Last Week

• Advanced Data Operations
  • Applying Functions to Vectors and Matrices
  • Grouped Summaries
  • Concatenating and Merging Data

This Week

• This week we finally get to a fun topic: data visualisation.
• There’s more to data visualisation than I could possibly cover in 90 minutes
• I focus on static, two-dimensional visuals
  • These are the kind that you are most likely to use.

Visual Summaries as an Aid

• Returning to the theme of this course, the aim of much of data science is to understand the whole picture of your data.
• If you can do this without reading your entire dataset, all the better!
• When making data visuals, I think it’s helpful to remember that they are, in many ways, a form of summary.
• Visualising data is not just about communicating results; it is also a powerful tool for you to understand important features of your own data.

Motivating Example

Motivating Example

Data Types/Structures

The type and structure of your data tells you what type of figure you need:

• Number of Dimensions
• Ordered or Unordered?
• Discrete or Continuous?

Visuals on a Two-Dimensional Medium

Most figures are created on a two-dimensional plane, where the dimensions are usually referred to as X (width) and Y (height).

These axes are the most versatile; they can be used to plot any kind of variable. The only trade-off is the overall size of the figure is determined by these two dimensions.

One-Dimension: Distributions

Visuals for one-dimensional data tend to be concerned with distributions; i.e. frequencies of values along some dimension.

Useful plots include:

• Histogram
• Box (and whiskers) plot
• Swarm plot
• Violin plot

Two-Dimensions: Relationships

Visuals for two-dimensional data often fulfil one of the following two purposes:

• Comparing distributions
• Plotting functions

In addition to all of the aforementioned plots, some examples of the latter include:

• Scatter plot
• Line plot
• Bar plot

Three-Dimensions and Higher: Levels

• While it is possible to draw plots that have a third, z axis, to show depth on a screen, I personally do not think it is very readable.
• There are many ways to vary visual elements to intuitively convey variation along further axes.

Showing Variation with Color

Colors can show variation along a multitude of data types.

• Discrete colors can differentiate unordered, discrete categories.
• Gradiated colors can represent ordered, continuous variation.
  • For example, see heatmaps

Showing Variation with Panels

Panelling is the use of multiple sub-plots within a single figure.

• Panelling can only show variation along a discrete variable.
• The order of the plots can be used to show variation along an ordered, discrete variable.

Other Ways of Showing Variation

Colors and panelling are not the only means.

• Shapes can be used to show categorical variation.
• Size/thickness and transparency can be used to show continuous variation.

Take-Away

When visualising data, ask yourself the following questions, then look through galleries to get an idea of what could work for you.

Are you:

• Making a comparison between groups?
• Trying to show conditional relationships between variables?
• Exploring your own data?

Two Libraries

• matplotlib is the primary library for building data-based visuals in Python.
  • Requires a lot of explicit commands to get it to look good, but allows for nearly complete customisation of all aspects.
• seaborn is a more recent library, built on top of matplotlib.
  • Provides fast and convenient methods for most figures you will ever need.
• Both libraries can be used in conjunction.

The Anatomy of a Data Visual

On the back end, all matplotlib-based visuals adhere to a similar tree-like structure. By learning this structure, you can locate and customise any element of a figure.

The Matplotlib Hierarchy

Here is a truncated version of the matplotlib hierarchy:

• Figure
  • Figure-level Methods (e.g. Title)
  • Axes (Subplots)
    • Subplot-level Methods (e.g. sub-title)
    • Graphical functions
      • Graphical primitives (shapes)
    • Axis pairs (x-axis and y-axis)
      • Axis labels
      • Axis ticks
        • Location
        • Labels
    • Legend

Figure

The figure is essentially the “canvas” upon which all visuals are made. Some parameters/methods set at this level include:

• Total size (in pixels)
• Super-title
• Saving to file

Axes (Subplots)

Subplots are the frames within which individual visuals are contained.

Most drawing methods are called at the subplot level:

• Plotting (drawing the graphical objects)
• Individual plot labels
• Legends

Graphical Functions

matplotlib and seaborn provide an enormous number of plotting functions. These functions:

• Take one or more equal-length vectors as inputs (the data).
  • This data may be in long- or wide-format.
• Draw objects accordingly to the relevant subplot
  • If the function is a matplotlib function, you should call it as a method of the relevant subplot.
  • If the function is a seaborn function, and there is more than one subplot, then you should pass the relevant subplot as a parameter to the function.

Customisable Aspects

Graphical objects take a large number of customisable parameters, such as:

• Color
• Transparency
• Line/dot style

X and Y Axis

Subplots have xaxis and yaxis methods. Call these to customise the following aspects:

• Ticks (the little notches along the axes)
  • Spacing/interval
  • Labels
    • Text
    • Orientation
  • Top/Bottom, Left/Right
• Axis labels

Figure

import matplotlib.pyplot as plt
f = plt.figure(figsize=(15, 8))

This does not create any visible objects, but it lays down the canvas that other things will go onto.

Note:

• Most of the plotting functionality is within the pyplot module of matplotlib.
• The output of plt.figure has been assigned to a variable, f. This will be our means of accessing the figure and its methods.
• The parameter figsize=(15, 8) has been passed to plt.figure. This tells matplotlib to create a canvas that is 1500x800 pixels.

Axes (One Subplot)

f, ax = plt.subplots(1, 1, figsize=(15, 8))
f.suptitle("This is a figure with a subplot")
ax.set_title("This is a subplot", color="r")

Axes (Two Subplots)

f, ax = plt.subplots(1, 2, figsize=(15, 8))
f.suptitle("This is a figure with two subplots")
ax[0].set_title("This is a subplot", color="r")
ax[1].set_title("This is another subplot", color="r")

Axes (Subplot Grid System)

f, ax = plt.subplots(2, 2, figsize=(15, 8))
f.suptitle("This is a figure with four subplots")
for i in range(2):
    for j in range(2):
        ax[i][j].set_title(f"Subplot [{i}][{j}]", color="r")

Graphical Functions (Scatter)

f, ax = plt.subplots(1, 1, figsize=(15, 8))
ax.scatter(data['x2'], data['x1'], color='r')

Graphical Functions (Line)

f, ax = plt.subplots(1, 1, figsize=(15, 8))
ax.plot(np.linspace(0, 10, 100), np.linspace(0, 5, 100), color='r')

Combining Graphical Functions (Scatter + Line)

f, ax = plt.subplots(1, 1, figsize=(8, 4))
ax.scatter(data['x2'], data['x1'], color='r', s=3)
ax.plot(np.linspace(-10, 20, 150), np.linspace(-3.5, 4, 150)**2)
ax.axhline(0, color='k', alpha=0.5, ls="--")
ax.axvline(0, color='k', alpha=0.5, ls="--")

Adding Axis Labels

[...]
ax.xaxis.set_label_text("X-Axis Label", color='r')
ax.yaxis.set_label_text("Y-Axis Label", color='r')

Customising Tick Locations (Manual)

[...]
ax.xaxis.set_ticks(range(-10, 40, 10))
ax.yaxis.set_ticks(range(-4, 25, 2))

Customising Tick Locations (Automatic)

ax.xaxis.set_major_locator(matplotlib.ticker.MultipleLocator(base=3))
ax.yaxis.set_major_locator(matplotlib.ticker.MultipleLocator(base=2))

Customising Tick Labels/Orientation

f, ax = plt.subplots(1, 1, figsize=(8, 4))
sns.boxenplot(bes_df['region'], bes_df['Age'], ax=ax)
ax.xaxis.set_ticklabels(ax.xaxis.get_ticklabels(), rotation=30)

Histogram (One Category)

Histogram (Two Categories)

Box and Whisker Plot

Swarm Plot (One Category)

Swarm Plot (Multiple Categories)

Violin Plot (One Category)

Heatmap