Interface IRadialBasisFunction<T>

Namespace

AiDotNet.Interfaces

Assembly

AiDotNet.dll

Defines a radial basis function (RBF) that measures similarity based on distance.

public interface IRadialBasisFunction<T>

Type Parameters

T

The numeric data type used for calculations (e.g., float, double).

Remarks

Radial basis functions are mathematical functions whose value depends only on the distance from a central point. They are commonly used in machine learning for creating complex models from simpler building blocks.

For Beginners: Think of a radial basis function as a "similarity detector" that works like this:

• It measures how similar or close two points are to each other
• The closer two points are, the higher the output value
• The function creates a smooth "hill" or "bump" shape centered at a specific point
• As you move away from the center, the function's value decreases

Common examples include the Gaussian (bell curve) function and the multiquadric function. These are used in many AI applications like:

• Function approximation (finding patterns in data)
• Classification (sorting data into categories)
• Time series prediction (forecasting future values)

Methods

Compute(T)

Calculates the value of the radial basis function at a given distance.

T Compute(T r)

Parameters

r T

The distance from the center point.

Returns

T

The function value at the given distance.

Remarks

This is the core function that determines the "shape" of the radial basis function.

For Beginners: This method takes a distance value and returns how strong the similarity is. Think of it like asking: "If I'm this far away from the center, how strong is the connection?"

For example, with a Gaussian RBF:

• When r = 0 (directly at the center), the function returns its maximum value (typically 1)
• As r increases (moving away from center), the value smoothly decreases toward 0
• The width parameter (often called sigma or epsilon) controls how quickly the value falls off

ComputeDerivative(T)

Calculates the derivative (rate of change) of the radial basis function with respect to distance.

T ComputeDerivative(T r)

Parameters

r T

The distance from the center point.

Returns

T

The derivative value at the given distance.

Remarks

The derivative tells us how quickly the function value changes as the distance changes. This is important for optimization algorithms that need to adjust the function parameters.

For Beginners: This method calculates how quickly the similarity changes as you move farther from or closer to the center. It's like measuring the steepness of the "hill" at a particular distance.

This is mainly used during the training process when the model needs to adjust itself to better fit the data. You typically won't need to call this directly unless you're implementing a custom learning algorithm.

ComputeWidthDerivative(T)

Calculates the derivative of the radial basis function with respect to its width parameter.

T ComputeWidthDerivative(T r)

Parameters

r T

The distance from the center point.

Returns

T

The derivative with respect to the width parameter at the given distance.

Remarks

This derivative is used when optimizing the width parameter of the radial basis function. The width parameter controls how quickly the function value decreases as distance increases.

For Beginners: The width of an RBF determines how far its influence reaches. This method helps the learning algorithm figure out whether to make the "hill" wider or narrower.

• A wider RBF (larger width) affects points farther away from its center
• A narrower RBF (smaller width) has a more localized effect

Like the regular derivative, this is mainly used during the training process and you typically won't need to call it directly unless implementing custom algorithms.