Linked Questions

I am confused as to why eigenvalues are the principal components. What is the intuition behind finding the eigenvectors of the covariance matrix for PCA?

I am trying to enhance the contrast in the images I get after scanning a surface using Thermography (Principal Component Thermography ~Rajic, which is basically an application of Principal Component ...

I've been studying PCA, and some of the terminology isn't very clear. I do not understand what they mean when they refer to a "principal component". One definition I have seen calls it the new ...

I am confused with the terminologies of score and principal component in PCA, it seems they are equivalent but there is also some difference. Could anyone explain to me?

Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix ...

In principal component analysis (PCA), we get eigenvectors (unit vectors) and eigenvalues. Now, let us define loadings as $$\text{Loadings} = \text{Eigenvectors} \cdot \sqrt{\text{Eigenvalues}}.$$ I ...

I'm currently going through a slide set I have for "factor analysis" (PCA as far as I can tell). In it, the "fundamental theorem of factor analysis" is derived which claims that the correlation ...

I am looking at this link http://strata.uga.edu/8370/lecturenotes/principalComponents.html where it says In interpreting the principal components, it is often useful to know the correlations of ...

Principal component regression (PCR) in fact is regression on PC scores but not PCs. Why then in so many books and tutorials do they say something like, in statistics, principal component ...

I have performed principal component analysis (PCA) of data matrix $X$ by doing singular value decomposition (SVD) $$ X = U S V', $$ where the columns of $V$ are the principal directions/axes and the ...

I often see the principal components of PCA described as "linear combinations of the original features". Say we want to compute the principal components of our $m \times n$ design matrix $A$ ($m$ ...

I am very new to R and statistics so this may be a simple question. I have a matrix (1000,756) containing 1000 years of winter sea-level pressure data (SLP) at 756 locations in the North Atlantic. I ...

I see that in PCA the first principal component maximizes the variances amongst all the points within the data set. What exactly does this mean, what does it show and what does every other principal ...

Are principal factors in principal component analysis always uncorrelated, or can they end up being correlated? If so, how and why?