Plotting data

Overview

Questions

• How can I visualize my data?

Objectives

• Display simple graphs with appropriate titles and labels.
• Get familiar with the plot function.
• Learn how to plot multiple lines at the same time.
• Learn how to show images side by side.
• Get familiar with the heatmap and imagesc functions.

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 visualise data. Visualisation deserves an entire lecture (or course) of its own, but we can explore a few features of MATLAB here.

We will start by exploring the function plot. The most common usage is to provide two vectors, like plot(X,Y). Lets start by plotting the average inflammation across patients over time. For the Y vector we can provide per_day_mean, and for the X vector we want to use the number of the day in the trial, which we can generate as a range with:

MATLAB

>> day_of_trial = 1:40;

Then our plot can be generated with:

MATLAB

>> plot(day_of_trial, per_day_mean)

Callout

Note: If we only provide a vector as an argument it plots a data-point for each value on the y axis, and it uses the index of each element as the x axis. For our patient data the indices coincide with the day of the study, so plot(per_day_mean) generates the same plot. In most cases, however, using the indices on the x axis is not desireable.

Callout

Note: We do not even need to have the vector saved as a variable. We would obtain the same plot with the command plot(1:40, mean(patient_data, 1)), or plot(mean(patient_data, 1)).

As it is, the image is not very informative. We need to give the figure a title and label the axes using xlabel and ylabel, so that other people can understand what it shows (including us, if we return to this plot 6 months from now).

MATLAB

>> title("Daily average inflammation")
>> xlabel("Day of trial")
>> ylabel("Inflammation")

That’s much better! Now the plot actually communicates something. As we expected, this figure tells us way more than the numbers we had seen in the previous section.

Let’s have a look at two other statistics: the maximum and minimum inflammation per day across all patients.

MATLAB

>> plot(day_of_trial, per_day_max)
>> title("Maximum inflammation per day")
>> ylabel("Inflammation")
>> xlabel("Day of trial")

Scripts

We often have to repeat a series of commands to achieve what we want, like with these plots. To be able to reuse our commands with more ease, we use scripts.

A more in depth exploration of scripts will be covered on the next episode. For now, we’ll just start by clicking new->script, using ctrl+N, or typing edit on the command window.

Any of the above should open a new “Editor” window. Save the file inside the src folder, as single_plot.m.

Alternatively, if you run

MATLAB

>> edit src/single_plot.m

it creates the file with the correct path and name for you.

Note: Make sure to add the src folder to your path, so that MATLAB knows where to find the script. To do that, right click on the src directory, go to “Add to Path” and to “Selected Folders”. Alternatively, run:

MATLAB

>> addpath("src")

Try copying and pasting the plot commands for the max inflammation on the script and clicking on the “Run” button!

Because we now have a script, it should be much easier to change the plot to the minimum inflammation:

MATLAB

>> day_of_trial = 1:40;
>> plot(day_of_trial, per_day_min)
>> title("Minimum inflammation per day")
>> ylabel("Inflammation")
>> xlabel("Day of trial")

These two are much more noisy than the mean, as we’d be expect.

Multiple lines in a plot

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It is often the case that we want to plot more than one line in a single figure. In MATLAB we can “hold” a figure and keep plotting on the same axes. For example, we might want to contrast the mean values accross patients with the inflammation of a single patient.

Lets reuse the code we have in the script, but save it as a new script called “multiline_plot.m”. You can do that using the dropdown menu on the save button, or by running this command on the terminal:

MATLAB

>> copyfile("src/single_plot.m","src/multiline_plot.m")

and then open the new file with edit src/multiline_plot.m, as before.

If we are displaying more than one line, it is important to add a legend. We can specify the legend names by adding ,DisplayName="legend name here" inside the plot function. We then need to activate the legend by running legend. So, to plot the mean values we first do:

MATLAB

>> day_of_trial = 1:40;
>> plot(day_of_trial, per_day_mean, DisplayName="Mean")
>> legend
>> title("Daily average inflammation")
>> xlabel("Day of trial")
>> ylabel("Inflammation")

Then, we can use the instruction hold on to add a plot for patient_5.

MATLAB

>> hold on
>> plot(day_of_trial, patient_5, DisplayName="Patient 5")
>> hold off

So this patient seems fairly average.

Remember to tell MATLAB you are done by adding hold off when you have finished adding lines to the figure!

Patients 3 & 4

Try to plot the mean across all patients and the inflammation data for patients 3 and 4 together.

Show me the solution

The first part for the mean remains unchanged:

MATLAB

>> day_of_trial = 1:40;
>> plot(day_of_trial, per_day_mean, DisplayName="Mean")
>> legend
>> title("Daily average inflammation")
>> xlabel("Day of trial")
>> ylabel("Inflammation")

Now we need to get the specific data for each patient. We can get the data for patients 3 and 4 as we did in the previous episode i.e. patient_data(3,:). Now we can either save that data in a variable, or we use it directly in the plot instruction, like this:

MATLAB

>> hold on
>> plot(day_of_trial, patient_data(3,:), DisplayName="Patient 3")
>> plot(day_of_trial, patient_data(4,:), DisplayName="Patient 4")
>> hold off

The result looks like this:

Patient 4 seems also quite average, but patient’s 3 measurements are quite noisy!

Multiple plots in a figure

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Note: The subplot command was deprecated in favour of tiledlayout in 2019.

It is often convenient to show different plots side by side. The tiledlayout(m,n) command allows us to do just that. The first two parameter define a grid of m rows and n columns in which our plots will be placed. To be able to plot something on each of the tiles, we use the nexttile command.

Lets start a new script for this topic:

MATLAB

>> edit src/tiled_plot.m

We can show the average daily min and max plots together with:

MATLAB

>> day_of_trial = 1:40;
>> tiledlayout(1, 2)
>> nexttile
>> plot(day_of_trial, per_day_max)
>> title("Max")
>> xlabel("Day of trial")
>> ylabel("Inflamation")
>> nexttile
>> plot(day_of_trial, per_day_min)
>> title("Min")
>> xlabel("Day of trial")
>> ylabel("Inflamation")

We can also specify titles and labels for the whole tiled layout if we assign the tiled layout to a variable and pass it as a first argument to title, xlabel or ylabel, for example:

MATLAB

>> day_of_trial = 1:40;
>> tlo=tiledlayout(1, 2);
>> title(tlo,"Per day data")
>> xlabel(tlo,"Day of trial")
>> ylabel(tlo,"Inflamation")
>> nexttile
>> plot(day_of_trial, per_day_max)
>> title("Max")
>> nexttile
>> plot(day_of_trial, per_day_min)
>> title("Min")

Where is the nexttile?

You can specify which tile you want to plot next by specifying the number as an argument to nexttile like so:

MATLAB

>> tiledlayout(3,5)
>> nexttile(3)

Note that, as opposed to numerical arrays, the indexing goes along the row first, and then jumps to the next column.

Resizing tiles

You can also choose a different size for a plot by occupying many tiles in one go. You do that by specifying the number of rows and columns you want to use in an array ([rows,columns]), like this:

MATLAB

>> nexttile([3,1])

And you can specify the starting tile at the same time, like this:

MATLAB

>> nexttile(8,[2,3])

Note that using a starting tile that overlaps another plot will erase that axes. For example, try:

MATLAB

>> nexttile(1,[2,2])

Clearing a figure

If you now try to plot something like the mean, as we had done before, you will notice that the plot is assigned to the second plot space in the tiled layout.

To clear the tiled layout, you can use the instruction

MATLAB

>> clf

which stands for “clear figure”.

Heatmaps

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If we wanted to look at all our data at the same time we need three dimensions: One for the patients, one for the day, and another one for the inflamation. One option is to use a heatmap, that is, use the colour of each point to represent the inflamation values.

In MATLAB, at least two methods can do this for us. The heatmap function takes a table as input and produces a heatmap:

MATLAB

>> heatmap(patient_data)
>> title("Inflammation")
>> xlabel("Day of trial")
>> ylabel("Patient number")

We gain something by visualizing the whole dataset at once; for example, we can see that some patients (3, 15, 25, 31, 36 and 60) have very noisy data. However, it is harder to distinguish the details of the inflammatory response.

Similarly, the imagesc function represents the matrix as a color image.

MATLAB

>> imagesc(patient_data)
>> title("Inflammation")
>> xlabel("Day of trial")
>> ylabel("Patient number")

Every value in the matrix is mapped to a color. Blue regions in this heat map are low values, while yellow shows high values.

Both functions provide very similar information, and can be tweaked to your liking. The imagesc function is usually only used for purely numerical arrays, whereas heatmap can process tables (that can have strings or categories in them). In our case, which one you use is a matter of taste.

Key Points

• Use plot(vector) to visualize data in the y axis with an index number in the x axis.
• Use plot(X,Y) to specify values in both axes.
• Document your plots with title("My title"), xlabel("My horizontal label") and ylabel("My vertical label").
• Use hold on and hold off to plot multiple lines at the same time.
• Use legend and add ,DisplayName="legend name here" inside the plot function to add a legend.
• Use tiledlayout(m,n) to create a grid of m x n plots, and use nexttile to change the position of the next plot.
• Choose the location and size of the tile by passing arguments to nextile as nexttile(position,[m,n]).
• Use heatmap or imagesc to plot a whole matrix with values coded as color hues.