I have the possibility to describe data with two different data structures, both data structures are some sort of approximation to the true data. I would like to compare the two data structures with respect, how much one explains variance in one data structure to the other. Therefore I decided to use PCA, nevertheless, I don't know if it is safe to say such statement: If the variance explained by the same number components N (e.g. 2) is higher in a data structure than in the other, the data structure loses some part of the information. For example as on the image in the attachment, if Data_structure_A gives more variance, then it loses more information than Data_structure_B?
PCA changes the basis of the data, hence, after applying PCA, we get a new dataset with same domain. Now, if the first 2 PCAs have a total variance of 80%, it means that they preserve 80% information of the main dataset. If the number is 60% it means that they preserve 60% information of the main dataset. Hence, the lower the total variance is, the higher is the information loss. But interesting fact is that PCA never tells if the information lost was relevant or irrelevant.
Results may vary because of how you apply your PCA, do you scale your datastructure before PCA ?
If you add the PCA plot here, it would be more and precise to say about it. Nonetheless, your posted pic 80% and 60% seems good outcome, it mean PCA says it has good relation.
According to PCA methodology, if data structure A retains or explain 80% of the total data variance vs. data structure B that retains 60% of the total data variance, it means that A describes more complete the original data than B. Hence, A loses less information of the original data set than B does. In other words, B loses more information than A.
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