Formulating a Precise Definition of "Space" in Chess Premise

I have always enjoyed playing recreational chess, so I know the basics and some general tactics / strategies. It was only recently though that I have gone more hardcore, so to speak, with my analysis. Namely, I'm taking the "big data" approach by looking at the freely available game logs (which contain hundreds of thousands of games). 

I realize there has already been expert machine-learning analysis done with this data and some of it published. However, I'm doing this just because I like chess and I like to dabble with programming. I don't expect to win any Nobel prizes, but I do expect to have fun along the way. Basically I think it's cool to test out the theories or rules of thumb for their effectiveness. Like I said, I'm trying to be humble/realistic about my model specification, and there are probably some things I cannot capture from the data. Some variables/features are easier to formulate than others; which brings me to my question.

I'm trying to figure out if I can create a variable (aka feature) for which player has more "space." Let's say we have this position:



White is said to have a space advantage here. Maybe it's my lack of expertise, and I'm not sure exactly what "space" is being referred to here; I see a few different things going on. The following are my three attempts to explain "space." (bear in mind I am aiming to reduce "space" to something quantitative, hence the nerdy-sounding explanations)


White's pieces have a shorter average distance to the end of the board than black's. White's pawn is all the way on the 5th rank, while black's pieces are closer to his starting position
White has more available moves. Black is looking rather cramped, some of his pieces are getting in the way of each other.
White controls more squares. White's light square bishop controls a longer diagonal than black's, and so forth.


This is the confusing part for me, because I could easily rationalize any of the above items as being "space." Citeris paribus, we could expect a correlation between some of these things, but eventually I have to settle on a precise definition of "space" if I'm to transform chess logs to a quantitative variable. 

Question: Is there a precise definition ( be it in the literature or an unspoken but widely understood axiom) of the concept of "space?" Perhaps none of my attempts to explain space are close, and there is a 4th better definition. Either way, please feel free to weigh in.

Note: All I'm asking is a precise definition. You do not have to reduce your definition to the quantitative (unless you want to!)

What is &#39;space&#39; on a chessboard? the accepted answer to this post hints at my 2nd definition: "space in terms of the number of possible legal moves you have." Is that the overall consensus though?
I define space as a mixture of mobility and squares controlled.


[fen "rbk3br/2p2p2/1pP2Pp1/pP4Pp/P6P/8/4R2K/4R3 w - - 0 0"]


Black is completely lost due to his lack of space.


[fen "8/2p2p2/1pP1kPp1/pP1rr1Pp/P6P/2K5/4R3/4R3 w - - 0 0"]


Black is just as cramped, but his greater mobility and more active king gives him a much better game.

EDIT:  From "Elements of Positional Evaluation" by Dan Heisman.  Section 3.3 Space

So to better understand space, we must once more return to mobility.  What is important to realize is that space depends on mobility; that is, mobility "defines" space.  This means that no matter how the pieces are situated, the player with more space is really the one with more actual and actual global mobility, despite what the pawn structure may seem to indicate.  For example, in a closed position where White's pawns seem more advanced, if Black's pieces, through open files or diagonals, can "point" through and around the pawn mass in some way that gives Black the superior actual mobility, then it is he who may seem to obtain the space advantage.  This is additionally made posible because pieces are not legally bound to stay behind either side's pawns.  Indeed, an over ambitious early push of a pawn mass somethimes leaves one's pieces scattered to the defensive at some later time because the opposition was not effectively reduced in total actual mobility and god behind the advanced pawns.  So, whereas space is an existing and useful term, it does not qualify as a basic element.