Day 2

Overview

Today, we will do more with matplotlib.

• bar graphs
• line graphs
• box plots (will be useful tomorrow)
• scatter plots
• choropleth plots (map plots)

Also we will learn to

• create figures with multiple sub-figures (called subplots)
• customize labels, colors, error bars etc.

In the exercises, we will use this to further visualize and analyze the campaign donations data.

matplotlib is quite powerful, and is intended to emulate matlab's visualization facilities. We will give you a basic understanding of how plotting works, which should be enough for a majority of the charts that you will want to create.

TODO: Add Comments about when to use each type of graph, and a section on colors/contrast?

a good link about color

TODO: Use subject instead of email text

Problem: internet says matplotlib not good for network graphs. Talk about them at all?

Introduction

When should you use visualizations

Purpose of visualizations.

Figure and Subplots

The package we will be using is matplotlib.pyplot. It provides a lot of shorthands and defaults (we used some of them yesterday when making line charts), but today we will do things the "right way".

A figure is the area that we will draw in. We can specify that it is 50 inches wide and 30 inches tall.

import matplotlib.pyplot as plt
fig = plt.figure(figsize=(50, 30))
subplot1 = fig.add_subplot(2, 3, 1)
subplot2 = fig.add_subplot(2, 3, 2)

It is common to create multiple subfigures or subplots in a single figure. fig.add_subplot(nrows, ncols, i) tells the figure to treat the area as a nrows x ncols grid, and return an Axes object that represents the i'th grid cell. You will then create your chart by calling methods on object. It helps me to think of an Axes object as a subplot.

For example, the above code creates a figure with the following layout. The black box is the area of the figure, while each blue box is a subplot in a 2x3 grid. The number in a blue box is the subplot's index.

It's important to mention that add_subplot does not actually create a grid, it just finds the area in an imaginary grid where a subplot should be and return an object that represents the area. Thus it is possible to do draw on overlapping subplots.

fig.add_subplot(2, 3, 1)
fig.add_subplot(2, 1, 1)

You will often see a shorthand for creating subplots when the number of rows and number of columns are less than 10. fig.add_subplot(xyz) returns the z'th subplot in a x by y grid. So fig.add_subplot(231) returns the first subplot in a 2x3 grid.

How Drawing Works

The functions that we will be using to create charts are simply convenience functions that draw and scale points, lines, and polygons at x,y coordinates. Whenever we call a plotting method, it will return a set of objects that have been added to the subplot. For example, when we use the bar() method to create a bar graph, matplotlib will draw rectangles for each bar, and return a list of rectangle objects so that we can manipulate them later (e.g., in an animation).

As you use matplotlib, keep in mind that:

• Many of the plotting functions will ask you to specify things similar to x,y coordinates / offsets.
• When you call a drawing function, it won't rearrange the layout of what was drawn before. It simply draws the pixels on top of what has been drawn before.
• You are ultimately adding points, lines and polygons on top of one another.

Let's Plot Some Graphs!

Let's get to drawing graphs! By the end of this tutorial, you will have experience creating bar charts, line charts, box plots, scatter plots, and choropleths (map plots). We will walk you through how to create a figure similar to

This figure creates subplots in a 3x2 grid, so let's first setup the figure and generate two sets of data. Both sets have the same x values, but different y values.

import matplotlib.pyplot as plt
import random
random.seed(0)

fig = plt.figure(figsize=(50, 30))

N = 100
xs = range(N)
y1 = [random.randint(0, 50) for i in xs]
y2 = range(N)

Bar Plots documentation

subplot.bar(left, height, width=0.8, bottom=None, **kwargs)

The bar plot function either takes a single left and height value, which will be used to draw a rectangle whose left edge is at left, and is height tall:

subplot.bar(10, 30)

or you can pass a list of lefts values and a list of height values, and it will draw bars for each pair of left,height value. For example, the following will create three bars at the x coordinates 10, 20 and 30. The bars will be 5, 8, 2 units tall.

subplot.bar([10, 20, 30], [5, 8, 2])

matplotlib will automatically scale the x and y axes so that the figure looks good. While the numbers along the x and y axes depend on the values of lefts and heights, the sizes of the bars just depend on their relative values.

The width keyword argument sets width of the bars It can be a single value, which sets the width of all of the bars, or a list that specifies the list of each bar. Set it relative to the differences of the left values. If the left values are spaced one unit apart and I am drawing 2 sets of bars, then I usually set the width to 1 unit / (2 + 1).

The bottom keyword argument specifies the bottom edge of the bars.

subplot.bar([10, 20, 30], [5, 8, 2], width=[5,5,5], bottom=[5, 10, 15])

The following code reproduces the bar graph. Since we want the bars to be evenly spaced apart, we set left to the numpy equivalent of range(len(xs)). Numpy arrays let us perform math operations on every element in the array. So left+width adds width to every element in left, which serves to shift the second set of bars to the right by width units.

import numpy as np
left = np.arange(len(xs))
width = 0.25

subplot = fig.add_subplot(3,2,1)
subplot.bar(left, ys, width=width)
subplot.bar(left+width, ys2, width=width, bottom=ys)

You can further customize your bar charts using the following popular keyword arguments:

• color='blue': set color to a hex value ("#ffffff"), a common color name ("green"), or a shade of grey ("0.8").
• linewidth=1: the width of the bar's border. set it to 0 to remove the border.
• edgecolor='blue': set the color of the bar's border.
• label='a name': give a set of bars a name. Later, we will teach you how to create legends that will display the labels.

Line Plots documentation

subplot.plot(xs, ys, **kwargs)

The plot command draws a line graph. It takes a list of x values and y values, and draws a line between every adjacent pair of points.

subplot.plot(xs1, ys1, xs2, ys2, ...) is a convenient shorthand for:

subplot.plot(xs1, ys1)
subplot.plot(xs2, ys2)
...

To reproduce the line graph, we can simply write

subplot = fig.add_subplot(322)
subplot.plot(xs, ys1, xs, ys2)

You can also customize the lines using the keyword arguments:

• color='green': same as color for bar graphs
• marker=None: specify the marker to draw at each point. I commonly use '*', '+', '.' or 'o'. Set it to None to not draw markers. The documentation has a full list of the available markers.
• label='a name': give a line a name. I usually call plot() for each line if I want to give each one a name.

Box Plots documentation

boxplot(data)

Boxplots are used to summarize and compare groups of numerical data. Each box summarizes a set of numbers and depicts 5 parameters:

• The smallest number
• The lower quartile
• The median
• The upper quartile
• The largest observation

subplot.boxplot will automatically compute these values, and also ignore numbers that it thinks are outliers. Don't worry about when and why they are used -- we will discuss that tomorrow. Just know that one box summarizes a set of numbers.

Unlike the other charts, you can't draw each box individually. The data variable is either a list of numbers, in which case it will compute and draw a single box:

subplot.boxplot(range(10))

or data can be a list of lists. In which case, it will compute and draw a box for each list. The following code reproduces the box plot shown earlier. We create sets of data (boxdata1, boxdata2, boxdata3) and create a box for each set.

subplot = fig.add_subplot(323)
boxdata1 = [random.randint(0, 20) for i in xrange(10)]
boxdata2 = [random.randint(20,40) for i in xrange(10)]
boxdata3 = [random.randint(40,60) for i in xrange(10)]
data = [boxdata1, boxdata2, boxdata3]
subplot.boxplot(data)

You can customize your box plots with the following keyword arguments

• vert=1: By default, the boxes are drawn vertically. You can draw them horizontally by setting vert=0
• widths=None: Like width in bar charts, this sets the width of each box

Scatter Plots documentation

subplot.scatter(x, y, s=20, c='blue', marker='o', alpha=None)

This method will draw a single point if you give it a single x,y pair

subplot.scatter(10, 10)

or you can give it a list of x and a list of y values

subplot.scatter([0, 1, 2], [9, 3, 10])

I've included the commonly used keyword arguments

• s=20: sets the size of each point to 20 pixels.
• c='blue': sets the color of each point to blue
• marker='o': each point will be drawn as a circle. The documentation lists large number of other markers
• alpha=None: the alpha (transparency) value of the points. Between 0 and 1.

Choropleths/Maps

Cartography is a very involved process and there is an enormous number of ways to draw the 3D world in 2D. Unfortunately, we couldn't find any native matplotlib facilities to easily draw US states and counties. It's a bit of a pain to get it working, so we've written some wrappers that you can call to draw colored state and counties in a subplot. We'll describe the api, and briefly explain how we went about the process at the end.

The API is defined in resources/util/map_util.py. You can import the methods using the following code:

import sys
# this adds the resources/util/ folder into your python path
# you may need to edit this so that the path is correct
sys.path.append('resources/util/')
from map_util import *

• draw_county(subplot, fips, color='blue'): draws the county with the specified fips county code. Most datasets that contain per-county data will include the fips code. If you don't include a color, we will pick a nice shade of blue for you.
• draw_state(subplot, state_name, color='blue'): draws the state with the full state name as specified by the official USPS state names. If you don't include color, we will pick a shade of blue for you.
• get_statename(abbr): retrieve the full state name from its abbreviation. The method is case insensitive, so get_statename('CA') is the same as get_statename('ca').

We also included a list of all fips county codes and state names in datasets/geo/id-counties.json and datasets/geo/id-states.json. We will use them to reproduce the map charts.

import json

# Map of Counties
#
subplot = fig.add_subplot(325)
# data is a list of strings that contain fips values
data = json.load(file('../datasets/geo/id-counties.json'))
for fips in data:
    draw_county(subplot, fips)


# Map of States
#
subplot = fig.add_subplot(326)
data = json.load(file('../datasets/geo/id-states.json'))
for state in data:
    draw_state(subplot, state)

The files are in JSON format, so we call json.load(file), which parses the files into python lists. The rest of the code simply iterates through the fips' and states, and draws them.

The gritty details

The process of drawing maps yourself requires a number of steps:

1. Download shape files. A shape file specifies the lat, lon positions that describe the border of an area (e.g., county, zip code, state).
2. Parse the shape files. They come in all types of formats. We downloaded the shape files that D3 uses. It comes in the GeoJS format, which is nice because json can parse it for us.
   • Remember how we mentioned that there lots of ways to draw the world in 2D. Our shape files use the Albers Equal Area Projection, which is also used by the US Census Bureau.
3. Once we have the shapes, we need to draw polygons in the subplot. Thankfully subplot.fill(xs, ys) fills in the region defined by the list of x,y points.
4. Our methods actually take any keyword argument that subplot.fill() accepts. So take a look at its documentation if you want to further customize your maps.

Customizing Subplots

We only touched a small part of what matplotlib can do. Here are some additional ways that you can customize subplots.

Keyword Arguments

• xerr=[]: list of floats that specify x-axis error bars.
• yerr=[]: list of floats that specify y-axis error bars

Additional Charting Methods

• subplot.loglog(xs, ys): plots a log-log line graph
• subplot.semilogx(xs, ys): plots the x-axis in log scale
• subplot.semilogy(xs, ys): plots the y-axis in log scale
• subplot.fill(x1,y1,x2,y2,x3,y3,...): draws a filled polygon with vertices at (x1,y1), (x2,y2), ....
• subplot.text(x,y,text): write text at coordinates x,y.

Subplot Customization

• subplot.clear(): clear everything that has been drawn on the subplot.
• subplot.legend(loc='upper center', ncol=2) - add a legend. You can specify where to place it using loc, and the number of columns in the legend.
• subplot.set_title(text): Set the subplot title.
• subplot.set_xlabel(text): Set the x-axis label
• subplot.set_xticks(xs): Draws x-axis tick marks at the points specified by xs. Otherwise matplotlib will draw reasonable tick marks.
• subplot.set_xticklabels(texts): Draw x-axis tick labels using the texts list.
• subplot.set_xscale(scale): Sets the x-axis scaling. scale is 'linear' or 'log'.
• subplot.set_xlim(minval, maxval): Set the x-axis limits
• subplot.set_ylabel()
• subplot.set_yticks()
• subplot.set_yticklabels()
• subplot.set_yscale()
• subplot.set_ylim(minval, maxval): Set the y-axis limits

Exercises

Exercise 1:

We will use yesterday's Obama vs McCain dataset and visualize it using different chart types.

Many people say that Obama was able to attract votes from "the common man", and had far more smaller contributions that his competitors. Let's plot a [histogram](LINK HERE) of each candidate's contribution amounts in $100 increments to see if this is the case. A histogram breaks a data range (donation amounts, in this case) into fixed size bucks (100 in this case), and counts the number of items that fall into each bucket. Plot both candidates on the same graph. You'll want to use a bar chart.

You'll find that it's difficult to read the previous chart because the donation amounts vary from -$1 Million to $8 Million, while the majority of the donations are less than 2000. One method is to ignore the outliers and focus on the majority of the data points. Let's only print histogram buckets within 3 standard deviations of the overall average donation.

For Obama, that's donations between [-$18000, $19000]. For McCain, that's between [-$22000, $22000]

Exercise 2:

Now create a cumulative line graph of Obama and McCain's donations. We can see that even though Obama and McCain have some very large contributions, the vast majority of their total donations were from small contributors. Also, not only did Obama get more donations, he also received larger donations.

Only after we've verified that the small donations were the major contributors, is it safe to zoom in on the graph!

Exercise 3:

Scatter plot of re-attribution by spouses for all candidates. It seems to be concentrated in a small group of Republican candidates.

At this point, we've only scratched the surface of one dimension (reattributions) of this interesting dataset. You could continue our investigation by correlating professions with candidates, visualize donations by geography, or see if there are any more suspicious and interesting data points.

Also, the 2012 campaign contributions are also available on the website, so you could use your analysis on the current election!

Exercise 4: Visualize County Health Data

The following are CSV files that contain the 2011 per-county health metrics. The first three columns contain the FIPS county code, the state and the county. The subsequent columns contain different metric values. The first file contains only Years of Preventable Life Loss (YPLL) values, which is used as a proxy for the health of a population. It is calculated as the sum of (Reference Age - Age at Death) for all deaths in a year. The reference age is often 75. The second file contains other metric values about each county.

• datasets/county_health_data/ypll.csv
• datasets/county_health_data/additional_measures_cleaned.csv

Visualize each of the following metrics on a map. Vary each county's color by the metric value.

• YPLL Rate
• % Child Illiteracy
• % Free Lunch
• % High Housing Costs
• % Diabetes

Take a look at the data first. There is a state-only row of data before data of the counties within the state. You should ignore that row. I personally use darker shades of blue to signify higher metric values. Here's some code that picks the shade of blue depending on a metric's current, maximum, and minimum values.

blues = ['#FFF7FB', '#ECE7F2', '#D0D1E6', '#A6BDDB', '#74A9CF',
         '#3690C0', '#0570B0', '#045A8D', '#023858']
MAXVAL = ...
MINVAL = ...
coloridx = int(( (value - MINVAL) / (MAXVAL - MINVAL) ) * (len(blues)-1)) )

The final charts should look something like

Done!

Now you have hands on experience with the most popular python plotting library! Matplotlib is far more power than what we have covered. Check out its documentation ()

• Always start by looking at your data with the simplest visualizations possible. For most datasets, a scatter plot or line graph is sufficient.
• First view a summary of the whole dataset so that you know which subsets are worth visualizing in more detail, and how significant the details really are.

Where do you go from here?

More info about visualizations Animations Interactive visualizations

Domain specific visualizations

Lots of visualizations specialized for unique applications.

Biology

Network graphs

Treemap

Other visualization tools

http://orange.biolab.si/features.html

Interactive visualizations

Applications. hard!