Classification and Representation

7 月第一天!!! oh~~ Summer~~ GOGO!

你有多自律，就有多自由。

Classification : article

Classification:

• EX:
  1. Email: Spam / Not Spam?
  2. Online Transactions: Fraudulent (Yes / No)?
  3. Tumor: Malignant / Benign?

   # binary classification problem
   y ⊂ {0, 1}    
   0: "Negative Class" (e.g., benign tumor)
   1: "Positive Class" (e.g., malignant tumor)  
  
   # multiclass classification problem
   y ⊂ {0, 1, 2, 3, ...}
  

• 使用 linear regression 來做 classification problems 通常不優!
  從大神的圖可以看到，如果再加一數值進到資料集裡面，曲線又會再做更便兒~

• 讓我們再想想

   Classdification: y = 0 or 1
     
   hθ(x) can be > 1 or < 0
  

Logistic Regression is actually a classification algorithm:

Logistic Regression: 0 ≤ hθ(x) ≤ 1

Hypothesis Representation : article

Logistic Regression Model:

• Want 0 ≤ hθ(x) ≤ 1

   hθ(x) = g ( θ^T * x )
  

• Sigmoid function (Logistic function):

   g(z) = 1 / 1 + e^-z
  

We Got:

• hθ(x) = 1 / 1 + e^-(θ^T * x)
  

• 

Interpretation of Hypothesis Output:

hθ(x) = estimated probability that y = 1 on input x

• EX:

          | x0 |   |     1     |
   if x = | x1 | = | tumorSize |
   hθ(x) = 0.7
  

  • Tell patient that 70 % chance of tumor being malignant
  • hθ(x) = P(y=1|x;θ), y = 0 or 1 “Probability that y = 1, given x, parameterized by θ”

     P(y=0|x;θ) + P(y=1|x;θ) = 1
     P(y=0|x;θ) = 1 - P(y=1|x;θ)
    

Decision Boundary : article

Logistic regression:

hθ(x) = g ( θ^T * x )
g(z) = 1 / 1 + e^-z

• y = 1 (θ^T * x) ≥ 0
• y = 0 (θ^T * x) < 0

Decision Boundary:

Non-linear decision boundaries:

漸漸回到手寫筆記王的港決了!!

圖像表示，代表 non-linear decision boundaries 有各式各種可能(形狀)