## Overview
Support Vector Machines (SVM) is a powerful supervised learning algorithm used for classification and regression tasks. It finds the optimal hyperplane that maximizes the margin between different classes.
## Key Components
1. **Hyperplane**
- A decision boundary that separates classes
2. **Support Vectors**
- Data points closest to the hyperplane that influence its position
3. **Margin**
- The distance between the hyperplane and the nearest support vectors
4. **Kernel Trick**
- Transforms non-linearly separable data into higher dimensions for better separation
## How It Works
1. **Define the Hyperplane**
- Finds the best decision boundary that maximizes the margin
2. **Identify Support Vectors**
- Determines key data points influencing the hyperplane
3. **Apply Kernel Trick (if needed)**
- Converts data into a higher-dimensional space for better separation
4. **Optimize the Cost Function**
- Uses techniques like Quadratic Programming or Gradient Descent
## Implementation Example
```python
from sklearn.svm import SVC
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score
# Initialize model
svm = SVC(kernel='rbf', C=1.0, gamma='scale')
# Train model
svm.fit(X_train, y_train)
# Make predictions
predictions = svm.predict(X_test)
accuracy = accuracy_score(y_test, predictions)
print(f'Accuracy: {accuracy:.2f}')
```
## Advantages
- Effective for high-dimensional data
- Works well with small datasets
- Robust to overfitting with proper regularization
- Can handle both linear and non-linear classification using kernels
## Disadvantages
- Computationally expensive for large datasets
- Difficult to tune hyperparameters
- Less interpretable compared to decision trees
## Hyperparameters
1. **Kernel Function (`kernel`)**
- `linear`: Works well for linearly separable data
- `rbf`: Best for non-linearly separable data
- `poly`: Polynomial kernel for complex decision boundaries
2. **Regularization Parameter (`C`)**
- Controls trade-off between margin size and misclassification
- High `C` → Low bias, may overfit
- Low `C` → High bias, better generalization
3. **Gamma (`gamma`)** (for RBF and Polynomial kernels)
- Defines how far an influence reaches
- High `gamma` → More complex model, risk of overfitting
- Low `gamma` → Simpler model, risk of underfitting
## Best Practices
1. **Feature Scaling**
- Normalize data for better performance
2. **Kernel Selection**
- Use `rbf` for non-linear problems
- Use `linear` when data is already well-separated
3. **Hyperparameter Tuning**
- Use Grid Search or Randomized Search for best `C` and `gamma` values
## Common Applications
- Image classification
- Text categorization
- Medical diagnosis
- Spam detection
- Handwriting recognition
## Performance Optimization
1. **Reduce Overfitting**
- Tune `C` and `gamma` for better generalization
2. **Speed Up Computation**
- Use Linear SVM (`kernel='linear'`) for large datasets
- Use Approximate SVM (SGDClassifier) for very large data
3. **Feature Engineering**
- Use PCA or feature selection to remove redundant features
## Evaluation Metrics
- Accuracy
- Precision
- Recall
- F1 Score
- ROC-AUC curve