Should one remove highly correlated variables before PCA?

Should one remove highly correlated variables before PCA?

I’m reading a paper where author discards several variables due to high correlation to other variables before doing PCA. The total number of variables is around 20. Does this give any benefits? It looks like an overhead to me as PCA should handle this automatically. This expounds upon the insightful hint provided in a comment by @ttnphns.

How is transforming the data before PCA is important?

Many other linear (eg, discriminant analysis, rank-PCA) or curvi-linear (logarithm, Box-Cox transform) methods can be characterized by an adequate processing of the table data corresponding to a particular metric (eg, metric Mahanalobis, Spearman correlation coefficient).

Do you need to normalize data for PCA?

Some claim that normalizing some data is not needed because the variability is about the same for all of your data. If this is true. PCA will give the same results if you normalize or not. So, normalizing your data will have no effect on the result. Thanks all, particularly Andrew.

What is principal component analysis ( PCA ) used for?

The Principal Component Analysis (PCA) is a method based on spectral analysis of the matrix of coefficients of linear correlation. The principal components are linear combinations of the original variables of the data table analyzed. This descriptive method has been developed for the detection of linear relations between variables.

How is correlation related to the PCA contribution?

Adjoining nearly correlated variables increases the contribution of their common underlying factor to the PCA. We can see this geometrically. Consider these data in the XY plane, shown as a point cloud:

How does a principal component analysis ( PCA ) work?

PCA reduces the high-dimensional interrelated data to low-dimension by linearly transforming the old variable into a new set of uncorrelated variables called principal component (PC) while retaining the most possible variation. The first component has the largest variance followed by the second component and so on.

How are eigenvalues related to variance in PCA?

Eigenvalues are the variance explained by each principal component, and to repeat, are constrained to decrease monotonically from the first principal component to the last. These eigenvalues are commonly plotted on a scree plot to show the decreasing rate at which variance is explained by additional principal components.

When to use covariance or correlation matrix in PCA?

You tend to use the covariance matrix when the variable scales are similar and the correlation matrix when variables are on different scales. Using the correlation matrix is equivalent to standardizing each of the variables (to mean 0 and standard deviation 1). In general, PCA with and without standardizing will give different results.

How is PCA used in a factor analysis?

In that case, PCA gives a solution for a different set of data, whereby each variable is scaled differently.

When to use correlation based PCA instead of mlpca?

As a consequence, this means I cannot interpret correlation-based PCA as an MLPCA model. In the cases where (1) the implied assumptions of covariance-based PCA do not apply and (2) an MLPCA interpretation is valuable, I recommend to use one of the MLPCA methods instead [1-4].