Radial basis function kernel
A radial basis function kernel is a similarity function whose value depends on the distance between inputs and typically decreases as that distance increases.
Grokking Machine Learning
A kernel based on a radial function whose value depends on the distance between an input point and a center point.
- How it is used
- Builds nonlinear SVM classifiers when linear boundaries cannot separate the data.
- How deep it goes
- Explains similarity features, summed radial functions, projected boundaries, and gamma width, without deriving the full kernel mathematics.
- Examples
- Uses one-dimensional points, two-dimensional triangle-and-square datasets, similarity tables, circular boundaries, and different gamma values.
- What you can do after
- Apply it via an SVM to classify datasets with complex curved regions.
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Bayesian Optimization in Action
An RBF kernel is a radial basis function covariance or similarity function whose value decreases with distance between inputs according to a length-scale parameter.
- How it is used
- Uses distance-based covariance to model similarity between inputs in Gaussian processes.
- How deep it goes
- Explains distance intuition, numerical behavior, GP integration, hyperparameter training, and limitations on structured data.
- Examples
- Demonstrates covariances for 0 versus 0.1 and 0 versus 10, plus GP modeling of MNIST images.
- What you can do after
- Build it with GPyTorch by adding an RBFKernel to a GP model and training its hyperparameters with Adam.
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Machine Learning Algorithms in Depth
A kernel function whose value typically decreases exponentially with the squared Euclidean distance between its input vectors.
- How it is used
- Uses RBF similarity in binary SVM classification and as covariance in Gaussian process regression.
- How deep it goes
- Defines and implements exponential squared-distance kernels; leaves their infinite-dimensional feature-vector equivalence as an exercise.
- Examples
- Implements a NumPy SVM kernel and a SciPy distance-based Gaussian process kernel for regression.
- What you can do after
- Build it from scratch as a similarity function for an SVM or a covariance function for Gaussian process regression.
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Related concepts
- squared exponential kernelequivalent to · A squared exponential kernel is a similarity or covariance function whose value decreases exponentially as the squared distance between inputs increases.
- kernel functionkind of · A kernel function is a mathematical function that measures similarity between pairs of inputs, often representing an inner product in an implicit feature space.
- Gaussian processused by · A Gaussian process is a probability distribution over functions in which every finite collection of function values has a joint Gaussian distribution.
- output scaleused by · An output scale is a covariance amplitude parameter that controls the range of a Gaussian process's function values and predictions.
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