Notations

Notations:

m: number of training examples
n = $n_x$ = dimension of input feature $x$, so $x \in R^{n_x}$
y $\in$ {0, 1} for Binary Classification
Set {$(x^{(1)}, y^{(1)}),  (x^{(2)}, y^{(2)}), ..., (x^{(m)}, y^{(m)})$} where $(x^{(i)}, y^{(i)})$ is the $i^{th}$ training example

Stacking data by columns:

• X = [$x^{(1)}, x^{(2)}, ..., x^{(m)}$] $\in R^{n_x \times m}$ is a matrix with each feature vector as column
• Y = [$y^{(1)}, y^{(2)}, ..., y^{(m)}$] $\in R^{1 \times m}$ is a (row) matrix with each output as column

Sigmoid function: $\sigma(z) = \frac{1}{(1 + e^{-z})}$ where $z = w^T x + b$ with $w \in R^{n_x}$, $b \in R$

w: weight is row vector $1 \times n_x$
b: bias term, is $\in R$
$n^{[i]}$: number of units in layer $i^{th}$

$W^{[i]}, b^{[i]}$ is the Weights and bias term in $i^{th}$ layer in the neural network

$a^{[i]}$: activation, refers to values that each layer passing on to subsequent layer
$z_i^{[j]}$: node $i^{th}$ in layer $j^{th}$ (input layer is layer 0)
$a^{[j](i)}$: activation resulted from $i^{th}$ training example on layer j