andy
1513f2b378
Affected files: STEM/AI/Classification/Classification.md STEM/AI/Classification/Decision Trees.md STEM/AI/Classification/Gradient Boosting Machine.md STEM/AI/Classification/Logistic Regression.md STEM/AI/Classification/Random Forest.md STEM/AI/Classification/Supervised.md STEM/AI/Classification/Supervised/README.md STEM/AI/Classification/Supervised/SVM.md STEM/AI/Classification/Supervised/Supervised.md STEM/AI/Learning.md STEM/AI/Neural Networks/Learning/Boltzmann.md STEM/AI/Neural Networks/Learning/Competitive Learning.md STEM/AI/Neural Networks/Learning/Credit-Assignment Problem.md STEM/AI/Neural Networks/Learning/Hebbian.md STEM/AI/Neural Networks/Learning/Learning.md STEM/AI/Neural Networks/Learning/README.md STEM/AI/Neural Networks/RNN/Autoencoder.md STEM/AI/Neural Networks/RNN/Deep Image Prior.md STEM/AI/Neural Networks/RNN/MoCo.md STEM/AI/Neural Networks/RNN/Representation Learning.md STEM/AI/Neural Networks/RNN/SimCLR.md STEM/img/comp-learning.png STEM/img/competitive-geometric.png STEM/img/confusion-matrix.png STEM/img/decision-tree.png STEM/img/deep-image-prior-arch.png STEM/img/deep-image-prior-results.png STEM/img/hebb-learning.png STEM/img/moco.png STEM/img/receiver-operator-curve.png STEM/img/reinforcement-learning.png STEM/img/rnn+autoencoder-variational.png STEM/img/rnn+autoencoder.png STEM/img/simclr.png STEM/img/sup-representation-learning.png STEM/img/svm-c.png STEM/img/svm-non-linear-project.png STEM/img/svm-non-linear-separated.png STEM/img/svm-non-linear.png STEM/img/svm-optimal-plane.png STEM/img/svm.png STEM/img/unsup-representation-learning.png
74 lines
2.1 KiB
Markdown
74 lines
2.1 KiB
Markdown
[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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- Classification
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- SVC
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- Regression
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- SVR
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- Alternative to Eigenmodels for supervised classification
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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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