RBF_and_Splines_Presentation.pptx machine learning

1. Radial Basis Functions and
Splines
Machine Learning Presentation
Shashanth - B.Tech 3rd Year (3-2
Semester)

2. 1. Introduction to RBF and Splines
• • Radial Basis Functions (RBF) and Splines are
powerful tools in approximation and
interpolation.
• • RBFs are used in supervised learning and
function approximation.
• • Splines are piecewise polynomial functions
used for interpolation and smoothing.
• • Both are widely applied in machine learning
and data fitting tasks.

3. 2. Radial Basis Functions (RBF)
• • RBFs are real-valued functions whose value
depends only on the distance from a center
point.
• • Common RBF: Gaussian, Multiquadric,
Inverse Multiquadric.
• • Function form: φ(r) = e^(-β||x - c||²)
• • Used in RBF Networks for classification and
regression.

4. 3. Splines in Machine Learning
• • Splines are piecewise-defined polynomials.
• • Types: Linear, Quadratic, Cubic Splines.
• • Cubic splines are most commonly used due
to their smoothness.
• • Useful in interpolation, smoothing noisy
data, and curve fitting.

5. 4. Applications of RBFs and Splines
• • RBFs:
• - Time series prediction
• - Classification problems
• - Surface reconstruction
• • Splines:
• - Image processing
• - Path planning in robotics
• - Data visualization and curve smoothing

6. 5. Comparison and Conclusion
• • RBFs are global approximators; splines are
local.
• • RBFs work well with scattered data; splines
need structured data.
• • Both provide smooth interpolation and are
efficient in modeling non-linear relationships.
• • Choice depends on the specific application
and data nature.

7. Thank You
• Any Questions?