2023-12-22 16:39:03 +00:00
|
|
|
|
---
|
|
|
|
|
|
tags:
|
|
|
|
|
|
- ai
|
2023-12-27 21:56:22 +00:00
|
|
|
|
- classification
|
2023-12-22 16:39:03 +00:00
|
|
|
|
---
|
2023-06-07 09:02:27 +01:00
|
|
|
|
[Towards Data Science: SVM](https://towardsdatascience.com/support-vector-machines-svm-c9ef22815589)
|
|
|
|
|
|
[Towards Data Science: SVM an overview](https://towardsdatascience.com/https-medium-com-pupalerushikesh-svm-f4b42800e989)
|
|
|
|
|
|
|
|
|
|
|
|
- Dividing line between two classes
|
|
|
|
|
|
- Optimal hyperplane for a space
|
|
|
|
|
|
- Margin maximising hyperplane
|
|
|
|
|
|
- Can be used for
|
2023-06-08 17:52:09 +01:00
|
|
|
|
- [Classification](../Classification.md)
|
2023-06-07 09:02:27 +01:00
|
|
|
|
- SVC
|
|
|
|
|
|
- Regression
|
|
|
|
|
|
- SVR
|
2023-06-08 17:52:09 +01:00
|
|
|
|
- Alternative to Eigenmodels for [supervised](../../Learning.md#Supervised) classification
|
2023-06-07 09:02:27 +01:00
|
|
|
|
- For smaller datasets
|
|
|
|
|
|
- Hard to scale on larger sets
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
- Support vector points
|
|
|
|
|
|
- Closest points to the hyperplane
|
|
|
|
|
|
- Lines to hyperplane are support vectors
|
|
|
|
|
|
|
|
|
|
|
|
- Maximise margin between classes
|
|
|
|
|
|
- Take dot product of test point with vector perpendicular to support vector
|
|
|
|
|
|
- Sign determines class
|
|
|
|
|
|
|
|
|
|
|
|
# Pros
|
|
|
|
|
|
- Linear or non-linear discrimination
|
|
|
|
|
|
- Effective in higher dimensions
|
|
|
|
|
|
- Effective when number of features higher than training examples
|
|
|
|
|
|
- Best for when classes are separable
|
|
|
|
|
|
- Outliers have less impact
|
|
|
|
|
|
|
|
|
|
|
|
# Cons
|
|
|
|
|
|
- Long time for larger datasets
|
|
|
|
|
|
- Doesn’t do well when overlapping
|
|
|
|
|
|
- Selecting appropriate kernel
|
|
|
|
|
|
|
|
|
|
|
|
# Parameters
|
|
|
|
|
|
- C
|
|
|
|
|
|
- How smooth the decision boundary is
|
|
|
|
|
|
- Larger C makes more curvy
|
|
|
|
|
|
- 
|
|
|
|
|
|
- Gamma
|
|
|
|
|
|
- Controls area of influence for data points
|
|
|
|
|
|
- High gamma reduces influence of faraway points
|
|
|
|
|
|
|
|
|
|
|
|
# Hyperplane
|
|
|
|
|
|
|
|
|
|
|
|
$$\beta_0+\beta_1X_1+\beta_2X_2+\cdot\cdot\cdot+\beta_pX_p=0$$
|
|
|
|
|
|
- $p$-dimensional space
|
|
|
|
|
|
- If $X$ satisfies equation
|
|
|
|
|
|
- On plane
|
|
|
|
|
|
- Maximal margin hyperplane
|
|
|
|
|
|
- Perpendicular distance from each observation to given plane
|
|
|
|
|
|
- Best plane has highest distance
|
|
|
|
|
|
- If support vector points shift
|
|
|
|
|
|
- Plane shifts
|
|
|
|
|
|
- Hyperplane only depends on the support vectors
|
|
|
|
|
|
- Rest don't matter
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
# Linearly Separable
|
|
|
|
|
|
- Not linearly separable
|
|
|
|
|
|
|
|
|
|
|
|
- Add another dimension
|
|
|
|
|
|
- $z=x^2+y^2$
|
|
|
|
|
|
- Square of the distance of the point from the origin
|
|
|
|
|
|
|
|
|
|
|
|
- Now separable
|
|
|
|
|
|
- Let $z=k$
|
|
|
|
|
|
- $k$ is a constant
|
|
|
|
|
|
- Project linear separator back to 2D
|
|
|
|
|
|
- Get circle
|
|
|
|
|
|
|
