Support Vector Machine (SVM) Algorithm

Support Vector Machine (SVM) is a popular supervised machine learning algorithm used for classification and regression tasks. It is especially powerful in high-dimensional spaces and for cases where the number of dimensions exceeds the number of samples.

How SVM Works

1. Core Idea: SVM aims to find a hyperplane that best separates the data into classes. The goal is to maximize the margin between the hyperplane and the nearest data points from each class (support vectors).
2. Key Concepts:
   • Hyperplane: A decision boundary that separates different classes.
   • Margin: The distance between the hyperplane and the nearest data points of each class. SVM maximizes this margin.
   • Support Vectors: The data points that lie closest to the hyperplane and influence its position.
3. Linear SVM:
   • Works for linearly separable data.
   • Finds a straight hyperplane to separate classes.
4. Non-linear SVM:
   • For non-linearly separable data, SVM uses a kernel function to map data to a higher-dimensional space where a linear separation is possible.

Kernel Functions in SVM

Kernels allow SVM to handle non-linear relationships. Common kernel functions:

1. Linear Kernel: K(xi,xj)=xi⋅xj​
2. Polynomial Kernel: K(xi,xj)=(xi⋅xj+c)d
3. Radial Basis Function (RBF) or Gaussian Kernel: K(xi,xj)=exp⁡(−γ∥xi−xj∥2)
4. Sigmoid Kernel: K(xi,xj)=tanh⁡(αxi⋅xj+c)

Advantages

1. Works well in high-dimensional spaces.
2. Effective for datasets with clear margin of separation.
3. Memory efficient as it uses only support vectors.

Disadvantages

1. Computationally expensive for large datasets.
2. Requires careful selection of kernel and hyperparameters.
3. Less effective when the classes overlap significantly.

Applications

1. Text classification (e.g., spam detection).
2. Image recognition.
3. Medical diagnostics.
4. Bioinformatics.

Python Implementation (Example)

SVM is a versatile algorithm that can be tuned for many scenarios, making it a powerful tool for machine learning practitioners.