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