What are Kernels in SVM? List popular kernels used in SVM along with a scenario of their applications

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The function of kernel is to take data as input and transform it into the required form. A few popular Kernels used in SVM are as follows: RBF, Linear, Sigmoid, Polynomial, Hyperbolic, Laplace, etc.

In Support Vector Machines (SVM), kernels are a crucial component that allows the algorithm to operate efficiently and effectively in non-linearly separable datasets. Kernels transform the input data into a higher-dimensional space, where it becomes easier to find a linear separation between classes.

Popular kernels used in SVM along with scenarios of their applications are:

  1. Linear Kernel:
    • Formula: �(�,�)=��⋅�K(x,y)=xT⋅y
    • Applications:
      • When the data is linearly separable or when the number of features is very high compared to the number of samples.
      • Text classification tasks where the feature space is high dimensional.
  2. Polynomial Kernel:
    • Formula: �(�,�)=(�⋅��⋅�+�)�K(x,y)=(γ⋅xT⋅y+r)d
    • Applications:
      • Image processing tasks where non-linear relationships exist between features.
      • Speech recognition where features are represented in a non-linear fashion.
  3. Radial Basis Function (RBF) Kernel:
    • Formula: �(�,�)=�−�∣∣�−�∣∣2K(x,y)=e−γ∣∣x−y∣∣2
    • Applications:
      • Pattern recognition in biomedical data analysis.
      • Financial forecasting where complex non-linear relationships exist between input variables.
  4. Sigmoid Kernel:
    • Formula: �(�,�)=tanh⁡(�⋅��⋅�+�)K(x,y)=tanh(γ⋅xT⋅y+r)
    • Applications:
      • Text and hypertext categorization where feature spaces are sparse and high-dimensional.
      • Bioinformatics for analyzing biological sequences.
  5. Custom Kernels:
    • In addition to the above predefined kernels, SVM allows users to define custom kernels tailored to specific dataset characteristics or domain knowledge.
    • Applications:
      • Any scenario where the relationship between features is known and can be effectively captured by a custom-defined kernel.

Choosing the appropriate kernel depends on the nature of the data and the problem at hand. Experimentation and cross-validation are often necessary to determine the best-performing kernel for a given task.