This video clip is demonstrating the Pollux cluster first system
uh just as a recap, the computational pipeline here
to generate this projection is we start with the set
of weights which at the moment are all initialized to
one as well as the input data here, all
of the dimensions that are a part of this data
set. And we run K means clustering on it
1000 times and take the best clustering result. This
is the best clustering result that's generated and then we
take that and project it down into this 2-D
space using some selected set of edges. In this
case I have, the centroids connected to
each other and the centroids connected to the nodes
within the cluster as well as the nodes within the
cluster are all connected. And so that means that
the distance between clusters currently matters and the distance internal
to clusters matters. So two clusters that are closer
together are more similar two observations that are closer together
are more similar. You can see that there's this
details on demand interaction that pops up whenever I hover
over one of the states to show what the exact
data is for each one of these variables. So
I want to replicate the usage case that was shown
in chapters seven and eight. Uh and that usage
cases trying to create a Midwestern States cluster. The
goal is that this cluster here in the top left
is going to be our Midwestern States cluster because it
already has seven of the 12 necessary states. And
so the first interaction is to grab the state Ohio
out of this kind of Southern and Middle Eastern States
cluster and pull it over into our Midwestern States when
I do so you can see that, well this
cluster expanded a little bit because it got something new
and unfamiliar introduced to it. And then all of
the weights that are listed over here have updated.
So because we're using a force directed graph, the
weights that are smaller have a greater impact on the
clustering assignments and the weights that are larger have less
of an impact. And so for example, the
high school graduation rate is 0.456. This is something
that's very important to this interaction that we just performed
Uh and something that's not going to be so important
is some larger value. So for one example,
the area of the state, 1.324 is something that
is not so important to this clustering assignment. Right now
Ohio is fixed in place if I release it,
it's gonna get pushed toward the outside of the
cluster because well, we've only given it one interaction
so far and the system isn't quite sure how Ohio
is supposed to fit into this best, so it's
kind of pushed to the outside for the moment.
Um but no other observations were reassigned to another cluster
at this point. The second interaction is to grab
Michigan and also bring Michigan up into this cluster.
So when I do that. Well now two other
things are going to get assigned West Virginia gets pulled
into this cluster of generally rural, low population density
states. Maine in Arizona and Nevada and New
Mexico and then also Minnesota got pulled into our Midwestern
States cluster, which again is something that we wanted
to happen because while Minnesota is a Midwestern state,
the system is starting to learn some of these commonalities
between the Midwestern States and pulling states in that meet
those commonalities. So I can release Michigan. Michigan gets pushed
toward the outside, Ohio starting to fit a little
bit better in the rest of the cluster. We
can move these states around a little bit and try
to see just how best they fit inside of the
projection. In this case, I tried to move
Ohio up to see if it was related to anything
Nebraska, Kansas, Oklahoma. It turns out it really
isn't. It wants to be closer to Indiana and
Michigan, which geographically makes sense. The next interaction
is going to be pulling Illinois up into this cluster
and that's going to change a whole set of things.
The important ones for this cluster here are,
it's going to grab Wisconsin and pull it into this
cluster, which is something we want because Wisconsin is
a Midwestern state, but it's also going to get
Arkansas and Kentucky and pull those two states into this
cluster. And well, in the census definition, these
are not part of the Midwestern States. And so
we don't want them into the cluster will have to
remove them afterward. So I pull Illinois in.
There's the big set of things that have changed Wisconsin,
Arkansas and Kentucky all got pulled into the Midwestern
cluster state. I'm gonna release Illinois also Rhode Island
and West Virginia got pulled into our nice rural low
population states. Okay, so now we have all
12 of the Midwestern States in this cluster, three
of them were pulled in by me directly and the
other two were ones that the system has learned and
so from here we probably want to grab the clus,
the states that don't belong and pull them out
of the cluster. The states that don't belong are
Montana and Kentucky and Arkansas and Oklahoma. And so
I'll start with Kentucky because that was one of the
most recent ones that got pulled in. When I
removed Kentucky, Montana automatically gets removed. It gets
pulled over into this more Western States plus Vermont cluster
but we pulled in Tennessee. So Tennessee and Kentucky
are pretty similar states geographically and demographically and so Tennessee
was probably something that was right on the edge of
also getting pulled into this cluster before and the slight
change in weights for pulling Kentucky over into this cluster
were just enough to happen to throw it over in
this case. And so to continue this demo,
I would need to pull Oklahoma out, pull Arkansas
out and also pull Tennessee out. And then we
would have the full Midwestern States cluster.