arrows : truefalse or list; controls the display of arrows corresponding to each principal component. The default is true. If the arrows option is given as a list, the arrows are shown and any elements of the list are passed as plot options to the arrow constructor.

arrowlabels : truefalse or list; specifies the labels shown on the arrows corresponding to each column of the data. The default is true. If the dataset is a DataFrame, then the biplot will automatically use the column names from the dataframe as labels. If the dataset is a Matrix, then the arrowlabels must be provided as a list, otherwise no labels are shown. The default arrow labels can be overridden by specifying a list containing the new values.

components : list; specifies the principal components used in the biplot. By default, Biplot uses the first two principal components for 2-D plots and the first three principal components for 3-D plots. The default is [1,2].

dimension : integer; specifies the number of dimensions, either 2 or 3 of the resulting biplot. The default is 2.

pcbiplot : truefalse; controls if with lambda = 1, observations are scaled up by $\sqrt{n}$ and variables are scaled down by $\sqrt{n}$. This is referred to as a "principal component biplot", Gabriel (1971).

points : truefalse or list; controls the display of points corresponding to the individual rows of the principal components. The default is true. If the points option is given as a list, the points are shown and any elements of the list are passed as plot options to the plot constructor.

pointlabels : truefalse or list; controls the display of point labels. The default is false. If the dataset is a DataFrame, the row names from the DataFrame are used. If the dataset is a Matrix, the numbers 1 through $n$ are used, where $n$ is the number of rows of the Matrix. The default point labels can be overridden by specifying a list containing the new values.

scale : numeric value between 0 and 1; controls if the variables are scaled by ${\mathrm{\lambda }}^{\mathrm{scale}}$ and the observations are scaled by ${\mathrm{\lambda }}^{1-\mathrm{scale}}$, where lambda are the singular values computed by the principal component analysis. The default is 1.

The Biplot command generates a biplot for the specified set of data. A biplot is a method of data visualization suitable for the results of a principal components analysis.

The first parameter, dataset, can be a numeric Matrix or DataFrame with 2 or more columns, or a record generated by a principal component analysis. In the case that dataset is either a Matrix or a DataFrame, a principal component analysis is run on the dataset and the results are used for the biplot.

$\mathrm{with}\left(\mathrm{Statistics}\right)\:$

$\mathrm{IrisDF}≔\mathrm{Import}\left(''datasets/iris.csv''\,\mathrm{base}=\mathrm{datadir}\right)$

$\mathrm{pca}≔\mathrm{PCA}\left(\mathrm{IrisDF}\left[\left[\mathrm{`Sepal\; Length`}\,\mathrm{`Sepal\; Width`}\,\mathrm{`Petal\; Length`}\,\mathrm{`Petal\; Width`}\right]\right]\right)\:$

$\mathrm{Biplot}\left(\mathrm{pca}\,\mathrm{size}=\left[600\,''golden''\right]\right)$

$\mathrm{Biplot}\left(\mathrm{pca}\,\mathrm{components}=\left[3..4\right]\,\mathrm{scale}=0.5\right)$

$\mathrm{Biplot}\left(\mathrm{pca}\,\mathrm{dimension}=3\,\mathrm{points}=\left[\mathrm{colorscheme}=\left[''valuesplit''\,\mathrm{IrisDF}\left[\mathrm{Species}\right]\right]\right]\,\mathrm{lightmodel}=\mathrm{none}\,\mathrm{orientation}=\left[-50\,50\,0\right]\right)$

$\mathrm{CCdata}≔\mathrm{Import}\left(''datasets/canada\_crimes.csv''\,\mathrm{base}=\mathrm{datadir}\right)$

$\mathrm{Biplot}\left(\mathrm{PCA}\left(\mathrm{CCdata}\,\mathrm{scale}=\mathrm{true}\right)\,\mathrm{points}=\mathrm{false}\,\mathrm{pointlabels}=\mathrm{true}\,\mathrm{arrows}=\left[\mathrm{color}=''Crimson''\right]\,\mathrm{axes}=\mathrm{normal}\,\mathrm{size}=\left[800\,''golden''\right]\,\mathrm{view}=\left[-1..1\,-0.5..0.5\right]\right)$

Gabriel, K.R. (1971). The biplot graphical display of matrices with applications to principal component analysis. Biometrika, 58, 453-467.

The Statistics[Biplot] command was introduced in Maple 2016.

For more information on Maple 2016 changes, see Updates in Maple 2016.

The Statistics[Biplot] command was updated in Maple 2019.

The components option was introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.