# How is PCA applied to (one-hot encoded) DNA sequence data?

I realize some questions have been asked already about one-hot encoding for PCA. The answer seems to be along the lines of 'The PCA will run, but does not necessarily make sense.'

However, I have a question regarding the application of PCA on one-hot encoded sequence data. For example, in this paper, the authors claim to first one-hot encode DNA sequences, and then apply PCA on some resulting matrix. I'm trying to understand this paper (I'm looking to apply a similar strategy for a different kind of sequence), but I don't see to what matrix they actually apply PCA.

The part I don't understand is this: If we one-hot encode using the categories "$$a,t,g,c,\_$$" (as stated in the paper)

a sequence $$\{gaatc\}$$ becomes: $$\begin{bmatrix} 0 & 1 & 1 & 0 & 0\\ 0 & 0 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 \\ \end{bmatrix}$$

a sequence $$\{aagctt\}$$ becomes: $$\begin{bmatrix} 1 & 1 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 1 & 1\\ 0 & 0 & 1 & 0 & 0 & 0\\ 0 & 0 & 0 & 1 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0\\ \end{bmatrix}$$

Meaning every sample is now a matrix. In "normal" PCA every sample is a vector, which we stack together into the matrix of which we determine the coveriance, etc.

So what is being done in case of one-hot encoded sequence data? How are these sample-matrices combined such that we can determine a (useful) covariance matrix?