stag.kde Namespace Reference

Classes
class	CKNSGaussianKDE
	A CKNS Gaussian KDE data structure. More...
class	ExactGaussianKDE
	A data structure for computing the exact Gauussian KDE. More...

Functions
def	gaussian_kernel (float a, stag.data.DataPoint u, stag.data.DataPoint v)
	Compute the Gaussian kernel similarity between the points u and v.
float	gaussian_kernel_dist (float a, float c)
	Compute the Gaussian kernel similarity for two points at a squared distance \(c\).

Function Documentation

gaussian_kernel()

def stag.kde.gaussian_kernel	(	float	a,
		stag.data.DataPoint	u,
		stag.data.DataPoint	v
	)

Compute the Gaussian kernel similarity between the points u and v.

Given a parameter \(a \geq 0\) and points \(u, v \in \mathbb{R}^n\), the Gaussian kernel similarity between \(u\) and \(v\) is given by

\[ k(u, v) = \exp\left( - a \|u - v\|^2_2 \right). \]

Note that the Gaussian kernel is sometimes parameterised by \(\sigma^2\), which is related to our parameter \(a\) by

\[ a = \frac{1}{\sigma^2}. \]

Parameters

a	the parameter a in the Gaussian kernel.
u	a data point \(u\)
v	a data point \(v\)

Returns

the Gaussian kernel similarity between \(u\) and \(v\).

gaussian_kernel_dist()

float stag.kde.gaussian_kernel_dist	(	float	a,
		float	c
	)

Compute the Gaussian kernel similarity for two points at a squared distance \(c\).

Given a parameter \(a \geq 0\), the Gaussian kernel similarity between two points at distance \(c\) is given by

\[ \exp\left( - a c \right). \]

Parameters

a	the parameter a in the Gaussian kernel.
c	the squared distance between two points.

Returns

the kernel evaluated at distance \(c\).