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Old 01-24-2020, 03:51 PM
jerrytuttle jerrytuttle is offline
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Default Principal Component Analysis

Let me rephrase my earlier post. I am having trouble understanding Principal Component Analysis, which I understand is now part of an Associate exam. Would someone kindly share a simple numerical example in Excel or R so I can follow the calculation, and also explain what one then does with the numerical result?

Thank you,
Jerry
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Old 01-24-2020, 04:52 PM
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Elements of Statistical Learning may be helpful.

Also, there's a PCA Wiki page that may be informative.

Finally, a perhaps interesting visual example is shown here.
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Old 01-24-2020, 05:20 PM
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see PAC's links above.

I always liked this application of PCA to Yield Curve analysis: https://www.moodysanalytics.com/-/me...-Modelling.pdf

The numerical results of PCA create new attributes for your data (each principal component is a new column for each data point).

Common application of PCA for exploratory data analysis: calculate PCA, then use the top 2 components as axes for a scatterplot. See what patterns emerge and analyze for meaning (you'll have to figure out what the components mean)

Last edited by BayesDeep; 01-25-2020 at 11:24 PM..
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Old 02-19-2020, 11:08 AM
lolz lolz is offline
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bump
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P FM IFM
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Old 03-06-2020, 10:36 AM
cashneuro cashneuro is offline
 
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Man. Well said. PCA is becoming a credible approach to actuarial analysis.
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Old 03-06-2020, 10:55 AM
silentassassin silentassassin is offline
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What in the who now?
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Old 03-09-2020, 11:17 AM
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whoanonstop whoanonstop is offline
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Quote:
Originally Posted by PAC View Post
Elements of Statistical Learning may be helpful.

Also, there's a PCA Wiki page that may be informative.

Finally, a perhaps interesting visual example is shown here.
You're suggesting ESL for someone who doesn't understand PCA?

A component is just a linear combination of your features.

The first principal component is the combination of features that give the largest variance.

The second principal component is the combination of features that give the largest variance while also being orthogonal to the first.

This can continue for each component until your # of principal components is equal to your original number of features.

As someone mentioned, if you like to play pretend, you can grab the first two principal components and make a 2D plot that will be hard to explain but will make a pretty picture none-the-less.

The only real redeeming factor of Principal components is the orthogonality, which has some nice properties when doing a basic regression.

-Riley
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Old 03-09-2020, 11:26 AM
The_Polymath The_Polymath is offline
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Quote:
Originally Posted by whoanonstop View Post
You're suggesting ESL for someone who doesn't understand PCA?

A component is just a linear combination of your features.

The first principal component is the combination of features that give the largest variance.

The second principal component is the combination of features that give the largest variance while also being orthogonal to the first.

This can continue for each component until your # of principal components is equal to your original number of features.

As someone mentioned, if you like to play pretend, you can grab the first two principal components and make a 2D plot that will be hard to explain but will make a pretty picture none-the-less.

The only real redeeming factor of Principal components is the orthogonality, which has some nice properties when doing a basic regression.

-Riley
PCA makes proxy modelling (by using PCA for Interest Rates and Inflation) on the liability side much easier as well.
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Old 03-09-2020, 11:35 AM
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PCA makes proxy modelling (by using PCA for Interest Rates and Inflation) on the liability side much easier as well.
Yeah, I suppose PCA could be useful for highly correlated features where the data is smallish.

A key point I forgot to add is that while PCA reduces the dimensionality, it does not reduce the number of features needed, at least not natively.

-Riley
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Old 03-09-2020, 09:50 PM
setseed(123) setseed(123) is offline
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Quote:
Originally Posted by whoanonstop View Post
You're suggesting ESL for someone who doesn't understand PCA?
The authors of the book also wrote one of the texts on the PA syllabus, ISLR. Both books along with a video series covering the chapters of the ISLR book can be found at the link.

https://www.r-bloggers.com/in-depth-...expert-videos/

There are a couple short video lessons in Chapter 10 on principle component analysis. A lab in R demonstrating PCA is also provided.
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