Plotting data

Last updated on 2023-08-21 | Edit this page

Overview

Questions

  • “How can I visualize my data?”

Objectives

  • “Display simple graphs with adequate titles and labels.”
  • “Get familiar with functions plot, heatmap and imagesc.”
  • “Learn how to show images side by side.”

Plotting

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 (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 the average (accross patients) inflammation over time. For the Y vector we can provide per_day_mean, and for the X vector we can simply use the day number, which we can generate as a range with 1:40. Then our plot can be generated with:

MATLAB 

>> plot(1:40,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 vactor saved as a variable. We would obtain the same plot with the command 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')
Average inflammation

Much better, now the image actually communicates something.

The result is roughly a linear rise and fall, which is suspicious: based on other studies, we expect a sharper rise and slower fall. Let’s have a look at two other statistics: the maximum and minimum inflammation per day across all patients.

MATLAB 

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

MATLAB 

>> plot(per_day_min)
>> title('Minimum inflammation per day')
>> ylabel('Inflammation')
>> xlabel('Day of trial')
Minumum inflammation

From the figures, we see that the maximum value rises and falls perfectly smoothly, while the minimum seems to be a step function. Neither result seems particularly likely, so either there’s a mistake in our calculations or something is wrong with our data.

Multiple lines in a plot

It is often the case that we want more than one line in a single plot. In matlab we can “hold” a plot and keep plotting on top. For example, we might want to contrast the mean values accross patients with the information of a single patient. If we are displaying more than one line, it is important we 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 

>> plot(per_day_mean,'DisplayName',"Mean")
>> legend
>> title('Daily average inflammation')
>> xlabel('Day of trial')
>> ylabel('Inflammation')
Average inflamation with legend

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

MATLAB 

>> hold on
>> plot(patient_5,'DisplayName',"Patient 5")
>> hold off
Average inflamation and Patient 5

Remember to tell matlab you are done by adding hold off when you are done!

Subplots

It is often convenient to combine multiple plots into one figure. The subplot(m,n,p)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. The third parameter indicates the position on the grid that we want to use for the “next” plot command. For example, we can show the average daily min and max plots together with:

MATLAB 

>> subplot(1, 2, 1)
>> plot(per_day_max)
>> ylabel('max')
>> xlabel('day')

>> subplot(1, 2, 2)
>> plot(per_day_min)
>> ylabel('min')
>> xlabel('day')
Max Min subplot

Heatmaps

If we wanted to look at all our data at the same time we need a three dimensions: One for the patients, one for the days, and another one for the inflamation values. An 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')
Heat map

We gain something by visualizing the whole dataset at once, but it is harder to distinwish the overly linear rises and fall over a 40 day period.

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

MATLAB 

>> imagesc(patient_data)
>> title('Inflammation')
>> xlabel('Day of trial')
>> ylabel('Patient number')
imagesc Heat map

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.

Is all our data corrupt?

Our work so far has convinced us that something is wrong with our first data file. We would like to check the other 11 the same way, but typing in the same commands repeatedly is tedious and error-prone. Since computers don’t get bored (that we know of), we should create a way to do a complete analysis with a single command, and then figure out how to repeat that step once for each file. These operations are the subjects of the next two lessons.

Keypoints

  • “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 subplot(m,n,p) to create a grid of m x n plots, and choose a position p for a plot.”