andrewsplot

Create an Andrews plot to visualize grouped sample data.

Load the fisheriris data set, which contains four measurements (sepal length, sepal width, petal length, and petal width) from three species of iris flowers.

load fisheriris

The matrix meas contains all four measurements for 150 flowers. The cell array species contains the species name for each of the 150 flowers.

Create an Andrews plot, grouping the sample data by species.

andrewsplot(meas,Group=species)

The plot displays each observation (flower) as a smooth function over the interval [0,1]. The color of each curve indicates the flower species.

Create a second, simplified Andrews plot that displays only the median and quartiles of each group.

andrewsplot(meas,Group=species,Quantile=0.25)

The plot shows the median values for each group as a solid curve and the values for the other quartiles as dotted curves of the same color.

Visualize multidimensional data by using Andrews plots. First, group the data. Then, use standardization and quartiles to see the difference between the groups.

Load the patients data set, which contains medical information for 100 patients. Specify the descriptive category names Smoker and Nonsmoker rather than 1 and 0. Then, create a table using the Diastolic, Systolic, Weight, Age, and Smoker variables.

load patients
Smoker = categorical(Smoker,logical([1 0]), ...
    ["Smoker","Nonsmoker"]);
patientData = table(Diastolic,Systolic,Weight,Age,Smoker);

Create an Andrews plot from the variables in patientData. Use the last variable to group the data by smoker status.

andrewsplot(patientData{:,1:end-1},Group=patientData.Smoker)

By default, the plot uses unstandardized data. The plot does not show a great difference between Smoker and Nonsmoker groups.

Standardize the numeric patientData variables before plotting.

andrewsplot(patientData{:,1:end-1},Group=Smoker,Standardize="on")

The resulting Andrews plot shows more variation between the Smoker and Nonsmoker groups. The plot is slightly crowded because it shows 100 curves, one for each patient in patientData.

Instead of displaying a curve for each observation, show the quartile curves for each group. The quartiles consist of the 25th percentile, median, and 75th percentile.

andrewsplot(patientData{:,1:end-1},Group=patientData.Smoker, ...
    Standardize="on",Quantile=0.25)

The quartile curves show differences between the Smoker and Nonsmoker groups. For example, at approximately 0.25, the two groups have quartile values that do not overlap.

Recall that each function displayed in the Andrews plot is a linear combination of the variables, whose coefficients change over time. (See Andrews Plot.) Compute the coefficients for the variables at time 0.25. This linear combination of the variables can help you differentiate between the groups.

t = 0.25;
variables = patientData.Properties.VariableNames(1:end-1)

variables = 1x4 cell
    {'Diastolic'}    {'Systolic'}    {'Weight'}    {'Age'}

coefficients = [1/sqrt(2) sin(2*pi*t) cos(2*pi*t) sin(4*pi*t)]

coefficients = 1×4

    0.7071    1.0000    0.0000    0.0000

At time 0.25, the Diastolic and Systolic variables have positive coefficients of similar magnitude, and the Weight and Age variables have 0 coefficients. The previous plot shows that, after the standardization of the data, the quartile curves for the Smoker group have positive values at time 0.25, and the quartile curves for the Nonsmoker group have negative values at time 0.25.

The plot and variable coefficients indicate that patients in the Smoker group tend to have higher Diastolic and Systolic values, providing one way to distinguish between the Smoker and Nonsmoker groups in patientData.

Adjust the appearance of an Andrews plot. You can set some plot properties in the call to andrewsplot. You can also specify the appearance of the plot before or after creating it.

Load the fisheriris data set, which contains four measurements (sepal length, sepal width, petal length, and petal width) from three species of iris flowers.

load fisheriris

The matrix meas contains all four measurements for 150 flowers. The cell array species contains the species name for each of the 150 flowers.

Create an Andrews plot using the measurement data in meas and the group data in species. Specify a nondefault color scheme (copper) for the grouped data by setting the color order before plotting.

colororder(copper(3))
andrewsplot(meas,Group=species)

Plot only the median, 25th percentile, and 75th percentile curves for each group in species. To make the plot lines thicker, specify the line width as 2. When you specify the LineWidth value in the call to andrewsplot, the function sets the line width of every curve in the plot to the same value.

andrewsplot(meas,Group=species,Quantile=0.25,LineWidth=2)

Recreate the previous plot, but increase the line width of only the curve representing the median measurements for the irises in the setosa group. First, create an array of Line objects p, where each object corresponds to a curve in the plot. Then, modify the LineWidth property of the first Line object in the array by using dot notation.

p = andrewsplot(meas,Group=species,Quantile=0.25)

p = 
  9x1 Line array:

  Line    (median)
  Line    (lower quantile)
  Line    (upper quantile)
  Line    (median)
  Line    (lower quantile)
  Line    (upper quantile)
  Line    (median)
  Line    (lower quantile)
  Line    (upper quantile)

p(1).LineWidth = 2;