• Eyes sense light reflecting & refracting off of surfaces
• A composite object is formed in our brain from various visual properties
• We perceive composite as a whole object, but we distinguish these properties
• For example: 2D location, length, width, area, shape, color, orientation
• We do not attend to everything we see
  
• We do not have good working memory for what we see

Humans have a limited set of visual properties that are detected very rapidly and accurately by our visual system before we are consciously aware of it

• We easily detect the presence or absence of a target within a visual field
• We easily detect texture boundary between two groups of elements
• We easily track an element with a unique visual feature in space and time

“Perception in Visualization”, Chris Healey, NC State

Find the red circle:

Find the red circle:

Find the red circle:

See: “Perception in Visualization”, Chris Healey, NC State

What hapens to our visual representation when we stop attending and look at something else?

• Sustained attention to objects do not make visual search more efficient
• Repeated visual searches are not more efficient
• Once we see a pattern, we match the pattern even when it isn’t there
• Moral: Do not make users search for things in your visualization, but draw attention to things explicitly

“Perception in Visualization”, Chris Healey, NC State

Humans are pattern matchers …

See the dolphin!

We cannot easily “unsee” things …

There is no spoon … er … dolphin!

We rely on memory, but our working visual memory is very limited

• Tasks to be done when visualizing information:
  • Encode numeric data visually
  • Encode cateogrical data visually
  • Encode distinctions between different pieces of information
  • Encode methods to associate data / distinctions to some context
    
• Objective: To make the reader’s decoding process as easy and error-free as possible

• Typically the categorical data we wish to encode in fact numeric:
  • Proportions: a continuous number between 0 and 1
  • Frequencies: a discrete integer or count
• So often the most fundamental encoding choices for numeric and categorical values to be plotted are the same

• Whether underlying variables are categorical or numeric, we often have multiple things on a plot. E.g.,
  • Proportions from different levels of some variable
  • Different categorical level values in a factor
  • Different numeric variable values
  • Different trend lines in a time series
• Because the reader needs to discern these as different things, our encoding must distinguish these for the reader in some way

• In order from most easily perceived to least:

  1. Position along a common scale, axis, and baseline
  2. Position along non-aligned axes
  3. Length, direction, angles of relative lines / slope
  4. Area
  5. Volume, curvature, arcs / angles within a shape
  6. Color or shading

Cleveland McGill (1984). “Graphical Perception: Theory, Experimentation, and Application to the Development of Graphical Methods.” Journal of the American Statistical Association, 79(387), pp. 531–554.

Often we need to separate or distinguish discrete visual items using:

• Distinct positions
• Different colors or shading
• Distinguishing symbols, words, or annotations
• Other plot elements (e.g., line thickness)

• Color can be used for a number of purposes:
  • Encoding numeric values
  • Distinguishing or highlighting visual elements
  • Mood & effect
• Perception of colors depends on context:
  • Medium: paper, poster, screen, projected presentation
  • Lighting: glare, contrast,
  • Audience: Colorblindness?

1. Proximity: When objects are close together, we often perceive them as a group

2. Similarity: When objects share similar attributes (color, shape, etc.), we often perceive them as a group

3. Enclosure: When objects are surrounded by a boundary, we often perceive them as a group

4. Closure: Sometimes partially open structures can still be perceived as a grouping metaphor (e.g., “\(\left[ \ldots \right]\)”)

5. Connectivity: When you draw curves or lines through data elements, this is often perceived as creating a connection between them

When objects are close together, we often perceive them as a group

When objects share similar attributes (color, shape, etc.), we often perceive them as a group

When objects are surrounded by a boundary, we often perceive them as a group

Sometimes partially open structures can still be perceived as a grouping metaphor

When you draw curves or lines through data elements, this is often perceived as creating a connection between them

Lines imply connection … don’t use them if there isn’t any

Group things so that the most important things to compare are closest

• Humans have different kinds of memory, stored differently and in different parts of the brain
  • Long-term vs. working memory
  • Verbal memory vs. visual memory
• Working memory for visual information is very limited
• Humans can retain roughly three chunks of information at a time
• Visualizations can help “chunk” information together

• We should avoid “fragmentation” (separating things that should be remembered together)
• So place the things most related closest together – things that you most want the reader to remember together
• Highlight and annotate things explicitly, if you want the reader to notice them

Suppose we want to visualize a Binomial distribution, \(n=15,\; p=0.25\)

library(ggplot2)

k = 0:15
pmf = dbinom(k,  size=max(k),  prob=0.25)
MyData = data.frame(k,  pmf)

ggplot(MyData,aes(x=k,  y=pmf)) + 
  geom_linerange(ymin=0,  ymax=pmf,  size=1.25) + 
  geom_point(size=3.5) + 
  ylab("Pr{k}") +
  theme(text=element_text(size=18, family="Times"))

Suppose we want to visualize a Normal distribution, \(\mu = 5, \sigma=2\)

library(ggplot2)

ggplot(data.frame(x=c(-5,15),y=c(0,1)),aes(x=x,y=y)) + 
  stat_function(fun=dnorm,args=list(mean=5,sd=2)) + 
  ggtitle("Normal Distribution, ~N(5,2)") +
  theme(text=element_text(size=18, family="Times"))

To get a rough picture of the distribution of a sample, use a histogram

library(ggplot2)

MyData = data.frame(val=rnorm(200))

ggplot(MyData,aes(x=val)) + 
  geom_histogram(binwidth=0.5, col="white", fill="darkblue") +
  xlab("Value") + ylab("Count") + ggtitle("Histogram of MyData") +
  theme(text=element_text(size=18, family="Times"))

Or a density plot

library(ggplot2)

MyData = data.frame(val=rnorm(200))

ggplot(MyData,aes(x=val)) + 
  geom_density(fill="pink",col=NA) +
  xlab("Value") + ylab("Density") + ggtitle("Density of MyData") +
  theme(text=element_text(size=18, family="Times"))

Or all of these

library(ggplot2)

MyData = data.frame(val=rnorm(200)) 

mu = mean(MyData$val)
sig = sqrt(var(MyData$val))

ggplot(MyData,aes(x=val)) + 
  geom_density(fill="pink",col=NA) +
  geom_histogram(binwidth=0.5, aes(y=..density..), col="white", alpha=0.4) +
  stat_function(fun=dnorm,arg=list(mean=mu,sd=sig), size=1.5, col="darkred") +
  xlab("Value") + ylab("Density") + 
  ggtitle("Estimating MyData Distribution") +
  theme(text=element_text(size=18, family="Times"))

Q-Q plots give us a way to see how close to a normal distribution
our data might be

Right Skew		Short Tails
Left Skew		Long Tails

MyData = data.frame(val=rnorm(200))

qqnorm(MyData$val,pch=19,col="darkgray")
qqline(MyData$val,lwd=2,col="darkred")

Dot plots use position to encode a numeric value, proportion, or frequency

library(ggplot2)

MyData = data.frame(State=state.name[1:10], Area=state.area[1:10])

ggplot(MyData,aes(x=Area,y=State)) +
  geom_point(size=4) +
  xlab("Area (sq. miles)") +
  theme(text=element_text(size=18, family="Times"))   

Dot plots use position to encode a numeric value, proportion, or frequency

Note: There’s no implicit meaning to the \(y\)-axis positions

So we can order the dot plot based on value typically to make it easier to read

library(ggplot2)

MyData = data.frame(State=state.name[1:10], Area=state.area[1:10])
MySortedData = transform(MyData, State=reorder(State,Area))

ggplot(MySortedData,aes(x=Area,y=State)) +
  geom_point(size=4) +
  xlab("Area (sq. miles)")  +
  theme(text=element_text(size=18, family="Times"))

Bar plots use length and position to encode a numeric value

library(ggplot2)

MyData = data.frame(State=state.name[1:10], Area=state.area[1:10])
MySortedData = transform(MyData, State=reorder(State,Area))

ggplot(MySortedData,aes(x=State,y=Area)) +
  geom_bar(stat="identity") +
  coord_flip() +
  ylab("Area (sq. miles)")  +   # Recall we flipped the axes ...
  theme(text=element_text(size=18, family="Times"))

Note: Again, these are ordered for ease of reading …

• Histograms visualize an estimate for a distribution of a numeric variable
• The bins in the histogram remain in the order given by the values
• While bar plots visualize the values of specific observations
• And the order of the bar plots presented is typically up to us

For example, use lines to connect the same algorithm at different points during a run

library(ggplot2)

fakeData = data.frame(evals=c(100,150,200,250),
                      performance=c(1000.1,1300.2,1410.6,1470.3),
                      ci=c(150,90,50,30))

ggplot(fakeData,aes(evals,performance)) +
  geom_errorbar(aes(ymin=performance-ci/2, ymax=performance+ci/2),
                size=0.5, width=10) +
  geom_line(color="darkblue", size=1.25) +
  geom_point(size=5) +
  xlab("Number of Evaluations") +
  ylab("Algorithm Performance") +
  theme(text=element_text(size=18, family="Times"))

Box plots give information about the median, inter-quartiles, outliers, as well as confidence inervals

library(ggplot2)

ggplot(mtcars, aes(1,y=mpg)) +
  geom_boxplot(notch=T, fill="pink") +
  theme(axis.text.x=element_blank(), axis.ticks.x=element_blank()) +
  xlim(c(0,2)) + 
  xlab("") + ylab("Mileage") + 
  ggtitle("Distribution of Car Mileage") +
  theme(text=element_text(size=18, family="Times"))

Use dodge to visualize multiple Binomial distributions

library(ggplot2)

k = 0:15
p = factor(c(rep(0.25,length(k)),rep(0.4,length(k))))
pmf = c(dbinom(k,  size=max(k),  prob=0.25), dbinom(k,  size=max(k),  prob=0.4))
MyData = data.frame(k,  p, pmf)

ggplot(MyData, aes(x=k,  y=pmf, group=p)) + 
  geom_linerange(ymin=0,  
                 aes(ymax=pmf, color=p),  
                 size=1.25, 
                 position=position_dodge(width=0.25)) + 
  geom_point(size=3.5, position=position_dodge(width=0.25), aes(color=p)) + 
  ylab("Pr{k}") +
  ggtitle("Two Binomial Distributions, n=15, p=0.25 and p=0.4") 

Label text is too small? Use theme()

You can use factors to separate different plots straightforwardly

library(ggplot2)
library(MASS)                         # Contains a lot of extra data sets

birthwt1 = birthwt                    # Copy a birth Wt / risk factor data set 
birthwt1$smoke = factor(birthwt$smoke) # Make "smoking during preg." a factor

ggplot(birthwt1, aes(x=bwt, fill=smoke)) + 
  geom_density(alpha=0.3) +
  xlab("Birth Weight (g)") +
  ylab("Distribution Density") +
  scale_fill_discrete(name="Mom Smoked?",
                      labels=c("No","Yes")) + 
  theme(text=element_text(size=20, family="Times"))

library(ggplot2)
library(MASS)                    # Contains a lot of extra data sets

bwt = birthwt$bwt                # Get the birth Wt / risk factor vector
smoke = as.factor(birthwt$smoke) # Make "smoking during preg." variable a factor
MyData = data.frame(bwt,smoke)

ggplot(MyData, aes(x=bwt, fill=smoke)) +
  geom_histogram(aes(y=..density..),
           binwidth=500,
           position=position_dodge(width=500),
           color="black") +
  xlab("Birth Weight (g)") +
  ylab("Distribution Density") +
  scale_fill_discrete(name="Mom Smoked?",
                      labels=c("No","Yes")) + 
  theme(text=element_text(size=20, family="Times"))

You can use stat_density2d to create contour density plots

library(ggplot2)
library(gcookbook)

ggplot(faithful, aes(x=eruptions, y=waiting)) +
  stat_density2d(aes(color=..level..), size=1.5) +
  xlab("Eruption Time (min)") +
  ylab("Time Between Eruptions (min)") +
  scale_color_continuous(name="Distribution\nDensity") +
  ggtitle("Old Gaithful Geyser Eruptions") + 
  theme(text=element_text(size=20, family="Times"))

Use geom_point for scatter plots of numeric values

library(ggplot2)
library(MASS)

ggplot(Boston,aes(x=age, y=medv, size=crim, color=dis)) + 
  geom_point() + 
  scale_size(range=c(2.5,10)) + 
  xlab("Age of Home") + 
  ylab("Median Home Value (thousands)") + 
  scale_size_continuous(name="Township\nCrime Rate") +
  scale_color_continuous(name="Distance to\nEmployment") +
  ggtitle("Houses of Boston") + 
  theme(text=element_text(size=20, family="Times"))

The standard R function pairs allows us to see all pairwise scatter plots

pairs(iris[1:4],pch=19)

If you install the GGally library, you get a ggplot version with ggpairs

library(GGally)

ggpairs(iris) + 
  theme(text=element_text(size=20, family="Times"))

• We can use group to separate trends in a dataset
• Color and line thickness can help distinguish these groups
• Still, too many separate lines are hard to decode

library(ggplot2)
library(gcookbook)

ggplot(uspopage, aes(x=Year, y=Thousands, group=AgeGroup)) +
  geom_line(aes(color=AgeGroup,size=AgeGroup)) +
  xlab("Year") + 
  ylab("Number of People in US (thousands)") + 
  theme(text=element_text(size=20, family="Times"))

• Stacking can make sense when:
  • a factor is ordered (ordinal categorical variable)
  • we care mainly about the aggregated values at any stack level
• Try to match stack order with legend order

library(ggplot2)
library(gcookbook)

Year = uspopage$Year
Thousands = uspopage$Thousands
AgeGroup = factor(uspopage$AgeGroup,levels=rev(levels(uspopage$AgeGroup)))
MyData = data.frame(Year,Thousands,AgeGroup)

ggplot(MyData, aes(x=Year, 
                  y=Thousands, 
                  fill=AgeGroup, 
                  order=-as.numeric(AgeGroup))) +
  geom_area()   +  scale_fill_grey(start=0.8, end=0) +
  xlab("Year")  +  ylab("Number of People in US (thousands)") + 
  theme(text=element_text(size=20, family="Times"))

We can make “grouped” boxplots using dodge

library(ggplot2)

ggplot(cabbage_exp, aes(x=Date, y=Weight, fill=Cultivar)) +
  geom_bar(stat="identity", position="dodge", color="white") + 
  scale_fill_brewer(palette="Set1") +
  theme(text=element_text(size=20, family="Times"))

By default, ggplot wants to stack …

library(ggplot2)

ggplot(cabbage_exp, aes(x=Date, y=Weight, fill=Cultivar)) +
  geom_bar(stat="identity", color="white") + 
  scale_fill_brewer(palette="Set1") +
  theme(text=element_text(size=20, family="Times"))

• Mosaic plots are like multi-dimensional bar plots
• Encode values using area
• In R, we need to install and load the library vcd
• The vcd mosaic function requires a somewhat more sophisticated data table structure (more on this in another lecture)

library(vcd)
mosaic(HairEyeColor) + 
  theme(text=element_text(size=20, family="Times"))

## NULL

Florence Nightengale used Coxcomb plots to convince the the Brittish that the biggest threat to their soldiers during the Crimean war were preventable diseases

nightengale = read.csv("http://eecs.ucf.edu/~wiegand/ids6938/datasets/nightengale.csv",header=TRUE)
Month = as.Date(paste("01",nightengale$Date),"%d %B %Y")
DeathType = factor(nightengale$DeathType,ordered=TRUE)
DeathRate = sqrt((1000*nightengale$NumDeaths/nightengale$AvgArmySize)/pi)
MyData = data.frame(Month,DeathType,DeathRate)

ggplot(MyData, aes(x=Month, 
                   y=DeathRate, 
                   fill=DeathType, 
                   order=as.numeric(DeathType))) + 
  geom_bar(stat="identity") +
  coord_polar() +
  scale_x_date(breaks=MyData$Month,labels=format(MyData$Month,"%b %Y")) + 
  theme(text=element_text(size=20, family="Times"))

library(ggplot2)

ggplot(iris,aes(x=Species, y=Sepal.Length)) + 
  geom_boxplot(outlier.size=3, notch=TRUE) +
  ylab("Iris Sepal Length (cm)") + 
  theme(text=element_text(size=20, family="Times"))

import matplotlib.pyplot as plt

fig, ax = plt.subplots()

fruits = ['apple', 'blueberry', 'cherry', 'orange']
counts = [40, 100, 30, 55]
bar_labels = ['red', 'blue', '_red', 'orange']
bar_colors = ['tab:red', 'tab:blue', 'tab:red', 'tab:orange']

ax.bar(fruits, counts, label=bar_labels, color=bar_colors)

ax.set_ylabel('fruit supply')
ax.set_title('Fruit supply by kind and color')
ax.legend(title='Fruit color')

plt.show()

import matplotlib.pyplot as plt
import numpy as np

# Fixing random state for reproducibility
np.random.seed(19680801)


N = 50
x = np.random.rand(N)
y = np.random.rand(N)
colors = np.random.rand(N)
area = (30 * np.random.rand(N))**2  # 0 to 15 point radii

plt.scatter(x, y, s=area, c=colors, alpha=0.5)
plt.show()

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(19680801)
fruit_weights = [
    np.random.normal(130, 10, size=100),
    np.random.normal(125, 20, size=100),
    np.random.normal(120, 30, size=100),
]
labels = ['peaches', 'oranges', 'tomatoes']
colors = ['peachpuff', 'orange', 'tomato']

fig, ax = plt.subplots()
ax.set_ylabel('fruit weight (g)')

bplot = ax.boxplot(fruit_weights,
                   patch_artist=True,  # fill with color
                   tick_labels=labels)  # will be used to label x-ticks

# fill with colors
for patch, color in zip(bplot['boxes'], colors):
    patch.set_facecolor(color)

plt.show()