神经网络基础视频笔记(一)

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1. Binary Classification
logistic regression is an algorithm to implement binary classification.

2. The saving mode of image

 A RGB image is saved as a three-dimension array(64*64*3) in the computer. We reshape the array into a new vector X(64*64*64*3, 1), which is the input of the neural network. We define the height of X as n_{x}The goal of Binary Classification is to learn a classifier. This is a process from 'x' to 'y'.  'y' is 0 or 1.
3. Notation
(1) (x,y) : a single training example.
(2) x:  n_{x}-dimensional feature vector. x\in \mathbb{R}^{n_{x}}
(3) y: The label of x. y\in \begin{Bmatrix} 0,1 \end{Bmatrix}(0 or 1 represents if it is the object we want to detect.) 
(4) m training example:\begin{Bmatrix} \bigl(\begin{smallmatrix} x^{(1)}, y^{(1)} \end{smallmatrix}\bigr), \bigl(\begin{smallmatrix} x^{(1)}, y^{(1)} \end{smallmatrix}\bigr) ,..., \bigl(\begin{smallmatrix} x^{(m)}, y^{(m)} \end{smallmatrix}\bigr) \end{Bmatrix}.  
(5) m_train: X = \begin{bmatrix} x^{(1)} ,x^{(2)} , ...,x^{(m)} \end{bmatrix} (X\in \mathbb{R}^{n_{x}\times m})
(6) m_test: Y = \begin{bmatrix} y^{(1)},y^{(2)},...,y^{m} \end{bmatrix} (Y\in \mathbb{R}^{1\times m})

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