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

This node plots a 1D Kernel density function based on an incoming data table

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

Name | Function |
---|---|

UNIFORM | K(u) = 0.5 (|u| ≤ 1), 0 (|u) > 1); aka 'Uniform' or 'Boxcar' |

TRIANGLE | K(u) = 1-|u| (|u| ≤ 1), 0 (|u) > 1) |

EPANECHNIKOV | K(u) = 3•(1-u²)/4 (|u| ≤ 1), 0 (|u) > 1) |

QUARTIC | K(u) = 15•(1-u²)²/16 (|u| ≤ 1), 0 (|u) > 1) |

TRIWEIGHT | K(u) = 35•(1-u²)³/32 (|u| ≤ 1), 0 (|u) > 1) |

TRICUBE | K(u) = 70•(1-|u|³)³/81 (|u| ≤ 1), 0 (|u) > 1) |

GAUSSIAN | K(u) = e^(-u²/2) / √(2π) |

COSINUS | K(u) = (π/4)•cos(πu/2) (|u| ≤ 1), 0 (|u) > 1) |

LOGISTIC | K(u) = 1/(e^u + 2 + e^-u) |

SIGMOID | K(u) = 2/(π•(e^u + e^-u)) |

SILVERMAN | K(u) = 0.5•e^(-|u|/√2)•sin((|u|/√2) + (π/4)) |

The bandwidth effects the 'smoothness' of the kernel density function. There are a number of methods to automatically guess a suitable bandwidth. In this node we only offer three options, as shown in the table below. For further details see the Wikipedia Multivariate Kernel Density estimation page.

The methods offered are:

Name | Function |
---|---|

Silverman | Bandwidth is estimated using the Silverman approximation (H = stdDev * [4 / ((d + 2) * n)]^(1 / (d + 4)), where d is thenumber of dimensions and n the number of datapoints) |

Scott | Bandwidth is estimated using the Scott approximation (H = stdDev / n^(1 / (d + 4)), where d is thenumber of dimensions and n the number of datapoints) |

User Defined | The user specifies the bandwidth (H) |

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

- Values Column
- The column in the incoming table containing the values from which to generate the kernel(s)
- Grouping Column
- An optional grouping column, to generate separate kernels for each series
- Show all-data kernel
- If a grouping column is selected, this option allows an additional kernel to be shown, which includes the entire data column, including those rows where the grouping column contains a missing value
- Kernel Estimator
- The Kernel function to apply at each data point. See above for details of the individual kernel estimators
- Values Column Bandwidth
- The bandwidth estimation method to used for the dataset. See above for details
- Bandwidth (H)
- User-defined bandwidth
- Number of grid points along axis
- The number of grid points to calculate the kernel density function value for
- Expand all kernels to whole range
- If a grouping column is selected, this option allows all kernel density functions to be calculated over the full range of the plot when axis autoranging is selected
- Auto-range x-Axis
- Should the x-Axis range be calculated automatically? If so, it will be extended beyond the most extreme values by 5% of the range between them.
- x-Axis Range
- The manual axis range
- Show legend
- If a grouping column is selected, this option shows a legend for the colours of the individual kernels on the plot. The colours will be derived from a color manager applied to the grouping column, or generated dynamically if there isnt an appropriate color manager
- Show bandwidth (H) on axis label or legend
- Should the bandwidth be shown on the axis label (or in the legend if a grouping column is selected)?

- Type of Image
- The type of the created image can either be png or svg. PNGs are mostly smaller, SVGs provide details about plot and the possibility to be changed individually
- Title of Graph
- The title of the graph shown above the generated image. If the title is not activated, no title will be shown
- Width of Image (in pixel)
- The width of the generated image, not the plot width
- Height of Image (in pixel)
- The height of the generated image, not the plot height
- Background Colour
- The color of the background of the plot. Hence this color is used for the empty space in a plot
- Plot background Alpha
- The transparency of the plot background can be modified using an additional alpha value. An alpha value of 1 does not change the background transparency. Decreasing the alpha value will increase the plot background transparency
- Scale Font Size
- Factor changes the font sizes within the JFreeChart view. A value greater the 1 increases all view fonts, a value between 0 and 1 decrease them

- 1D Kernel Density Plot
- View showing the 1D Kernel Density Plot

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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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