KernelDensityFunction (ELKI: Environment for DeveLoping KDD-Applications Supported by Index-Structures)

All Known Implementing Classes:

BiweightKernelDensityFunction, CosineKernelDensityFunction, EpanechnikovKernelDensityFunction, GaussianKernelDensityFunction, TriangularKernelDensityFunction, TricubeKernelDensityFunction, TriweightKernelDensityFunction, UniformKernelDensityFunction
```
public interface KernelDensityFunction
```
Inner function of a kernel density estimator.
Note: as of now, this API does not support asymmetric kernels, which would be difficult in the multivariate case.

Since:

0.6.0

Author:

Erich Schubert

Method Summary

All Methods Instance Methods Abstract Methods
Modifier and Type	Method	Description
`double`	`canonicalBandwidth()`	Get the canonical bandwidth for this kernel.
`double`	`density(double delta)`	Density contribution of a point at the given relative distance `delta >= 0`.
`double`	`getR()`	Get the R integral of the kernel, \int K^2(x) dx
`double`	`standardDeviation()`	Get the standard deviation of the kernel function.

- Method Detail
  - density
```
double density(double delta)
```
    Density contribution of a point at the given relative distance delta >= 0.
    Note that for delta < 0, in particular for delta < 1, the results may become invalid. So usually, you will want to invoke this as:
    kernel.density(Math.abs(delta))
    
    Parameters:
    
    delta - Relative distance
    
    Returns:
    
    density contribution
  - canonicalBandwidth
```
@Reference(authors="J. S. Marron, D. Nolan",
           title="Canonical kernels for density estimation",
           booktitle="Statistics & Probability Letters, Volume 7, Issue 3",
           url="https://doi.org/10.1016/0167-7152(88)90050-8",
           bibkey="doi:10.1016/0167-71528890050-8")
double canonicalBandwidth()
```
    Get the canonical bandwidth for this kernel.
    Note: R uses a different definition of "canonical bandwidth", and also uses differently scaled kernels.
    
    Returns:
    
    Canonical bandwidth
  - standardDeviation
```
double standardDeviation()
```
    Get the standard deviation of the kernel function.
    
    Returns:
    
    Standard deviation
  - getR
```
double getR()
```
    Get the R integral of the kernel, \int K^2(x) dx
    TODO: any better name for this?
    
    Returns:
    
    R value