Performed on an ordered (ascending) set of numbers and labels of size N. There must be only 2 unique labels (Label 1 and label 2).
Seperate the list into N - 1 grouping sets such that:Set | Left | Right |
1 | ![]() |
![]() ![]() ![]() |
2 | ![]() ![]() |
![]() ![]() |
![]() |
![]() |
![]() |
N-1 | ![]() ![]() ![]() ![]() |
![]() |
Choose the smallest Info value as the final info value.
Sorting: Sort first by value (ascending), then by labels (ascending). Duplicate values: Calculate the info_n for the section that has duplicates. Then reorder the section by sorting labels(desc) and calculate the interior of the duplicate section (of size duplicateN 1) again. Do the same for all sections that have duplicates.grouping 1 2 1 1 2 ordered 1 1 2 1 2 values 1 8 3 7 5 1 3 5 7 8 5 values so there will be 4 cut points 1 1 2 1 2 a=1/5 b=1/1 c=2/4 entropy(b)= 0 entropy(c)= 1 info = 0.8000 1 1 2 1 2 a=2/5 b=2/2 c=1/3 entropy(b)= 0 entropy(c)= 0.9183 info = 0.5510 1 1 2 1 2 a=3/5 b=2/3 c=1/2 entropy(b)= 0.9183 entropy(c)= 1 info = 0.9510 1 1 2 1 2 a=4/5 b=3/4 c=0/1 entropy(b)= 0.8113 entropy(c)= 0 info = .6490 The smallest value is 0.5510
grouping 1 2 2 1 1 ordered 1 2 1 1 2 values 1 8 5 8 8 1 5 8 8 8 5 values so there will be 4 cut points 1 2 1 1 2 1 5 8 8 8 a=1/5 b=1/1 c=2/4 entropy(b)= 0 entropy(c)= 1 info =0.8 -- Info won't change if we reorder the the duplicate by group (desc) 1 2 1 1 2 1 5 8 8 8 a=2/5 b=1/2 c=2/3 entropy(b)= 1 entropy(c)= 0.9183 info = 0.9510 -- Duplicate section first run 1 2 1 1 2 1 5 8 8 8 a=3/5 b=2/3 c=1/2 entropy(b)= 0.9183 entropy(c)= 1 info = 0.9510 1 2 1 1 2 1 5 8 8 8 a=4/5 b=3/4 c=0/1 entropy(b)= 0.8113 entropy(c)= 0 info = .6490 -- Duplicate section second run. Reordered by group(desc) 1 2 2 1 1 1 5 8 8 8 a=3/5 b=1/3 c=2/2 entropy(b)= 0.9183 entropy(c)= 0 info = 0.5510 1 2 2 1 1 1 5 8 8 8 a=4/5 b=2/4 c=1/1 entropy(b)= 1 entropy(c)= 0 info = 0.8000 The smallest value is 0.5510