Andrew Ng 's machine learning lecture note (9)

Artificial Neuron Model

   (1)

(2)We should learn some denotion first to understand the above second model.

For the activation units ,we have the below expression :

Finally , we can get the conclusion that the layer J's theta is a matrix. 

stands for the number of the layer J's units . stands for the number of the layer (J+1)'s units

Vetorization rise implementation

In order to make our calcus more simple, we have the following new denotions and formulars.

 

is a transition variable . 

Finally ,   

Pay attention : When programing , it's necessary to add the bias unit manually in the process of calculating new alpha.

One vs all algorithm in neuron model

Assume that we have n classes to be classified , our model has m layers then our output layer should look like :

And it can be      ... ...

Each one represents one situation of output ,like the following example