1). Does it use the Shannon Entropy function? (Not specified in documentation)
2). Does it work on 3D arrays? (Seems to).
3). What are its Min (assume 0) and Max values? (Not specified in documentation).
Thanks,
Phil
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asked Sep 2, 2022 at 12:07
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1 Answer
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list = RandomChoice[{a, b, c}, 1000];
tallies = Tally[list]
(* {{b, 316}, {c, 331}, {a, 353}} *)
Base E (default)
Entropy[list] == -Total[#*Log[#] & /@ (tallies[[All, 2]]/Length[list])]
(* True *)
Base 2
Entropy[2, list] == -Total[#*Log2[#] & /@ (tallies[[All, 2]]/Length[list])]
(* True *)
Base 10
Entropy[10, list] == -Total[#*Log10[#] & /@ (tallies[[All, 2]]/Length[list])]
(* True *)
EDIT: The entropy is maximized when all of the choices are equally likely. For n equally likely choices, the entropy is Log[n]/Log[b] where b is the base.
answered Sep 2, 2022 at 15:16
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$\begingroup$ Log[Exp[1]] == 1 so why divide by Ln[e]? $\endgroup$ Commented Sep 2, 2022 at 17:46
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Log[n]/Log[b]is the result for an arbitrary positive base. Forb == Eit does simplify toLog[n]. $\endgroup$ Commented Sep 2, 2022 at 18:42