Kernel Loop Start

This node allows the user to select one or more Kernel Estimators and one or more Kernel Symmetries (if the 'Is Multi-dimensional?' option is selected). All combinations are looped through, with the values in each in the 'Kernel Estimator' and 'Kernel Symmetry' flow variables.

Kernel Estimators

A variety of kernel estimators are available, as shown in the table:

UNIFORMK(u) = 0.5 (|u| ≤ 1), 0 (|u) > 1); aka 'Uniform' or 'Boxcar'
TRIANGLEK(u) = 1-|u| (|u| ≤ 1), 0 (|u) > 1)
EPANECHNIKOVK(u) = 3•(1-u²)/4 (|u| ≤ 1), 0 (|u) > 1)
QUARTICK(u) = 15•(1-u²)²/16 (|u| ≤ 1), 0 (|u) > 1)
TRIWEIGHTK(u) = 35•(1-u²)³/32 (|u| ≤ 1), 0 (|u) > 1)
TRICUBEK(u) = 70•(1-|u|³)³/81 (|u| ≤ 1), 0 (|u) > 1)
GAUSSIANK(u) = e^(-u²/2) / √(2π)
COSINUSK(u) = (π/4)•cos(πu/2) (|u| ≤ 1), 0 (|u) > 1)
LOGISTICK(u) = 1/(e^u + 2 + e^-u)
SIGMOIDK(u) = 2/(π•(e^u + e^-u))
SILVERMANK(u) = 0.5•e^(-|u|/√2)•sin((|u|/√2) + (π/4))

In the 2D case, u is a vector. The 'Kernel Symmetry' option controls how the 1-dimensional 'Kernel Estimator' is applied, as shown in the table

RADIAL_MULTIPLICATIVEThe kernel estimator is applied multiplicatively across dimensions, e.g. K(u) = K(u(x)) • K(u(y)), where u(x) is the x-dimension component of u, and u(y) the y-dimension component
SPHERICALThe kernel estimator is applied spherically symmetrically - i.e. any point of the same distance from the kernel estimator center has the same value. This is equivalent to K(u) = K(√uᵀu)

This node was developed by Vernalis Research. For feedback and more information, please contact


Kernel Estimators
The Kernel Estimator(s) to loop through
Kernel Symmetries
The kernel Symmetries looped through if 'Is Multi-dimensional?' is selected

Input Ports

Input table for Kernel Density analysis

Output Ports

The input unchanged input table, with flow variables for Kernel Estimator and optionally Kernel Symmetry


This node has no views


  • No workflows found



You want to see the source code for this node? Click the following button and we’ll use our super-powers to find it for you.