topic PCA on correlation and covariance matrix in Discussions

PCA on correlation and covariance matrix

kjwx109 — Fri, 09 Jun 2023 00:48:48 GMT

Hello,

I am not an expert user so please be gentle with me.

I have performed PCA on some standardised data (with 2 variables) in JMP14 and noted that the two scores plots are almost mirrored across the PC1 axis. Why are they reflected in this manner? (Also, they are not perfect reflections. Why is this?)

Re: PCA on correlation and covariance matrix

kjwx109 — Mon, 02 May 2022 09:27:46 GMT

Sorry, I should have pointed out that the "mirror images" refer to PCA performed on the correlation matrix and the covariance matrix.

Re: PCA on correlation and covariance matrix

Mark_Bailey — Mon, 02 May 2022 13:45:35 GMT

The covariance is the fundamental quantity, but the analysis is dominated by the measures with the largest scales and ranges. Centering and scaling first can help avoid the dominance of a few variables. You standardized the data first, so the covariance and correlation results well be similar.

Re: PCA on correlation and covariance matrix

Raaed — Mon, 02 May 2022 17:38:43 GMT

PCA in exploratory data analysis is commonly used to reduce dimensionality by dropping each data point onto only the first few base components to obtain data with lower dimensionality while preserving as much data variance as possible. (Orthogonal property)

Orthogonal coordinates are defined as the set of coordinates d q = ( q 1, q 2, ..., q d ) where all coordinate surfaces meet at right angles (note: superscripts are indices, not exponents). The ordinate surface of a given q k coordinate is the curve, surface, or epitaxy on which q k is a constant.