Question: Hi everyone,
I am trying to understand a bit deeper what actually a PCA plot means in a more practical way. So please don't link me any kind of explanation...I am just trying to make myself clear on a personal exercise.

Answer: Hey, that is not a '*PCA plot*' - it's a bi-plot comparing eigenvector (PC) 1 versus eigenvector (PC) 2. There will be more eigenvectors in your dataset at which you should additionally look. Each eigenvector will additionally have an associated eigenvalue, which alludes to its 'importance' (see below).

#Intro to PCA

PCA is a very powerful technique and can have much utility if you can get a grasp of it and what it means. It was initially developed to analyse large volumes of data in order to tease out the differences/relationships between the logical entities being analysed (for example, a data-set consisting of a large number of samples, each with their own data points/variables). **It extracts the fundamental structure of the data without the need to build any model to represent it.** This ‘summary’ of the data is arrived at through a process of reduction that can transform the large number of variables into a lesser number that are uncorrelated (i.e. the ‘principal components'), whilst at the same time being capable of easy interpretation on the original data.

*[Source: my own manuscript: https://benthamopen.com/contents/pdf/TOBIOIJ/TOBIOIJ-7-19.pdf]*

#The formulae and variance

The formulae to derive the eigenvectors and their associated eigenvalues are fundamentally based on variance (well, covariance). Thus, **what PCA is summarising in your dataset is variance, or, better put, how your entities covary amongst each other**. The eigenvectors are then ordered based on how much variation they explain in your dataset. PC1 / eigenvector 1 will always explain the most variation due to this ordering of the PCs. Thus, as to which genomax has correctly pointed in his comment above, the largest source of variation in your dataset is between MF1_S1 and the other samples, for whatever reasons we are not to know.

The variation explained by each eigenvector/PC is represented by a Scree plot. **The explained variation of all PCs will sum to 100% - PCA will extract every ounce of variation that exists in your dataset**

#What does this mean practically?

Practically, if you look at the numbers behind your PC1, you'll first notice that each gene/transcript/variable has been assigned a value... a weighting that allows us to infer its importance in relation to PC1, and, thus, its importance in relation to the source of variation between MF1_S1 and your other samples.

In your example, it looks like you're using DESeq2's in built function to build the bi-plot. Don't use that. Instead use the `prcomp()` function in R and then take a look at your eigenvectors, which will be stored in a variable called '*x*', e.g., `prcomp(MyData)$x`

#PCA is multi-dimensional

Remember that PCA is much more than just this bi-plot that you've posted. PCA is multidimensional and, as mentioned, will extract every ounce of variation that exists in your dataset, which can be visualised by pairwise comparisons of each PC...

The 'key' that you may be seeking could be hidden in these other PCs, but this depends greatly on your experimental set-up and what you are ultimately hoping to achieve by running whatever experiment it is that you're running.

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That's PCA explained to the general audience.