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Welcome to section 34 Principal Component
Analysis, or PCA.

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Before you get some hands on experience
coming up with PCA,

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in the practical exercises, we're going
to take a look at the intuition behind it.

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PCA is considered to be one of the most

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used unsupervised
algorithms, and can be seen

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as the most popular dimensionality
reduction algorithm.

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PCA is used

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for operations
such as visualization, feature extraction,

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noise filtering, and can be seen in
algorithms used for stock market

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predictions and gene analysis,
just to name a few.

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The goal of PCA

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is to identify
and detect correlation between variables.

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If there's a strong correlation
and it's found,

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then you could reduce the dimensionality,
which really what PCA is intended for.

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You find the directions

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of maximum variance
in high dimensional data,

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and then you project it into a smaller
dimensional subspace while retaining

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most of the information, usually again
with PCA.

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The goal to reduce the dimensions of a
deep dimensional data set by projecting it

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onto a k dimensional subspace
where K is less than D,

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and for a overall breakdown
and wrap up of the PCA,

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we can see here that the mean functions

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of the PCA algorithm
would be to standardize the data,

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obtain the eigenvectors and eigenvalues

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to then
sort the eigenvalues in descending order.

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Construct the projection matrix W

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from the selected k eigenvectors

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and to transform the original data set,

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and you can explore it further
if you follow that link.

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But one thing I want to examine here

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with PCA and I think the visualization
is really helpful

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if we visit the following link, it's
going to take us to this page

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where we can actually view it in 2D
and 3D examples.

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Now with PCA in a 2D,
you can start to see the relationship

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and how PCA is playing out
amongst the variables in the data.

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You can also on this site drag them

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around, drag the data points around

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to see the PCA.

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The coordinates,
adjust within the system.

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But really what I think is helpful
is the 3D example with the 3D example,

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you can actually see the relationship,
the data within this model

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and comparing it to the 2D, you know,
within the higher dimensional space,

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obviously it can be a much easier
visualization.

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And I think this is helpful
really to kind of grasp what PCA is doing.

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And if we drag
the data points around again,

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just for a test, we can click on the show

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PCA to reset that and we'll show it.

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And we can see the PCA here.

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We can actually move the model around.

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Since it's not on that 2D plot,
we can visualize it within the 3D example.

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All right.

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So to wrap PCA up short and sweet

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PCA is not like linear regression,
although it may look like it

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because rather than attempting to predict
the values, PCA is attempting

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to learn about the relationship
between the x and y values.

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It's quantified
by finding a list of principal axes.

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And I think one of the best ways
is to look at the visualizations.

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You don't compare it to 2D and 3D
dimension,

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the analysis and the visualizations
that we looked at before.

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In addition, you know, on a side
note, PCA does have a weakness.

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It is highly affected by outliers
in the data, but PCA is considered

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to be one of the most used,
and it's extremely popular to use.

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And I think once you start working through
the practical, it will make more sense.

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If you have any questions, please
let us know and enjoy machine learning.