Deep Learning by Andrew Ng (2)

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 2021/03/04   Share

Basics of Neural Network Programming

1. Binary Classification

Logistic regression is an algorithm for binary classification.

Example for binary classification:

Have an input of an image, we want to output a label to recognize this image as being either cat(1) or non cat(0).

There are certain ways an image is represented in a computer. To store an image, computer stores three separate matrices, corresponding to the red, green and blue channels of this image.

So if your input image is 64 pixels by 64pixels, then you would have three 64*64 matrices, and the dimension of input x (feature vector) will be 64*64*3.

$n_{x} = 64 \cdot 64 \cdot 3 = 12288$

input:

$X = \begin{bmatrix}x^{(1)}, x^{(2)}, x^{(3)}, ...\end{bmatrix}$

for each $x^{(i)}$ there are $n_x$ features.

$X.shape = (n_x, m)$

output:

$Y = \begin{bmatrix}y^{(1)}, y^{(2)}, y^{(3)}, ...\end{bmatrix}$ $y^{(i)} = 1 or 0$ $Y.shape = (1, m)$

2. Logistic Regression

Given input feature $x$ , want $\hat{y} = P(y=1|x)$ .

That means we want $\hat{y}$ to be or approach the probability of the chance that $y$ is equal to one given the input feature $x$ .

$x \in R^{n_x}$ $Parameters: w \in R^{n_x}, b \in R$ $Output: \hat{y} = \sigma(w^T \cdot x + b)$ $\sigma(z) = \frac{1}{1 + e^{-z}}$

So, if $z$ large, $\sigma(z) \approx \frac{1}{1+0} = 1$

if $z$ large negative, $\sigma(z) \approx \frac{1}{1+\infty} = 0$

Author：twowd

原文链接：http://wow3.tech/2021/03/04/Deep-Learning-by-Andrew-Ng-2/

发表日期：March 4th 2021, 6:44:57 pm

更新日期：March 4th 2021, 11:10:37 pm

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1. Binary Classification
2. Logistic Regression

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