indicates that the first neuron θ (j) \theta^{(J) in the second layer represents the weighting matrix from the J J layer to the J+1 j+1 layer, for example The theta (1) \theta^{(1)} represents the weight matrix θ (j) of the first layer to the second level, and the UV \theta^{(j)}_{uv} represents the weight of the first U nerve from the V neuron to the j+1 layer of the J layer, for example, in the following figure, Theta (1) \theta^{(1)}_{23 Represents the weight of the 2nd neuron from the 3rd neuron in the first layer to the second layer, note that the subscript UV refers to the weight of the v->u rather than the u->v, the following figure also gives the first layer to the second layer of the title of the general, if the section J has SJ S_ J neurons (excluding the bias neuron), the j+1 layer has sj+1 s_{j+1} neurons (also excluding bias neurons), then the dimension of the weight matrix Θj \theta^{j} is (Sj+1x (