Visualizing Tabular Data

Plotting

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The mathematician Richard Hamming once said, “The purpose of computing is insight, not numbers,” and the best way to develop insight is often to visualize data. Visualization deserves an entire lecture of its own, but we can explore a few features of Julia’s Plots.jl library here. While Julia has several plotting libraries, Plots.jl is a powerful and flexible option that works well for most use cases. First, we will load Plots and use its functions to create and display a heat map of our data:

JULIA

Pkg.add("Plots")
using Plots

heatmap(data)

This will display a heat map where colors represent the magnitude of values in a matrix data. You can customize it further by adding labels, colorbars, and other visual elements. Each row in the heat map corresponds to a patient in the clinical trial dataset, and each column corresponds to a day in the dataset. Darker (blue) pixels in this heat map represent lower values, while lighter (yellow) pixels represent higher values. As we can see, the general number of inflammation flare-ups for the patients rises and falls over a 40-day period.

Let’s calculate the average inflammation per day across all patients and plot it:

JULIA

plot(mean(data, dims=1)', 
     xlabel="Day", 
     ylabel="Average inflammation", 
     title="Average inflammation over time", 
     legend=false)

This line of code creates a plot showing the average inflammation over time. The options xlabel="Day" and ylabel="Average inflammation" label the axes, title="Average inflammation over time" adds a title to the graph, and legend=false hides the legend since only one line is being shown.

This plot shows how the average inflammation changes day by day, across all patients. It typically starts low, increases steadily, and then decreases — supporting the idea that the treatment takes effect after about three weeks.

JULIA

plot(maximum(data, dims=1)', 
     xlabel="Day", 
     ylabel="Maximum inflammation", 
     title="Maximum inflammation over time", 
     legend=false)

JULIA

plot(minimum(data, dims=1)', 
     xlabel="Day", 
     ylabel="Minimum inflammation", 
     title="Minimum inflammation over time", 
     legend=false)

The maximum value rises and falls in a linear pattern, while the minimum values appear to follow a step-like function. Neither of these trends seems biologically plausible, so there may be an error in the data or in how it was collected. These insights would have been difficult to uncover without visualizing the results.

Grouping Plots

With Plots.jl, it is easy to group multiple plots into a single figure. We first create the individual subplots and save them in variables. Then, we combine them into one figure using the layout argument.

JULIA

p1 = plot(mean(data, dims=1)', title="Average", ylabel="average", xlabel="Day", legend=false)
p2 = plot(maximum(data, dims=1)', title="Maximum", ylabel="max", xlabel="Day", legend=false)
p3 = plot(minimum(data, dims=1)', title="Minimum", ylabel="min", xlabel="Day", legend=false)

plot(p1, p2, p3, layout=(1, 3))
savefig("inflammation.svg")

With the layout argument to arrange three plots in one row. The call to savefig stores the figure as a svg file. You can change the filename extension to save in other formats like .pdf or .png.

By using grouped plots, we can compare different trends side by side — for example, while the average inflammation rises and falls gradually, the minimum appears to jump in discrete steps. This visual comparison helps us spot unusual patterns that would be hard to detect just by looking at numbers.

Challenge

Plot Scaling

Why do all of our plots stop just short of the upper end of our graph?

Show me the solution

By default, Plots.jl scales the axes to fit the data range exactly, so lines often stop right before the plot edge.

Challenge

Plot Scaling (continued)

If we want to change this, we can manually set the y-axis limits using the ylims keyword argument. Try updating your plotting code so that all subplots share the same y-axis.

Show me the solution

JULIA

p1 = plot(mean(data, dims=1)', title="Average", ylabel="average", xlabel="Day", ylims=(0, 20), legend=false)
p2 = plot(maximum(data, dims=1)', title="Maximum", ylabel="max", xlabel="Day", ylims=(0, 20), legend=false)
p3 = plot(minimum(data, dims=1)', title="Minimum", ylabel="min", xlabel="Day",ylims=(0, 20), legend=false)

plot(p1, p2, p3, layout=(1, 3))

Key Points

• Use the Plots.jl package to create simple and flexible visualizations.