Mathematics Asked by Lucozade on December 5, 2020

In principal component analysis (PCA), one can choose either the covariance matrix or the correlation matrix to find the components. These give different results because, I suspect, the eigenvectors between both matrices are not equal. (Mathematically) similar matrices have the same eigenvalues, but not necessarily the same eigenvectors. Several questions: (1) Why this difference? (2) Does PCA make sense, if you can get two different answers? (3) Which of the two methods is ‘best’? (4) Since PCA operates on standardized (not) raw data in both cases, i.e., scaled by their standard deviation, does it make sense to use the results to draw conclusions about the dominance of variation for the actual, unstandardized data?

The problem with not standardizing, i.e. with not scaling the variables by their standard deviation, is that if, for example, one variable is measured in centimeters and another in dollars, then changing centimeters to meters can actually change the eigenvectors, so an arbitrary choice of units can alter the results. Hence I'd use the correlation matrix.

Answered by Michael Hardy on December 5, 2020

1 Asked on September 23, 2020 by user801111

2 Asked on September 22, 2020 by aa_bb

abstract algebra commutative algebra finitely generated modules projective module

0 Asked on September 21, 2020 by rage

1 Asked on September 20, 2020 by ton910

abstract algebra extension field field theory minimal polynomials

1 Asked on September 19, 2020 by simey

1 Asked on September 18, 2020 by abhishek

1 Asked on September 18, 2020 by blargoner

adjoint functors category theory continuity general topology

3 Asked on September 18, 2020 by samuel-a-morales

3 Asked on September 16, 2020 by yastown

1 Asked on September 16, 2020 by fleccerd

1 Asked on September 15, 2020 by maddy

1 Asked on September 14, 2020 by hlee

1 Asked on September 14, 2020 by user9026

1 Asked on September 13, 2020 by paul-j

4 Asked on September 13, 2020 by global05

contest math modular arithmetic problem solving solution verification

1 Asked on September 10, 2020 by donald-hobson

1 Asked on September 9, 2020 by lad

abstract algebra polynomials ring theory solution verification

1 Asked on September 8, 2020 by qp212223

0 Asked on September 8, 2020 by jacob-denson

Get help from others!

Recent Answers

- Lex on Does Google Analytics track 404 page responses as valid page views?
- Joshua Engel on Why fry rice before boiling?
- Peter Machado on Why fry rice before boiling?
- haakon.io on Why fry rice before boiling?
- Jon Church on Why fry rice before boiling?

Recent Questions

- How Do I Get The Ifruit App Off Of Gta 5 / Grand Theft Auto 5
- Iv’e designed a space elevator using a series of lasers. do you know anybody i could submit the designs too that could manufacture the concept and put it to use
- Need help finding a book. Female OP protagonist, magic
- Why is the WWF pending games (“Your turn”) area replaced w/ a column of “Bonus & Reward”gift boxes?
- Does Google Analytics track 404 page responses as valid page views?

© 2023 AnswerBun.com. All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP