PairwiseSmoothDensityHistogram

PairwiseSmoothDensityHistogram[{{y₁₁,…,y_1n},…,{y_m1,…,y_mn}}]

creates an array of smooth density histograms by plotting the data columns against each other in pairs.

Details and Options

PairwiseSmoothDensityHistogram is a form of plot matrix.
It plots high-dimensional data by creating a grid of individual plots of just two data columns at a time.
The plot compares column y_i={y_1i,y_2i,…,y_mi} against column y_j={y_1j,y_2j,…,y_mj} by plotting a smooth density histogram of the points {y_kj,y_ki} in panel {i,j}.

The panel at row and column shows how the data columns y_i and y_j relate to each other. There are different types of features of the data that can be identified from those panels. Once the feature has been identified, it can also be quantified by further analysis of the data.
Correlation and covariance are measures of dependence between variables:

Use Correlation and Covariance to do detailed analysis of correlation.
The density of points is a measure of the number of points per unit area. The panels in PairwiseSmoothDensityHistogram effectively show the two-dimensional marginal densities:

Use PairwiseDensityHistogram and PairwiseSmoothDensityHistogram to more directly visualize the densities.
Clusters are groups of similar points, indicating categories:

PairwiseSmoothDensityHistogram takes the same options as Graphics, with the following changes and additions:

AspectRatio	1	ratio of height to width for each panel
Background	None	background to use for each plot
Frame	Automatic	whether to draw frames around each panel
FrameTicks	Automatic	whether to label frame edges with ticks and labels
GridLines	Automatic	whether to include gridlines in panels
GridLinesStyle	Automatic	style for gridlines
HeaderAlignment	Center	horizontal and vertical alignments of headers
HeaderBackground	Automatic	background colors to use for headers
HeaderDisplayFunction	Automatic	function to use to format headers
Headers	Automatic	labels to use for each data column y_i
HeaderStyle	None	styles to use for headers
PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
PlotHighlighting	Automatic	highlighting effect for points
PlotLayout	Automatic	how to arrange the panels
PlotLegends	Automatic	legends for data
PlotMarkers	None	markers to use to indicate each point
PlotStyle	Automatic	graphics directives to determine styles of points
PlotTheme	$PlotTheme	overall theme for the plot
Spacings	Automatic	horizontal and vertical spacings

PlotLayout can have the following settings:

		"Descending"	data columns going down and to the right
		"Ascending"	data columns going up and to the right
		"DescendingHalfMatrix"	lower half of the descending layout
		"AscendingHalfMatrix"	upper half of the ascending layout

Headers specifies the labels to use for each column in the data, and will generally be displayed above each column and after each row in the final plot.
Possible settings include:

	None	leave the plot columns and rows unlabeled
	Automatic	automatically label columns and rows
	All	always include column and row labels
	"Indexed"	number the columns and rows 1, 2, …, n
	{lbl₁,lbl₂,…,lbl_n}	use the given labels lbl_i

HeaderAlignment determines how data column labels are aligned with regard to the plot columns and rows.
HeaderAlignment can take the following forms:

	Center	center the labels in the header positions
	{h,v}	separate horizontal and vertical alignments within the header position
	{cols,rows}	use col for plot columns and row for plot rows

HeaderBackground and HeaderStyle can take the following forms:

	None	use ambient styling
	sty	use the style sty for all headers
	{sty₁,sty₂,…,sty_n}	use the given styles sty_i for successive headers
	{cols,rows}	use col for plot columns and row for plot rows

HeaderDisplayFunction determines how headers are displayed.
Possible settings are:
Automatic automatic formatting

None use unprocessed labels
The arguments to ColorFunction are y_i1,y_i2,…,y_in. By default, the color function arguments are scaled per data column to be between 0 and 1.
Use ColorFunctionScalingNone to use unscaled values, or ColorFunctionScaling{cfsc₁,cfsc₂,…} to selectively scale column values.
Possible settings for PlotHighlighting include:
Automatic automatically highlight positions in the panels

None disable interactive highlighting

Examples

open allclose all

Basic Examples (3)

Create an array of smooth density histograms from data with labeled columns:

Compare all columns in a dataset:

Provide header names for the data:

Scope (2)

Data (2)

Plot datasets:

Plot arrays of values:

Options (19)

AspectRatio (2)

By default, PairwiseSmoothDensityHistogram uses an equal height-to-width ratio:

Use a fixed height-to-width ratio:

ColorFunction (3)

Color by scaled coordinate:

Specify gray-level intensity by scaled coordinate:

Use named color gradients:

GridLines (2)

By default, PairwiseSmoothDensityHistogram does not draw gridlines:

Draw a grid on top of the plot:

Headers (3)

By default, PairwiseSmoothDensityHistogram does not label columns:

Number the columns for unlabeled data:

Provide header names for the columns:

HeaderBackground (2)

By default, PairwiseSmoothDensityHistogram uses a white header background:

Set a header background color:

PlotLabel (1)

Add an overall label to the plot:

PlotLayout (3)

Switch the orientation of the diagonal elements:

Show plots below the diagonal:

Only show plots above the diagonal:

PlotTheme (2)

Use a theme with simple ticks and gridlines in a bright color scheme:

Change color scheme:

Spacings (1)

Change the space between the plots:

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PairwiseSmoothDensityHistogram

Details and Options

Examples

Basic Examples (3)