Multi-plot example – scatterplot matrix plots

In this section, we will learn how to have several plots in the same figure.

The key new method that allows multiple plots in the same figure is fig.subplot(nrows, ncols, plotIndex). This method, an overloaded version of the fig.subplot method we have been using up to now, both sets the number of rows and columns in the figure and returns a specific subplot. It takes three arguments:

• nrows: The number of rows of subplots in the figure
• ncols: The number of columns of subplots in the figure
• plotIndex: The index of the plot to return

Users familiar with MATLAB or matplotlib will note that the .subplot method is identical to the eponymous methods in these frameworks. This might seem a little complex, so let's look at an example (you will find the code for this in BreezeDemo.scala):

import breeze.plot._

def subplotExample {
  val data = HWData.load
  val fig = new Figure("Subplot example")

  // upper subplot: plot index '0' refers to the first plot
  var plt = fig.subplot(2, 1, 0)
  plt += plot(data.heights, data.weights, '.')

  // lower subplot: plot index '1' refers to the second plot
  plt = fig.subplot(2, 1, 1)
  plt += plot(data.heights, data.reportedHeights, '.', colorcode="black")

  fig.refresh
}

Running this example produces the following plot:

Now that we have a basic grasp of how to add several subplots to the same figure, let's do something a little more interesting. We will write a class to draw scatterplot matrices. These are useful for exploring correlations between different features.

If you are not familiar with scatterplot matrices, have a look at the figure at the end of this section for an idea of what we are constructing. The idea is to build a square matrix of scatter plots for each pair of features. Element (i, j) in the matrix is a scatter plot of feature i against feature j. Since a scatter plot of a variable against itself is of limited use, one normally draws histograms of each feature along the diagonal. Finally, since a scatter plot of feature i against feature j contains the same information as a scatter plot of feature j against feature i, one normally only plots the upper triangle or the lower triangle of the matrix.

Let's start by writing functions for the individual plots. These will take a Plot object referencing the correct subplot and vectors of the data to plot:

import breeze.plot._
import breeze.linalg._

class ScatterplotMatrix(val fig:Figure) {

  /** Draw the histograms on the diagonal */
  private def plotHistogram(plt:Plot)(
  data:DenseVector[Double], label:String) {
     plt += hist(data)
     plt.xlabel = label
  }

  /** Draw the off-diagonal scatter plots */
  private def plotScatter(plt:Plot)(
    xdata:DenseVector[Double],
    ydata:DenseVector[Double],
    xlabel:String,
    ylabel:String) {
      plt += plot(xdata, ydata, '.')
      plt.xlabel = xlabel
      plt.ylabel = ylabel
  }

...

Notice the use of hist(data) to draw a histogram. The argument to hist must be a vector of data points. The hist method will bin these and represent them as a histogram.

Now that we have the machinery for drawing individual plots, we just need to wire everything together. The tricky part is to know how to select the correct subplot for a given row and column position in the matrix. We can select a single plot by calling fig.subplot(nrows, ncolumns, plotIndex), but translating from a (row, column) index pair to a single plotIndex is not obvious. The plots are numbered in increasing order, first from left to right, then from top to bottom:

0 1 2 3
4 5 6 7
...

Let's write a short function to select a plot at a (row, column) index pair:

  private def selectPlot(ncols:Int)(irow:Int, icol:Int):Plot = {
    fig.subplot(ncols, ncols, (irow)*ncols + icol)
  }

We are now in a position to draw the matrix plot itself:

  /** Draw a scatterplot matrix.
    *
    * This function draws a scatterplot matrix of the correlation
    * between each pair of columns in `featureMatrix`.
    *
    * @param featureMatrix A matrix of features, with each column
    *   representing a feature.
    * @param labels Names of the features.
    */
  def plotFeatures(featureMatrix:DenseMatrix[Double], labels:List[String]) {
    val ncols = featureMatrix.cols
    require(ncols == labels.size,
      "Number of columns in feature matrix "+ "must match length of labels"
    )
    fig.clear
    fig.subplot(ncols, ncols, 0)

    (0 until ncols) foreach { irow =>
      val p = selectPlot(ncols)(irow, irow)
      plotHistogram(p)(featureMatrix(::, irow), labels(irow))

      (0 until irow) foreach { icol =>
        val p = selectPlot(ncols)(irow, icol)
        plotScatter(p)(
          featureMatrix(::, irow),
          featureMatrix(::, icol),
          labels(irow),
          labels(icol)
        )
      }
    }
  }
}

Let's write an example for our class. We will use the height-weight data again:

import breeze.linalg._
import breeze.numerics._
import breeze.plot._

object ScatterplotMatrixDemo extends App {

  val data = HWData.load
  val m = new ScatterplotMatrix(Figure("Scatterplot matrix demo"))

  // Make a matrix with three columns: the height, weight and
  // reported weight data.
  val featureMatrix = DenseMatrix.horzcat(
    data.heights.toDenseMatrix.t,
    data.weights.toDenseMatrix.t,
    data.reportedWeights.toDenseMatrix.t
  )
  m.plotFeatures(featureMatrix,List("height", "weight", "reportedWeights"))

}

Running this through SBT produces the following plot: