I am creating a set of chess positions to be used [as a data set] for a project. It's based on supervised machine learning, but I need to have labeled data (see more italicized text below) before any machine learning can be done. I wish to label each position as open or closed or possibly some combination of the two.
I started out with assigning each position to just "open" or "closed," but this wasn't clear for a lot of the positions. Then I decided to go with a third label, semi-open/semi-closed, which is like the middle and in between open and closed. I’ve labeled most of the positions, but there are many positions that I still haven’t comfortably labeled with a distinct class.
I know that open positions are characterized as having pawnless ranks, files, and diagonals, while closed positions have them clogged up with pawns. In open positions you can usually centralize your pieces, while closed positions give you a hard time moving an arbitrary piece to a random location on the board. There are many other related patterns, features, and qualities.
I can easily go with my gut feeling when assigning "closed" to a position that has 7 pawns on each side with each pawn blockading another, and "open" to a position that has pawns only on the flanks and in their starting squares. However, it's hard for me to classify some positions such as these two examples:
[White "Position1"] [Black "Open/Semi/Closed/Etc"] [FEN "8/5Qpk/p6p/P1b5/4pPn1/2Pp3P/1P1BbqP1/R3R2K w - - 0 1 "]
[White "Position2"] [Black "Open/Semi/Closed/Etc"] [FEN "3r1rk1/pp2pp1p/2p3pb/2P5/4P3/4nNPb/PP2P2P/R1RNK2B w - - 0 1 "]
What would you assign to the examples above and why? For example: one position is more open than the other due to characteristic XYZ, or the second position should not be considered closed since there's an open file, and so on.
Should I just ditch the whole binary-ish labeling (classification) and instead assign a variable number (regression) describing how open or closed a position is (e.g. 0% to 100% open?) Or is there still a way for positions to go into a few categories, which means that we can have "rigorous" definitions of the categories of openness? And "rigorous" as in having few contradictions and preferably can be applied by a human without too much difficulty.