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A.4.5.18 KDE Form

The KDE form () plots a discrete Kernel Density Estimate giving a smoothed frequency of data values along the horizontal axis, using a fixed-width smoothing kernel. (for a variable-bandwidth kernel, see KNN). This is a generalisation of a histogram in which the bins are always 1 pixel wide, and a smoothing kernel is applied to each bin. The width and shape of the kernel may be varied.

This is suitable for cases where the division into discrete bins done by a normal histogram is unnecessary or troublesome.

Note this is not a true Kernel Density Estimate, since, for performance reasons, the smoothing is applied to the (pixel-width) bins rather than to each data sample. The deviation from a true KDE caused by this quantisation will be at the pixel level, hence in most cases not visually apparent.

This form may be used in the Histogram, Plane or Time plot windows.

Example KDE plot

Example KDE plot

KDE form configuration panel

KDE form configuration panel

These options always appear in the form configuration panel:

Colour
Selects the basic colour for the dataset.
Transparency
Adjusts the transparency of the bars or line. For bar styles which are already partially transparent, this fades them further.
Fill
Determines how the density function is represented. The options are:
Thickness
Controls line thickness where applicable. This is only relevant for bar styles that draw a finite thickness line, so has no effect for solid filling.
And these options appear in the form configuration panel for the Plane window, or the Bins control () for the Histogram window:
Smoothing
Configures the smoothing width for kernel density estimation. This is the characteristic width of the kernel function to be convolved with the density to produce the visible plot.

Sliding the slider to the right makes the kernel width larger. The width in data units is shown in the text field on the right (if the X axis is logarithmic, this is a factor). Alternatively you can click the radio button near the text field, and enter the width in data units directly.

Kernel
The functional form of the smoothing kernel. The functions listed refer to the unscaled shape; all kernels are normalised to give a total area of unity.

The available options are:

Cumulative
If true, the histogram bars plotted are calculated cumulatively; each bin includes the counts from all previous bins.
Normalise
Defines how, if at all, the bars are normalised. The available options are: When used in the Time plot only, additional options per_second, per_day etc are available corresponding to the frequency over the named time unit.


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TOPCAT - Tool for OPerations on Catalogues And Tables
Starlink User Note253
TOPCAT web page: http://www.starlink.ac.uk/topcat/
Author email: m.b.taylor@bristol.ac.uk
Mailing list: topcat-user@jiscmail.ac.uk