Machine learning algorithms: logistic regression classification algorithms and applications (including video tutorials and source code)

I. Introduction logistic regression

1 machine learning methods, logistic regression (Logistic regression) for solving a binary (0 or 1) the problem, i.e., the party is a classification algorithm.
• Typical applications:
• image classification
• Spam Detection
• the purchase of goods prediction
• ...

2, Sigmoid function
Sigmoid function, also called logical function (Logistic function)

 

official

 

 

Intuitive understanding
• arbitrary input mapping to the [0,1] linear regression we can get a predicted value, then the value is mapped to the Sigmoid function thus completing the conversion by the value of the probability, that is, the classification task .

3, logistic regression linear regression vs

Are regression
• objective regression is a linear regression (-∞, + ∞) • logistic regression regression target is (0, 1), it is often used as a classification
• We will fit a regression function on P (Y = 1 | X)

linear regression----> logistic regression

 

4, logistic regression
for binary classification problem, we can:

 

We will f (x, w) seen as a possibility (probability), then we can get:

 

 

5, maximum likelihood probabilities
for all N samples, all of the correct classification probability is

 

So our goal is to maximize J (w).

 

6, the log-likelihood probability
will not optimize the expression directly, then we logarithmic

 

So our goal is to maximize L (w)

 

7、最大log似然求解
We could learn w by maximizing the log likelihood using gradient ascent

 

 

二、二分类分类器处理多分类问题

1. 一对多（One v.s. other）
2. 一对一（One v.s. One）

二分类扩展到多分类

一对多（One v.s. other） • 区分[cat, dog, bird]
• 二值分类器：clf_bin
• 猫的分类器：
• if_cat = clf_bin((X_cat,Y_cat), (X_ncat,Y_ncat))
• 狗的分类器：
• if_dog = clf_bin((X_dog,Y_dog), (X_ndog,Y_ndog))
• 鸟的分类器：
• if_bird = clf_bin((X_bird, Y_bird), (X_nbird, Y_nbird))

1、一对多（One v.s. other）

 

 

一对多（One v.s. other）

1. 分类，输入样本x
2. 使用if_cat, if_dog, if_bird三个分类器进行分类
3. 哪个分类器的值大就是哪一类

二分类扩展到多分类

一对一（One v.s. One） • 区分[cat, dog, bird]
• 二值分类器：clf_bin
• 猫/狗的分类器：catdog_clf = clf_bin(..,..)
• 猫/鸟的分类器：catbird_clf = clf_bin(..,...)
• 狗/鸟的分类器：dogbird_clf = clf_bin(..,..)

1、一对一（One v.s. One）

1. 分类，输入样本x
2. 使用catdog_clf, catbird_clf, dogbird_clf三个分类器进行分类

3. 然后进行投票，票数多赢，比如两个分类器都投cat，那么就是cat

   
   
    

   

 

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