So I'll spend a little bit
of time talking about,
some very important representations.
So much of our data,
is represented in the hierarchical format.
And so graphs and
trees are very often on the most
common ways that we represent data.
So I think it's valuable for us to talk
just briefly about some of the different
options that we have for thinking about
representing graph and tree data.
So the most common way that
we represent data in a graph
format excuse me, in a tree is something
that we call a node link diagram.
And a node link diagram really takes
each different node that has children,
and represents the children
at an indented way.
So in this particular node linked diagram,
the root of the tree is all the way
to the left, and each of the different
leaves are shown at the second column and
the third column, and far right
you'll see all the different leaves.
Well one of the most common
things I think I'm asked is,
how do I squeeze more data into my my,
my tree.
Well one of the ways is
by rather than using
a single hierarchy and making it flat.
But we can do here is have a radial
layout, and this radial layout
allows the same amount of data, excuse me,
a significantly higher amount of data
to be presented and it's shown in a way
that all of it can be visible at once.
And this idea of the node
link diagram can also be used
in this idea that here called thread arcs
that are used to show networks
that occur over time.
And so you can show a single note, and
the way that its children propagate.
This is very interesting
here in thread arc.
The idea is that this particular
representation is used to show the way
that a particular conversational
threads are propagating.
You can see for example on
the conversation in the middle on the left
that an original conversation has started
and then without comment another one, and
then another one, and another one.
And then finally someone
comments on the very last one.
Whereas if you look at for example,
the one on the top right, the first,
the original comment, then spawns one,
two, three, four, five comments.
And then the second comment
has a child unto itself.
Separately, if you're interested in
showing not just the relationships.
So the things that these graphs
are excellent at showing
is the hierarchical relationship.
But sometimes the relationship does not
just include one of containment, but
it also includes one of magnitude.
So for this particular kind of diagram,
something here called a tree
map can become very useful.
So a tree map is also a hierarchical
diagram like the tree, but
each child node is organized,
according to the area.
So you can see here in the top left,
that's a node with no children.
Whereas, go one below it,
that node has three children and
the one on the bottom has a magnitude
far greater than the two above it.
So something like this
is occasionally used.
You might have seen something like this,
for
example, on a disk defragmenting program.
Another way that networks are often shown
is something here called a chord diagram.
And this chord diagram allows you to
actually show relationships and magnitude.
And so
this one would work by mousing over one of
the particular edges which
are shown on the outside, and
the relationships are shown by arcs
connecting each of the nodes and the width
of the arc is proportional to the
magnitude, the weight of the connection.
And so you can see here, this particular
diagram shows a hierarchy and
magnitude at the same time.
Another way that you might care
to show something like this,
is something called the Sankey diagram.
That the Sankey Diagram is
designed to show the magnitude and
flow through a network at the same time.
So, this particular diagram shows how
energy is produced and consumed in the UK.
So, what you can see,
for example, is on top,
nuclear is the principle producer
of electricity in the UK.
And if you go, and
you can see that about half way down,
there is a bar that represents a node
where transportation, excuse me,
thermal generation is then used,
and, and that is the consumer of
nuclear power, and that is then passed
on to the right to downstream consumers.
So what you can do is you can see how,
for example, things like oil imports and
oil reserves on the bottom left
are then passed into liquid
form to various refineries.
And you can see the magnitude
of the bar here,
excuse me the height of the bar represents
the magnitude of the relationship.
So you can see that there's a number of
ways that one could take the same data,
that is included in a graph structure and
it choose to
highlight hierarchy, time, and magnitude.
And depending on how you would choose
to differently represent them,
if you want to show hierarchy and
magnitude, then the tree map is for you.
If you want to show time and hierarchy,
then think about a thread arc.
If you want to show a deep number
of hierarchical relationships,
then think about the node link diagram.
And if you're interested
in showing hierarchy and
magnitude, think about the core diagram.
And if you're interested
in showing magnitude and
time, then think about a Sankey diagram.
But each of this different
methods allows you
to take some of the different dimensions
of date and bring them to the fore front.
So let's connect this back to some of
the things that we discussed previously.
So, something like a tree map, right?
A tree map takes, so, what are the most
visible elements in the tree map?
Area.
In the tree map the magnitude of the leaf
is proportional to the area that
it contains, that it encloses.
And if you think back to our few chapters
ago where we described what are the most
salient features to human perception when
it comes to identifying differences?
It's area, right?
It was shape, excuse me,
it was location and area.
So, by choosing to represent
magnitude in area,
the tree map is making that
magnitude the most salient feature.
Whereas, if you look at how
magnitude is represented in
the chord diagram, it's actually
a secondary feature to layout.
And what you can see is each of the nodes
on the edge the size of the node and
it's relative location
to nodes next to it,
demonstrate the,
those are the more salient features.
So the things that stand out in this graph
the most are the edges around the outside,
and the relationships that
are drawn between them.
The Sankey diagram does the same thing for
relationship and it's encoding time and
it's giving time,
in this particular example, to the x-axis.
So when we look at this and
we say why is time so
salient, it's because they've
taken position, the x-axis, and
turned it into one of the most
meaningful features of the graph itself.
So if you're thinking about how do
I choose which of the following,
types of representation I,
to, to use for my own data.
You can think about what
are the particular dimensions that have
the most importance, and
then which of these different encodings,
bring out those dimensions.
And that's one of the ways that
you will end up looking for
the ways that the most important parts of
your data become the most perceptible.