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PROFESSOR: All right.

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All right.

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So we're going to
continue now and kind of

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get into the examples
part of the course.

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And again, this
is really the part

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that people should really--
I strongly encourage

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people doing examples.

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How many people got a
chance to try the examples

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in the-- very good.

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And we got a couple of
questions for people.

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And most of the time we got
another e-mail from them

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right away that said,
no, got it to work.

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So we're very
pleased about that.

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The great thing about
working at Lincoln Labs

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is people are pretty good
at figuring stuff out.

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We have some experience
this and before.

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Obviously, our parallel
MATLAB technology,

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we've release that out.

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Many, many people use it.

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And for the most part,
we're proud to say

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that whenever we get a question
from the outside world,

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and it's not
working, it's usually

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the person hasn't taken
severely active steps to ignore

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the documentation.

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But if they follow it at all,
they're generally pretty safe.

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So I'm going to get into
the example code here.

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So the example code this
is-- oh, that's not,

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D4Muser_share, that's incorrect.

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It's tools lower case examples.

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I should correct these slides.

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Oh, nice.

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There we go.

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Great.

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That is an x, right?

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I hope so.

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Oh yes, thank you.

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Great.

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All right.

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So this is where
the example code is.

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We're going to go over here.

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Your assignment, should
you choose to undertake it,

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is to pick a picture,
hopefully something

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that's interesting to you.

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Doesn't have to
be straight lines,

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it could be anything where
you could create, draw edges,

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or something, you
could take some photo

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and put it through one of
those Photoshop effects

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and turn it into a line
drawing or something

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and then start
labeling vertices.

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You do want to limit the
number of lines though.

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I would recommend
20 would be the most

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number of lines you do.

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Because this can
get fairly involved.

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You might start with
something fairly small.

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So select a picture.

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Label the edges and vertices.

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Create an incidence matrix.

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And then just compute
the adjacency matrix

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from the instance matrix
using this formula.

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You can certainly use d4m
if you want to do that.

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But it's fine to do it by hand.

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It's fine to do it by
hand, in which case

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you'd want to a very small one.

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Doing it once by hand is useful.

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Twice marginally.

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And then the third
time, not useful.

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Just like in high school, right?

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They make you do
matrix multiplied

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by hand like actually a lot.

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A lot.

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So that's the example
in the assignment.

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If you do this on
a piece of paper

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and scan it and email it to
me before the next lecture,

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I will give you
some feedback on it

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before the following lecture.

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If you give it to me
after that too bad.

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I just won't give you feedback.

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So there's no credit.

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But this gives you some
incentive to get it done.

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If you want feedback from me
about what you did makes sense

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or if you encountered
like I picked this picture

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and now I don't
understand-- I did my best

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but I have questions
about how I did this.

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Does it make sense?

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I'd be happy to do that.

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So just scan it, email it to me,
or if it is electronic format

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you can do that as well.

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So the lecture portion
and now go back here.

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And let's see here,
we go to examples.

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All right.

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So we're in the intro,
EdgeArt directory,

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start my MATLAB shell.

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00:05:05,000 --> 00:05:05,500
MATLAB.

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00:05:11,740 --> 00:05:14,410
This takes about 15
seconds for it to do this.

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This particular
thing always CDs me

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to the location
of the directory.

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00:05:27,580 --> 00:05:32,400
You need to do that in
order to see the examples.

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I think most MATLAB users
are familiar with that.

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But just some that are not.

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Here is the actual adjacency
matrix of that painting.

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So there it is.

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Same thing we just saw.

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So this is the data set that
we're going to work with here.

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00:06:00,540 --> 00:06:02,820
So I'm going to do EA1.

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00:06:02,820 --> 00:06:08,200
Again, all the examples
are numbered in order,

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00:06:08,200 --> 00:06:10,650
kind of that you're supposed
to proceed through them.

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And if see a file in
a directory that's

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00:06:13,230 --> 00:06:16,220
like couple capital letters,
which are the first two

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00:06:16,220 --> 00:06:20,650
letters of the directory or the
abbreviation of the directory

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00:06:20,650 --> 00:06:23,740
in a test, that is the examples.

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The other files are
just supporting files.

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You are not expected
to run those.

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You can try running them
but they'll probably

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cause you problems if you
run them by themselves.

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All right, here we go.

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So we just ran that example.

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Let's see what we got.

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I think that worked.

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00:07:03,780 --> 00:07:09,510
So the first thing we did
here is we read in our data.

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00:07:09,510 --> 00:07:12,604
So we have this Read CSV,
very useful function.

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00:07:15,920 --> 00:07:17,590
Not necessarily the fastest.

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00:07:17,590 --> 00:07:20,770
In some of the later
examples we have a sort

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00:07:20,770 --> 00:07:25,500
of a super fast
reader, which does

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almost no formatting for you.

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00:07:27,240 --> 00:07:30,150
Just reads in the
triples as raw triples.

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Because a lot of times if you're
reading a very large CSV file,

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00:07:34,510 --> 00:07:36,750
you may not want to construct
the full associative

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00:07:36,750 --> 00:07:39,629
array out of the way we
would just do it by default.

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And you can just read in
the triples very quickly

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then do some manipulations.

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Or a lot of times the
first thing you'll do

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is recreate an associated array
and then get the triples out

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of it, because you want to
work on the triples directly.

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And so we do have
ways for doing that.

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So we now created
the incidence matrix

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into an associative array.

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00:08:01,270 --> 00:08:07,960
And let me just show you that.

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So if I go disp(E), so that
shows you the incidence matrix.

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These are its internal
structures here.

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These are the row keys.

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So those are the
labels of the edges.

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00:08:23,250 --> 00:08:29,440
They have been converted to
Luxor graphically sorted order.

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00:08:29,440 --> 00:08:30,580
We have the column keys.

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But there's so many that
MATLAB chooses not to print out

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the full list here.

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But it's again, a Luxor
graphically sorted

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list of the unique labels.

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These are the different
values that we have.

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So you remember we had
an order column, which

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is one, two, three, blue, green,
orange, pink, silver, etc.

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And here and then the
overall adjacency matrix,

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which connects the row keys to
their value keys is 19 by 21.

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00:09:04,410 --> 00:09:06,710
19 rows by 21 columns.

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This actually shows a mixed use.

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Some of these are
essentially exploded, right?

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The fact that we have each edge.

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But some of the
values are actually

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storing real stuff here.

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Blue, green, orange, etc.

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So you don't have to go
all the way with one.

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00:09:23,044 --> 00:09:24,210
You can mix them too around.

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You can create dense
matrices that look more

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like traditional tables.

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And there's sometimes
that you want to do that.

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And other times
you can completely

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00:09:32,180 --> 00:09:34,480
explode it out and do
things like that as well.

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So we go back.

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We just want to work
with the vertices.

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So we're going to ignore
this color and order columns.

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So we're going to create
our first projection is

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00:09:51,450 --> 00:09:53,560
to just work with the vertices.

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So we have this little shorthand
here called StartsWith,

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00:09:56,640 --> 00:09:59,110
if you give it a character.

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00:09:59,110 --> 00:10:01,700
And it will create
a little query

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00:10:01,700 --> 00:10:05,500
that will get just things
that start with that.

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00:10:05,500 --> 00:10:07,020
And very useful thing.

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00:10:07,020 --> 00:10:08,130
It's very efficient too.

185
00:10:08,130 --> 00:10:11,650
It actually formally
creates the two boundaries.

186
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It figures out what the
maximum range is for that.

187
00:10:14,850 --> 00:10:17,337
And then just needs to look
up the beginning and the end.

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00:10:17,337 --> 00:10:19,670
It [? can ?] [? assume ?]
lexicographical order and then

189
00:10:19,670 --> 00:10:21,930
it can just grab the middle.

190
00:10:21,930 --> 00:10:24,350
We have a regular
expression approach to it,

191
00:10:24,350 --> 00:10:26,550
which works fine on
small associative arrays.

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00:10:26,550 --> 00:10:28,591
But this is much more
efficient because it's just

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00:10:28,591 --> 00:10:32,310
basically two lookups and go.

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It also works if this E was
actually a binding to a table

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00:10:38,590 --> 00:10:39,910
in a database.

196
00:10:39,910 --> 00:10:42,410
You can use this same syntax,
while the regular expression

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00:10:42,410 --> 00:10:43,630
syntax doesn't really work.

198
00:10:43,630 --> 00:10:44,441
Yes?

199
00:10:44,441 --> 00:10:44,940
[INAUDIBLE]

200
00:10:49,650 --> 00:10:53,290
PROFESSOR: So that's the
delimiter of the string.

201
00:10:53,290 --> 00:10:56,760
It's a string list
with one entry in it.

202
00:10:56,760 --> 00:10:58,120
So this is a string list.

203
00:10:58,120 --> 00:11:00,610
All our strings are lists here.

204
00:11:00,610 --> 00:11:03,060
Well, because this
also allows me--

205
00:11:03,060 --> 00:11:06,841
could've been anything
that was unique to that.

206
00:11:06,841 --> 00:11:08,840
And it didn't have to be
the same delimiter that

207
00:11:08,840 --> 00:11:09,942
was the one inside.

208
00:11:09,942 --> 00:11:12,150
It could have been a new
line, could have been a tab,

209
00:11:12,150 --> 00:11:13,116
could move whatever.

210
00:11:13,116 --> 00:11:14,990
I just picked comma
because it was convenient

211
00:11:14,990 --> 00:11:17,130
but could have been a space.

212
00:11:17,130 --> 00:11:19,910
Because you could have multiple
arguments to the StartsWith.

213
00:11:19,910 --> 00:11:22,790
If you want to say I want starts
with this and starts with this

214
00:11:22,790 --> 00:11:25,120
and starts with this, you
just give it a whole list

215
00:11:25,120 --> 00:11:27,531
and it will go and
do that all for you.

216
00:11:27,531 --> 00:11:29,030
And so that's why
we do it that way.

217
00:11:29,030 --> 00:11:32,150
Wherever possible, we try
and accept a list of strings.

218
00:11:32,150 --> 00:11:33,860
And then do the right thing.

219
00:11:33,860 --> 00:11:35,400
So basically, this
is saying, get me

220
00:11:35,400 --> 00:11:37,290
all columns that
start with V. So that

221
00:11:37,290 --> 00:11:38,630
would be all the vertices.

222
00:11:38,630 --> 00:11:41,000
And this is the colon,
which as you know

223
00:11:41,000 --> 00:11:44,930
and I want the full row of that.

224
00:11:44,930 --> 00:11:50,020
These had these values
of-- which were the order

225
00:11:50,020 --> 00:11:51,940
group that they were in.

226
00:11:51,940 --> 00:11:54,780
And so we don't
care about those.

227
00:11:54,780 --> 00:11:58,084
We want to convert them back
to regular numeric numbers.

228
00:11:58,084 --> 00:11:59,500
And so we have
this shorthand here

229
00:11:59,500 --> 00:12:01,580
called double Logi, which
basically just takes

230
00:12:01,580 --> 00:12:05,630
the logical and then does the
double thing mathematically.

231
00:12:05,630 --> 00:12:08,370
Formally, you would use to
call this the infinity norm

232
00:12:08,370 --> 00:12:11,390
on strings, if that
even makes sense.

233
00:12:11,390 --> 00:12:14,430
But it basically just says, if
there's a value there converted

234
00:12:14,430 --> 00:12:17,420
to a double precision one.

235
00:12:17,420 --> 00:12:21,642
If there's not a value there,
it's just a sparse 0, not--

236
00:12:21,642 --> 00:12:23,350
And we do this all
the time because a lot

237
00:12:23,350 --> 00:12:25,760
of times we want to do
math on these things.

238
00:12:25,760 --> 00:12:27,810
It's like regular math.

239
00:12:27,810 --> 00:12:30,330
We want to compute the
vertex adjacency graph.

240
00:12:30,330 --> 00:12:33,370
So we do that with
our square in function

241
00:12:33,370 --> 00:12:36,120
here, our inner square product.

242
00:12:36,120 --> 00:12:39,440
So that basically
takes our matrix

243
00:12:39,440 --> 00:12:43,340
and uses the edge as the common
key to join them together.

244
00:12:43,340 --> 00:12:45,040
And we use or
display full function

245
00:12:45,040 --> 00:12:47,380
to actually show what we got.

246
00:12:47,380 --> 00:12:54,540
And so now you see the
vertex adjacency matrix here.

247
00:12:54,540 --> 00:12:56,410
And then the number
is the number

248
00:12:56,410 --> 00:13:00,920
of times those vertices
are on the same edge.

249
00:13:00,920 --> 00:13:03,040
So it's obviously symmetric.

250
00:13:03,040 --> 00:13:05,730
And you see here
these vertices here,

251
00:13:05,730 --> 00:13:08,070
which are part of this
common hyper edge,

252
00:13:08,070 --> 00:13:12,000
we have this sort of
6 9 6 structure here,

253
00:13:12,000 --> 00:13:14,450
various other types of
symmetric structures

254
00:13:14,450 --> 00:13:17,080
going on here showing
you the counts,

255
00:13:17,080 --> 00:13:20,360
how many times those vertices
appeared on the same edge.

256
00:13:20,360 --> 00:13:22,700
These are obviously
cliques, because they

257
00:13:22,700 --> 00:13:25,301
are all vertices that are
on the same hyper edge line.

258
00:13:25,301 --> 00:13:26,717
So if you have the
same hyper edge

259
00:13:26,717 --> 00:13:30,260
line whenever you do
the squaring operation,

260
00:13:30,260 --> 00:13:35,277
you see it as this clique
in this operation here.

261
00:13:39,750 --> 00:13:45,770
We can also do the square
out function, which computes

262
00:13:45,770 --> 00:13:47,130
the edge adjacency matrix.

263
00:13:47,130 --> 00:13:53,740
So now we want to ask, which
edges share common vertices?

264
00:13:53,740 --> 00:13:56,250
And so that's this
structure here.

265
00:13:59,020 --> 00:14:02,417
It shows you these
are the various edges.

266
00:14:02,417 --> 00:14:03,500
And again, it's symmetric.

267
00:14:03,500 --> 00:14:05,125
And you can see all
kinds of structures

268
00:14:05,125 --> 00:14:08,530
in here about which
vertices share-- which

269
00:14:08,530 --> 00:14:13,390
edges share common vertices.

270
00:14:13,390 --> 00:14:16,320
And that is pretty much
it for this example.

271
00:14:16,320 --> 00:14:17,980
Very simple example.

272
00:14:17,980 --> 00:14:19,990
Hopefully it gets
you to the point

273
00:14:19,990 --> 00:14:23,510
where you can begin to try
out the homework assignment.

274
00:14:23,510 --> 00:14:28,618
And if there's any
questions that people have,

275
00:14:28,618 --> 00:14:29,490
let's try this.

276
00:14:29,490 --> 00:14:31,350
Here, one thing that's
fun to do spy(E).

277
00:14:34,186 --> 00:14:35,600
See if that works.

278
00:14:50,840 --> 00:14:53,460
I think between PowerPoint,
Quick Time and everything

279
00:14:53,460 --> 00:14:57,080
else it's just
about-- there it is.

280
00:14:57,080 --> 00:14:58,750
Wow, that took a long time.

281
00:14:58,750 --> 00:15:02,330
So this shows that
adjacency matrix.

282
00:15:02,330 --> 00:15:04,197
So spy works.

283
00:15:04,197 --> 00:15:06,530
And I don't know if we showed
that in the first example,

284
00:15:06,530 --> 00:15:10,390
but the spy function, the
standard MATLAB sparse plotting

285
00:15:10,390 --> 00:15:13,380
function, very useful way to
just sort of look at the stuff,

286
00:15:13,380 --> 00:15:16,620
all those previous charts I
showed you on the examples

287
00:15:16,620 --> 00:15:17,790
were done this thing.

288
00:15:17,790 --> 00:15:20,150
And a little feature
that sometimes

289
00:15:20,150 --> 00:15:22,620
causes MATLAB to crash
because it doesn't really like

290
00:15:22,620 --> 00:15:23,870
doing things too aggressively.

291
00:15:23,870 --> 00:15:28,582
But if you click on it, it
shows you the row and the column

292
00:15:28,582 --> 00:15:30,040
and the value
associated with that,

293
00:15:30,040 --> 00:15:31,960
and also prints it out here.

294
00:15:31,960 --> 00:15:33,410
Likewise here.

295
00:15:33,410 --> 00:15:36,830
So you see row, column,
that gives you the order.

296
00:15:36,830 --> 00:15:41,450
And this tells you the row
is G2, its column, its color,

297
00:15:41,450 --> 00:15:43,240
its value is green.

298
00:15:43,240 --> 00:15:46,257
So actually, I lied to you.

299
00:15:46,257 --> 00:15:47,590
That was just the first example.

300
00:15:50,780 --> 00:15:51,830
Senior moment there.

301
00:15:51,830 --> 00:15:53,805
We have two more to go.

302
00:15:53,805 --> 00:15:54,890
Lot more fun.

303
00:15:54,890 --> 00:15:59,460
See, you're all excited
that class ended early.

304
00:15:59,460 --> 00:16:01,510
Here's the other examples.

305
00:16:01,510 --> 00:16:05,077
So again, what we do is we're
reading in the data set.

306
00:16:05,077 --> 00:16:06,410
We're displaying the full thing.

307
00:16:06,410 --> 00:16:08,701
So you can see there's the
full beast I just showed you

308
00:16:08,701 --> 00:16:09,655
the spy plot.

309
00:16:09,655 --> 00:16:11,530
Now, I'm going to use
some analytics on this.

310
00:16:11,530 --> 00:16:14,740
So one thing I want to do is
just get the orange edges.

311
00:16:14,740 --> 00:16:19,090
So I can say, get
me the column color.

312
00:16:19,090 --> 00:16:21,870
And because orange
is held in the value,

313
00:16:21,870 --> 00:16:23,890
I can actually compare
it with the string.

314
00:16:23,890 --> 00:16:28,230
So I say, return me the
matrix, the associative array

315
00:16:28,230 --> 00:16:33,440
of the row, color and
everything equal to orange.

316
00:16:33,440 --> 00:16:35,490
So that returns me
another associative array.

317
00:16:35,490 --> 00:16:38,230
The result of this
whole logical expression

318
00:16:38,230 --> 00:16:40,330
is another associative array.

319
00:16:40,330 --> 00:16:45,000
I can then get the rows for
those associative arrays.

320
00:16:45,000 --> 00:16:54,440
And I've found all
edges that are orange.

321
00:16:54,440 --> 00:16:58,570
And I can then pass
that, get those rows

322
00:16:58,570 --> 00:17:01,190
and pass that back
into the original one

323
00:17:01,190 --> 00:17:05,280
to get just the orange edges.

324
00:17:05,280 --> 00:17:09,140
So this just shows you
this composable ability

325
00:17:09,140 --> 00:17:12,220
is very powerful, same
ability that MATLAB has.

326
00:17:12,220 --> 00:17:14,849
One does similar statements
in MATLAB all the time.

327
00:17:14,849 --> 00:17:16,364
And so it's very composable.

328
00:17:16,364 --> 00:17:17,780
This would be a
very complex query

329
00:17:17,780 --> 00:17:19,180
to do in other approaches.

330
00:17:19,180 --> 00:17:20,680
And you can do it
very quickly here.

331
00:17:20,680 --> 00:17:20,990
Yes?

332
00:17:20,990 --> 00:17:21,489
Question?

333
00:17:21,489 --> 00:17:23,310
[INAUDIBLE] would that
be called to route

334
00:17:23,310 --> 00:17:27,932
since it is in the row with
the argument [INAUDIBLE]?

335
00:17:30,860 --> 00:17:31,870
No.

336
00:17:31,870 --> 00:17:34,170
It doesn't.

337
00:17:34,170 --> 00:17:35,980
It doesn't.

338
00:17:35,980 --> 00:17:40,220
What we could do is
overload it so if you passed

339
00:17:40,220 --> 00:17:43,910
an associative array with
just a single argument

340
00:17:43,910 --> 00:17:48,250
and have it behave like when
you pass in the MATLAB logical

341
00:17:48,250 --> 00:17:50,000
and do that kind
of intersection,

342
00:17:50,000 --> 00:17:51,980
we could think about that.

343
00:17:51,980 --> 00:17:55,590
But MATLAB actually
relies on then converting

344
00:17:55,590 --> 00:18:00,460
the matrix to a vector and
then using that singular--

345
00:18:00,460 --> 00:18:02,335
basically, it takes that
logical, converts it

346
00:18:02,335 --> 00:18:05,120
to a single [? index, ?]
which kind of gets us

347
00:18:05,120 --> 00:18:08,590
into an area where it's
very fuzzy and gray.

348
00:18:08,590 --> 00:18:11,080
So we definitely
thought about that

349
00:18:11,080 --> 00:18:16,910
and there are places where we
line up with MATLAB very nicely

350
00:18:16,910 --> 00:18:19,790
because the mathematics
of associative arrays

351
00:18:19,790 --> 00:18:23,200
and linear algebra really
line up very nicely.

352
00:18:23,200 --> 00:18:25,180
And there's places
where they intersect.

353
00:18:25,180 --> 00:18:28,317
There's things you can do
in with associative arrays

354
00:18:28,317 --> 00:18:29,900
that you can't do
with linear algebra.

355
00:18:29,900 --> 00:18:33,490
For example, we can matrix
multiply any two associative

356
00:18:33,490 --> 00:18:34,160
arrays.

357
00:18:34,160 --> 00:18:35,676
There's no conformance
requirements.

358
00:18:35,676 --> 00:18:37,550
That is, they don't have
the same-- normally,

359
00:18:37,550 --> 00:18:43,190
when you multiply two matrices--
the inner dimensions have

360
00:18:43,190 --> 00:18:44,140
to match, basically.

361
00:18:44,140 --> 00:18:47,850
The columns of the left
argument and the rows

362
00:18:47,850 --> 00:18:50,160
of the right argument
must be the same length.

363
00:18:50,160 --> 00:18:52,470
In associative arrays that
requirement doesn't exist.

364
00:18:52,470 --> 00:18:55,990
You can multiply or add
any two associative arrays.

365
00:18:55,990 --> 00:18:58,470
We'll get into that much
more in the next class.

366
00:18:58,470 --> 00:19:01,370
But that's a very powerful
feature that people like.

367
00:19:01,370 --> 00:19:04,960
But there's other places where
it doesn't really make sense.

368
00:19:04,960 --> 00:19:09,150
So things like, what is the
upper triangular section

369
00:19:09,150 --> 00:19:12,630
of an associative array gets to
be a little bit-- huh, what's

370
00:19:12,630 --> 00:19:13,420
that mean?

371
00:19:13,420 --> 00:19:15,680
So excellent question though.

372
00:19:15,680 --> 00:19:16,820
Excellent question though.

373
00:19:16,820 --> 00:19:18,560
So we can display this.

374
00:19:18,560 --> 00:19:24,170
So this just shows we
found all the edges that

375
00:19:24,170 --> 00:19:27,330
had color orange.

376
00:19:27,330 --> 00:19:29,060
But we don't have to
just-- that's a way

377
00:19:29,060 --> 00:19:30,980
of using the values to select.

378
00:19:30,980 --> 00:19:35,240
We could, of course, use
StartsWith in the rows,

379
00:19:35,240 --> 00:19:36,870
just say StartsWith
O and G. I just

380
00:19:36,870 --> 00:19:40,540
happened to label all my rows
that orange rows began with O

381
00:19:40,540 --> 00:19:43,070
and green rows begin with G.

382
00:19:43,070 --> 00:19:44,960
So we can do StartsWith
O G. So that's

383
00:19:44,960 --> 00:19:47,910
example of those two
range queries being

384
00:19:47,910 --> 00:19:49,240
done at the same time.

385
00:19:49,240 --> 00:19:51,250
And so that gives us EOG.

386
00:19:51,250 --> 00:19:59,610
And again, we can see now we
get the orange and green rows.

387
00:19:59,610 --> 00:20:01,490
So that just shows you that.

388
00:20:01,490 --> 00:20:05,025
And then we'll wrap up here with
the last example, which is EA3.

389
00:20:08,270 --> 00:20:10,800
Now, we get to do
some really fun stuff.

390
00:20:10,800 --> 00:20:15,410
Again, we're reading
in our data set,

391
00:20:15,410 --> 00:20:19,620
converting, just
getting the vertices.

392
00:20:19,620 --> 00:20:23,760
And then converting it
to numeric 0's and 1's.

393
00:20:23,760 --> 00:20:28,970
I'm going to now just
get the orange edges.

394
00:20:28,970 --> 00:20:32,230
And I'm going to
get the green edges.

395
00:20:32,230 --> 00:20:33,710
All right.

396
00:20:33,710 --> 00:20:38,710
And now I'm going to essentially
do the cross correlation

397
00:20:38,710 --> 00:20:39,960
of the orange and green edges.

398
00:20:39,960 --> 00:20:42,180
So I'm going to
transpose one of them

399
00:20:42,180 --> 00:20:43,954
and matrix multiply
with the other ones.

400
00:20:43,954 --> 00:20:45,620
We don't do square
in here because they'

401
00:20:45,620 --> 00:20:47,210
are different matrices.

402
00:20:47,210 --> 00:20:49,110
In fact, I would say
that people often

403
00:20:49,110 --> 00:20:51,210
do the cross-correlation
more often

404
00:20:51,210 --> 00:20:53,260
than just square the
matrix with itself.

405
00:20:53,260 --> 00:20:55,410
You have one set
with another set

406
00:20:55,410 --> 00:20:58,510
and you want to cross correlate
them, a very common operation.

407
00:20:58,510 --> 00:21:01,980
And so that's just
transpose EVG here.

408
00:21:01,980 --> 00:21:04,680
And that gets that.

409
00:21:04,680 --> 00:21:09,330
And as you can see, the
results of that inner product

410
00:21:09,330 --> 00:21:11,690
was empty.

411
00:21:11,690 --> 00:21:14,580
But the result of the
outer product is full.

412
00:21:14,580 --> 00:21:18,650
So you guys can think
about why that is.

413
00:21:18,650 --> 00:21:28,630
And so this just shows you the
common-- how many edges these

414
00:21:28,630 --> 00:21:31,520
appeared with together.

415
00:21:31,520 --> 00:21:33,672
This shows you that
there was no-- well,

416
00:21:33,672 --> 00:21:34,880
you guys can figure that out.

417
00:21:34,880 --> 00:21:36,700
I'll let you do your homework.

418
00:21:36,700 --> 00:21:41,430
Now, another thing that we
often want to do is basically,

419
00:21:41,430 --> 00:21:50,470
this showed us which edges
had common shared vertices

420
00:21:50,470 --> 00:21:53,160
together.

421
00:21:53,160 --> 00:21:58,500
But it didn't tell us we
lost the actual vertices.

422
00:21:58,500 --> 00:21:59,860
We just know that there's three.

423
00:21:59,860 --> 00:22:01,020
And a lot of times we want them.

424
00:22:01,020 --> 00:22:02,603
This is sometimes
called the pedigree.

425
00:22:02,603 --> 00:22:03,980
You do a correlation.

426
00:22:03,980 --> 00:22:07,040
And then you would
like-- you say these two

427
00:22:07,040 --> 00:22:08,130
things are correlated.

428
00:22:08,130 --> 00:22:11,270
I want to get to the connector
back to the original record

429
00:22:11,270 --> 00:22:13,100
so I can go back to
my e-matrix and really

430
00:22:13,100 --> 00:22:15,720
find that out and present
that as the evidence

431
00:22:15,720 --> 00:22:17,750
that these things are
connected together.

432
00:22:17,750 --> 00:22:19,210
We don't want to lose that.

433
00:22:19,210 --> 00:22:23,170
So we have invented special
new matrix multiplies

434
00:22:23,170 --> 00:22:25,410
in the land of
associative arrays.

435
00:22:25,410 --> 00:22:30,170
One of them we call
a CatKeyMul, which

436
00:22:30,170 --> 00:22:33,750
you view the matrix
multiply as sort of there's

437
00:22:33,750 --> 00:22:36,930
a key, a common key,
this row column key

438
00:22:36,930 --> 00:22:39,610
that's being joined together.

439
00:22:39,610 --> 00:22:42,370
Well, we can preserve that
and store that in a value,

440
00:22:42,370 --> 00:22:45,570
instead of say the count
or something like that.

441
00:22:45,570 --> 00:22:50,880
So we do CatKeyMul
EV0 transpose EVG.

442
00:22:50,880 --> 00:22:54,010
And then when we display
that, we not only

443
00:22:54,010 --> 00:22:57,730
see which edges were
connected, but we also

444
00:22:57,730 --> 00:23:00,360
have preserved the
list of the vertices.

445
00:23:00,360 --> 00:23:02,610
It's essentially a
concatenated list

446
00:23:02,610 --> 00:23:05,030
of those keys,
very useful thing.

447
00:23:07,860 --> 00:23:11,000
One has to be so very
powerful technique.

448
00:23:11,000 --> 00:23:14,634
One definitely has to be careful
about using this technique

449
00:23:14,634 --> 00:23:15,300
if it generates.

450
00:23:15,300 --> 00:23:19,090
It's going to generate
extremely, extremely long lists

451
00:23:19,090 --> 00:23:19,690
here.

452
00:23:19,690 --> 00:23:23,310
That can really cause us
to behave very slowly.

453
00:23:23,310 --> 00:23:25,710
In particular, when
asked to be careful,

454
00:23:25,710 --> 00:23:29,850
if you do a CatKeyMul
on a matrix with itself,

455
00:23:29,850 --> 00:23:32,221
why do you think you would
have to be careful with that?

456
00:23:32,221 --> 00:23:32,721
Anyone?

457
00:23:35,310 --> 00:23:37,890
Remember, that dense
diagonal that happened

458
00:23:37,890 --> 00:23:39,656
whenever we squared matrices?

459
00:23:39,656 --> 00:23:43,410
So that means this thing
will have an enormous number

460
00:23:43,410 --> 00:23:45,720
of entries along the diagonal.

461
00:23:45,720 --> 00:23:47,680
So you have to be
very careful when

462
00:23:47,680 --> 00:23:50,340
you use this kind of function
to correlate something

463
00:23:50,340 --> 00:23:50,920
with itself.

464
00:23:50,920 --> 00:23:52,680
It's better to correlate
two distinct sets

465
00:23:52,680 --> 00:23:55,972
because they tend to not have
that dense diagonal, which can

466
00:23:55,972 --> 00:23:57,180
be a little bit of a problem.

467
00:23:57,180 --> 00:23:58,660
There's ways to get around that.

468
00:23:58,660 --> 00:24:00,960
There's hacks and tricks
and stuff like that.

469
00:24:00,960 --> 00:24:03,030
But at a certain level,
really dense diagonala--

470
00:24:03,030 --> 00:24:05,113
I mean, essentially be
listing every single vertex

471
00:24:05,113 --> 00:24:07,990
in your data set-- you could
be listing every single vertex

472
00:24:07,990 --> 00:24:10,950
in your data set almost every
single time, multiple times

473
00:24:10,950 --> 00:24:11,760
along the diagonal.

474
00:24:11,760 --> 00:24:13,910
That would get very, very bulky.

475
00:24:13,910 --> 00:24:16,640
So just a little word
of caution there.

476
00:24:16,640 --> 00:24:18,990
And so now, I've
baited you once.

477
00:24:18,990 --> 00:24:20,780
But this really is the end.

478
00:24:20,780 --> 00:24:23,220
So are there any
questions on the examples

479
00:24:23,220 --> 00:24:25,370
before we cut it off here?

480
00:24:25,370 --> 00:24:28,610
Is there a question
back here somewhere?

481
00:24:28,610 --> 00:24:29,970
No?

482
00:24:29,970 --> 00:24:30,470
All right.

483
00:24:30,470 --> 00:24:30,700
Great.

484
00:24:30,700 --> 00:24:31,360
Thank you very much.

485
00:24:31,360 --> 00:24:32,026
I appreciate it.

486
00:24:32,026 --> 00:24:34,030
And we'll see you next week.

487
00:24:34,030 --> 00:24:37,440
And again, think of a
picture, draw some lines,

488
00:24:37,440 --> 00:24:43,570
make an incidence
matrix, have fun with it,

489
00:24:43,570 --> 00:24:45,707
compute the degree of
your significant other.

490
00:24:48,430 --> 00:24:50,370
Bad idea?

491
00:24:50,370 --> 00:24:51,920
Good.