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Kernel Loop Start

Vernalis JFreeChart-based plotting nodes version 1.30.1.v202103301200 by Vernalis (R&D), UK

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:

NameFunction
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

NameFunction
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 knime@vernalis.com

Options

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

Input Ports

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Input table for Kernel Density analysis

Output Ports

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

Best Friends (Outgoing)

Installation

To use this node in KNIME, install Vernalis KNIME Nodes from the following update site:

KNIME 4.3

A zipped version of the software site can be downloaded here.

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Developers

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