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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 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 below, if Data_structure_A gives more variance, then it loses more information than Data_structure_B?

enter image description here

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It is not the best use of Principal Component Analysis (PCA) to compare information loss for different data structures.

It would be more appropriate to use Information Theory. Information Theory is the study of data compression. It provides many tools to make quantitative comparisons across different encoding schemes.

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  • $\begingroup$ That's a good point. But could you narrow down your answer, e.g. some group of methods? It would be very helpful! $\endgroup$ – Daniel Wiczew Jun 2 '20 at 15:39
  • $\begingroup$ I can not suggest specific methods because I'm unclear about the specific data and specific data structure. $\endgroup$ – Brian Spiering Jun 2 '20 at 16:43
  • $\begingroup$ Brian Spiering - the data structure is a set of graphs, that have feature vector associated with a node or weighted edges. It is explained in detail here: datascience.stackexchange.com/questions/75284/… $\endgroup$ – Daniel Wiczew Jun 2 '20 at 20:20

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