# PCA: High explained variance in just one principal component

I am new to PCA and I'm trying to interpret some results I have regarding some biological data and having some difficulties fully understanding. Basically, this data is composed of solutions (set of 1,2,3,etc... biological reactions) that correspond to columns (reactions) that contain fluxes (Values). It is something like this :

           Reaction A   Reaction B Reaction C
sol_1          10            20         30
sol_2           5            3          2
sol_3           10          40          40


Since I have a lot of solutions and I would like to further analyse only 2 or 3, my objective is to do a PCA (alongside some HCA) to find patterns and group solutions together to reduce my solution pool number.

In a model I have done, I have these results:

My main questions are:

1. What can be interpreted regarding such a high explained variance in just one dimension (comparing to previously results I have)?
2. Regarding the score plot (individuals plot) what kinda of interpretation can be done from that visualisation? cause it seems that there are 4 main groups and that they have symmetry between each other.

Any questions you have or further information I can detail please ask! And any insight will be helpful . Thank you !

PCA is a good way to study populations. So, a good starting point is to know which axis represents samples and which represents variables or features. In your case, it seems like solutions are samples.

1. In many naturalistic datasets, it's common to see eigen-spectrum plots that look like (A). So it's difficult to interpret much from it other than your samples lie on a line in the space defined by the reactions.

For example for two reactions you will get a plot that looks like this:

1. The score plot might be more useful in your case. Because they are useful for clustering, finding outliers, and identifying implicit patterns such as temporal behavior. To take advantage of this, you'll need to use your knowledge of the solutions to figure out what you can say about the score plot being grouped the way it has. For example, let's say you collected the data during different times of the day (morning, evening, etc.) and from these plots you realize that each group corresponds to one of those times.

For example, a clustered score plot, might belong to a dataset like this:

• Thank you for your answer! In my case solutions represent samples and reactions represent variables indeed. Regarding the score plot, my samples are not related time, they happen all at the same time. The difference between solutions is just the reacions. For instance, sol_1 may delete Reaction A and B in it and sol_2 may delete Reaction C and B in it (deleting means giving it a 0 flux). So perhaps all I can interpret from my score plot is just, from the last example, that sol_1 and sol_2 may be close to each other as they share reaction B in common? Oct 4, 2018 at 11:31
• In addition, is there something to interpret or a pattern that can be found by having that symmetry in the scoreplot? Is it related to the variance being mostly explained in just one component? Oct 4, 2018 at 11:32
• @TiagoRoseiro Regarding your first comment, whether or not the solutions clustered together share only one variable (e.g., reaction B) is difficult to say. A more accurate conclusion would be to say: solutions that are grouped together can be described by a unique linear combination of the reaction variables. Oct 4, 2018 at 22:32
• Regarding your second question: symmetry could mean that your data is symmetric around it's center. So for example, imagine my second plot, but without the middle part where the intersection happens. Oct 4, 2018 at 22:35