Visualization in Python

09/02/2022

Data Visualization Tips

Why?

For us: Explore data, make hypotheses, find trends
For others: Communicate data or findings

Show the Data

Above else, show the data. Maximize the data-ink ratio.

Edward Tufte

Visual Channels

Colormaps

Map quantities from number to color
Whenever you use color, you use one

Sequential

From one hue (or saturation) to another
Also change lightness
Good for extremes
Little contrast in middle

Diverging

Focus point in middle
Great for neutral point + deviations, e.g. profits

Qualitative

Show discrete values
good contrast

Perceptually Uniform Sequential

Carefully designed to show quantitative info

Miscellaneous

Lots of others
Colorful…but actually not that good

Problems

So what’s the problem with these other colormaps. This is an evaluation of the grey color map. Let's look at the panels on the right first. There are three heat maps here. So each pixel here represents a floating point value on some scale. On the left you see at the top the perceived changes in the color map, using a model of the human visual system. You can see that it's pretty constant. And at the bottom left you can see the the color map as a path in the 3d color space. This space is not RGB, it's a CIE color space that corresponds more to how humans perceive color. In the RGB space, humans can detect finer nuances in green than in red, for example.

Each color map is a path in this 3d space. And ideally, you'd like this to be a smooth path, and you'd like the speed to be constant. The perceptual contrast at the top is something like the derivative, or speed, of the color map going through the perceptual space.

Problems

matplotlib

Alternatives

pandas: convenience plotting
seaborn: good for complex statistical plots
bokeh: produces visualizations for browser
ggplot translations/interfaces: based on famous R plotting library

matplotlib in Jupyter

%matplotlib inline

sends png to browser
static image (e.g., no zooming)
no changes to previous figures

%matplotlib notebook

interactive widget
can update previous figures
need to create separate figures explicitly

Figures and Axes

figure: one window or image file
axes: one drawing area + coordinate system

Creating Figures and Axes

fig = plt.figure()
- Create figure with 1 set of axes
- Can add more later
- Sets "current" figure
fig, ax = plt.subplots(n, m)
- Creates figure with \(n\) x \(m\) axes (regular grid)
Just plot!
- Automatically creates figure
- Future plot commands will draw on that

More axes

import matplotlib.pyplot as plt

# ax = plt.subplot(n, m, i)
# places ax at position i in n x m grid
# (1-based index)
ax11 = plt.subplot(2, 2, 1)
ax21 = plt.subplot(2, 2, 2)
ax12 = plt.subplot(2, 2, 3)
ax22 = plt.subplot(2, 2, 4)

# OR:
# fig, axes = plt.subplots(2, 2)
# ax11, ax21, ax12, ax22 = axes.ravel()

More axes

import matplotlib.pyplot as plt

# ax = plt.subplot(n, m, i)
# places ax at position i in n x m grid
# (1-based index)
ax11 = plt.subplot(2, 2, 1)
ax21 = plt.subplot(2, 2, 2)
ax2 = plt.subplot(2, 1, 2)

Two Interfaces

Stateful: applies to "current" figure and axes
Object oriented: explicitly use object

sin = np.sin(np.linspace(-4, 4, 100))
plt.subplot(2, 2, 1)
plt.plot(sin)
plt.subplot(2, 2, 2)
plt.plot(sin, c='r')

fig, axes = plt.subplots(2, 2)
axes[0, 0].plot(sin)
axes[0, 1].plot(sin, c='r')

Two interfaces

plt.title
plt.xlim, plt.ylim
plt.xlabel, plt.ylabel
plt.xticks, plt.yticks
ax = plt.gca()   # get current axes
fig = plt.gcf()  # get current figure

ax.set_title
ax.set_xlim, ax.set_ylim
ax.set_xlabel, ax.set_ylabel
ax.set_xticks, ax.set_yticks (& ax.set_xtick_labels)

plot

import matplotlib.pyplot as plt
import numpy as np
data = np.sin(np.linspace(-4,4,100))
fig, ax = plt.subplots(2, 4, figsize=(10,5))
ax[0,0].plot(data)
ax[0,1].plot(range(100), data) # same as above
ax[0,2].plot(np.linspace(-4,4,100),data)
ax[0,3].plot(data[::10], 'o')
ax[1,0].plot(data, c='r')
ax[1,1].plot(data, '--')
ax[1,2].plot(data, lw=3)
ax[1,3].plot(data[::10], '--o')
plt.tight_layout() # makes stuff fit - usually works

scatter

x = np.random.uniform(size=50)
y = x + np.random.normal(0, .1, size=50) # add noise
fig, ax = plt.subplots(2, 2, figsize=(5,5),
					   subplot_kw={'xticks': (), 'yticks': ()})
ax[0,0].scatter(x,y)
ax[0,0].set_title("scatter")
ax[0,1].plot(x,y,'o')
ax[0,1].set_title("plot")
ax[1,0].scatter(x,y, c=x-y, cmap='bwr', edgecolor='k')
ax[1,1].scatter(x,y, c=x-y, s=np.abs(np.random.normal(scale=20, size=50)),
				cmap='bwr', edgecolor='k')
plt.tight_layout()

histogram

fig, ax = plt.subplots(1, 3, figsize=(10,3))
ax[0].hist(np.random.normal(size=1000))
ax[1].hist(np.random.normal(size=1000), bins=100)
ax[2].hist(np.random.normal(size=1000), bins="auto")

bars

heatmaps

You can plot heatmaps with the imshow command. Previous to matplotlib v2 this automatically enabled interpolation, which you can see at the top right. Interpolation might hide data or might give the impression of more data then there is, by showing a smooth transition. You should always disable interpolation for heatmaps. At the bottom you can see some results with a gray colormap and with a diverging color map. Here, the background is zero and it makes sense to represent the neutral differently. So I ensured that white is mapped to zero, and we can clearly distinguish positive from negative entries, which is much harder with the other color maps. Doing colorbars on multiple axes can be tricky. You need to store the matplotlib image that is returned by imshow in an object, and then call the colorbar command with the image and the axes to which you want to attach the colorbar.