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[MUSIC]. 
Last time, we talked about data types, 

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dimensions and how to map data to visual 
attribute based on the number of data 

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dimensions. 
Clearly there's a large design space for 

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this visual encoding. 
Information visualization is about 

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choosing the most effective visual 
encoding for a given data set. 

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In this lecture, we're going to describe 
how to do that. 

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We saw earlier that there are different 
data types. 

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And those can be mapped to a set of 
visual attributes. 

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And some mapping are better than others. 
So now we have a challenge. 

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How do we pick the best mapping of all 
possibilities? 

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So in order to do this we're going to 
follow three basic principles. 

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Importance ordering, expressiveness and 
consistency. 

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This was first described by Jock McKinley 
in 1986. 

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So importance ordering has to do with 
encoding the most important information 

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in a most perceptually active way. 
Expressiveness has to do with depicting 

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all the data and only the data. 
And finally consistency means the 

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property of the image, the visual 
attributes should match the properties of 

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the data. 
I'll go into more detail on how to do 

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this on the following slides. 
We'll start with importance ordering. 

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We've seen this slide before. 
Now as we discussed earlier, decades of 

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research have taught us that certain 
visual attributes more accurately 

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represent quantitative data to the human 
brain. 

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Mackinlay defined expressiveness in the 
following manner: he said a set of facts 

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is expressible in a visual language if 
the sentences: i.e the visualizations in 

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the language express all the facts in the 
set of data and only the facts in the 

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data. 
So what does this mean? 

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Well, using color hue we cannot express 
the fact that one item is greater than 

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another. 
So color hue simply can't represent 

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ordinal data. 
Ordinal or quantitative data. 

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So color hues simply can't represent 
ordinal or quantitative data. 

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It's best you use phenomenal data. 
On the other hand you don't want to 

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express facts that are not in the data. 
So a length is interpreted as a 

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quantitative value. 
In this incorrect use of a bar chart, the 

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length of the bars say something untrue 
about the data. 

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So on the x axis we have the national 
origin of these cars, now on the y axis 

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the make and model. 
Now the length of the bars suggests an 

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ordering on the axis. 
So it implies that somehow Germany is 

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greater than the USA. 
So therefore using bars for nominal data 

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is an incorrect choice. 
Number three, we have consistency. 

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The properties of the image, the visual 
attributes should match the properties of 

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the data. 
What this means, is you don't want to do 

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something like mapping one dimensional 
data to two or three dimensional visual 

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representations. 
This diagram represents why that is not a 

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good idea. 
So here we have the price per barrel of 

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oil represented as the height of a three 
dimensional barrel. 

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You can see the obvious problem here. 
Look at 1974. 

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The price is $10.95 and then for 1979, 
the price is $13.34. 

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Well this is less than a 30% increase. 
And yet the 1979 barrel looks 

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significantly larger than the 1974 
barrel. 

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So clearly this is an inconsistent 
representation. 

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The three-dimensional representation is 
implying something false about the 

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underlying data. 
Let's move to a data encoding exercise. 

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Here we have a data set of cars. 
We have the model on the first column. 

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The country of origin, the year, the 
number of cylinders, the horsepower, the 

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miles per gallon and finally the weight 
in pounds. 

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I would like you to create a 
visualization that encodes all seven 

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dimensions in this data set. 
Make the perceptually appropriate choices 

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and be prepared to explain. 
I will describe the steps you need to do 

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and show you Bertin's examples once more. 
So step one the terminal which columns 

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represents nominal, ordinal or quantative 
data. 

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Step two review the transvisual 
attributes on the next slide and assign 

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the most perceptually appropriate choices 
to each data set. 

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Step three create a visualization that 
encodes as many of the seven dimensions 

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as you can. 
Don't worry if you can't get all of them 

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but, but do try to do so. 
To review here are Bertin's visual 

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attributes. 
Position, size, value, texture, color, 

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orientation and shape. 
Are you done? 

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Here's one attempt made by one of my 
students. 

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So this is an attempt at encoding seven 
variables from the cars dataset in a 

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single visualization. 
So this student chose to put two of the 

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quantitative variables, horsepower and 
miles per gallon on the x and y axis. 

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The third ratio data weight he encoded 
with area of the marks. 

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Not a bad choice since you, you can only 
put two of those ratio variables on axes. 

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He also chose to encode cylinders, which 
are quantitative integral data by using 

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the shape of the mark. 
And then finally he used color hue for 

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the region, Europe, Japan or US. 
And color value or lightness for the 

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year. 
Additionally in his visualization you can 

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mouse over each of the marks and the name 
of the model of the car would pop-up. 

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So, what do you think of this 
visualization? 

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What works, what doesn't and what could 
you do better? 

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I'll leave that critique as an exercise 
for you.