This visualization is intended to make
groups of related variables immediately
obvious and therefore easy for the investigator
to pick out of a huge initial list of variables
and relationships.
In this case, we're going to use the Maximal Information
Coefficient, or MIC, that we've recently
developed to explore some data.
As a reminder, MIC is a novel measure
of dependence that detects almost all types
of relationships and data, meaning that it can detect
linear patterns, and exponential patterns,
and cyclical patterns, etc.
And what's special about it is that it can detect
these patterns equally well.
This spring graph shows each variable
in our dataset as a ball, and each relationship that
is identified by the statistical algorithm as a stick,
or spring between balls.
Each spring between balls exerts forces
on the balls to which it's connected
that are proportional to the association
between those variables-- in this case, measured by MIC.
So for example, variables that are very strongly related
will be pulled together by the springs connecting them.
And variables that are only weakly associated
will not be as attracted to each other.
Furthermore, users can intuitively
interact with this graph by adding or removing variables,
or relationships between variables,
and seeing how the physical model reacts to these changes.
To begin examining a dataset from the World Health
Organization, we can tell the simulation
to include the next strongest relationships found
amongst the variables in our dataset one by one.
If we continue doing this, eventually we
see that small clusters of connected variables
begin to form.
And if we continue further, we see
how different clusters of related variables
begin to connect to each other.
Finally, we begin to get a high-level view
of the structure of this data set.
We can also turn on a heat map in which strong association is
indicated by red, and weaker association
as indicated by blue.
So we can immediately spot pockets
of tightly related variables.
We can also manipulate this graph
to get a sense of the physical strength of some
of these relationships.
Let's take a look at some of the clusters
of variables that have formed.
Here we have maternal mortality rates
as part of a cluster of related variables
that includes healthy life expectancy in females
and infant mortality rates.
But we also see that it's connected
to another cluster over here through variables
like health expenditure.
And these health expenditure variables
are related to income variables in countries.
And these income variables are themselves
in turn related to a small cluster
of environmental variables like electric power
consumption, energy usage, and CO2 emissions.
Independently, these income variables
are also related to a string of technology variables
like internet users, and broadband subscribers,
and personal computers per capita.
If we look somewhere far away on this graph,
we see something that's unrelated to that cluster.
For example, here we have the proportion
of our population over the age of 60,
which is associated with things like cancer rates.
This visualization really gives us
a sense of which variables are related to which
other variables in our dataset, and more importantly,
through which variables.
In particular, because of the generality
of our measure of dependence-- MIC-- despite the fact
that all these relationships may look differently
from each other in actuality, we can rank them on the same scale
and begin to construct a graph that shows how the variables
cluster based on just how related they are, rather
than constraining ourselves to just,
for example, how linearly related
the variables are to each other.