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hello I'm Josh stommer
and welcome to stat quest today we're
gonna be talking about the main ideas
behind principle component analysis and
we're going to cover those concepts in
five minutes if you want more details
than you get here be sure to check out
my other PCA video
let's say we had some normal cells
if you're not a biologist imagine that
these could be people or cars or cities
or etc they could be anything even
though they look the same we suspect
that there are differences these might
be one type of cell or one type of
person or car or city etc these might be
another type of cell and lastly these
might be a third type of cell
unfortunately we can't observe
differences from the outside so we
sequence the messenger RNA in each cell
to identify which genes are active this
tells us what the cell is doing if they
were people we could measure their
weight blood pressure reading level etc
okay here's the data
each column shows how much each gene is
transcribed in each cell for now let's
imagine there are only two cells if we
just have two cells then we can plot the
measurements for each gene this gene
gene one is highly transcribed in cell
one and lowly transcribed in cell two
and this gene gene 9 is lowly
transcribed in cell 1 and highly
transcribed in cell 2
in general cell one and cell to have an
inverse correlation this means that they
are probably two different types of
cells since they are using different
genes
now let's imagine there are three cells
we've already seen how we can plot the
first two cells to see how closely they
are related now we can also compare cell
one to sell three cell one and cell
three are positively correlated
suggesting they are doing similar things
lastly we can also compare cell two to
cell three the negative correlation
suggests that cell two is doing
something different from cell 3
alternatively we could try to plot all
three cells at once on a three
dimensional graph cell one could be the
vertical axis cell two could be the
horizontal axis
and sell three could be depth we could
then rotate this graph around to see how
the cells are related to each other but
what do we do when we have four or more
cells draw tons and tons of to sell
plots and try to make sense of them all
or draw some crazy graph that has an
axis for each cell and makes our brain
explode
no both of those options are just plain
silly
instead we draw a principal component
analysis or PCA plot
a PCA plot converts the correlations or
lack thereof among the cells into a 2d
graph
cells that are highly correlated cluster
together this cluster of cells are
highly correlated with each other
so are these and so are these to make
the clusters easier to see we can
color-code them once we've identified
the clusters in the PCA plot we can go
back to the original cells and see that
they represent three different types of
cells doing three different types of
things with their genes BAM
here's one last main idea about how to
interpret PCA plots the axes are ranked
in order of importance
differences among the first principal
component access PC one are more
important than differences along the
second principal component access PC two
if the plot looked like this
where the distance between these two
clusters
is about the same as the distance
between these two clusters
then these two clusters are more
different from each other than these two
clusters before we go you should know
that PCA is just one way to make sense
of this type of data there are lots of
other methods that are variations on
this theme of dimension reduction these
methods include heat maps tea Snee plots
and multiple dimension scaling plots the
good news is that I've got stat quests
for all of these so you can check those
out if you want to learn more note if
the concept of dimension reduction is
freaking you out check out the original
stat quest on PCA I take it nice and
slow so it's clearly explained hooray
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