In the following, e=0 means use all attributes and e>0 means stop after finding e better projections
The way this works is that in builds "e" projection as follows:
- Draw a line between two randomly selected points.
- All the other points are then mapped to this point using cosine rule.
- The error of this line is the mean distance to all the points around it (found using Pythagoras)
- Keep projection if its error is less than best projection found so far
In the e>0 experiments, the weight given to each projection is biased by the error of each projection:
- Weight[X] = error of [X] / error[W]
After all that, its Euclidean distance times weight over the projections.
In the following, note how e=0 is not as critical as other factors (except in big datasets like China). The LHS number comes from ScottKnott which ignores small effect size (Hedges' corrected g = 0.17) and which uses bootstrapping (500 samples, 95% confidence) to test for differences.
----| 0 |----------------------
1, k=4,n=1,e=0, 18, 36, 66,|, 36, 48, 4029,>,-*- | ,<,
1, k=2,n=1,e=0, 17, 37, 63,|, 37, 46, 3800,>,-*- | ,<,
1, k=1,n=1,e=0, 21, 40, 68,|, 40, 47, 1943,>,-*- | ,<,
2, k=4,n=1,e=1, 33, 61, 145,|, 61, 112, 4551,>, --*---- | ,<,
2, k=4,n=1,e=2, 33, 61, 145,|, 61, 112, 4551,>, --*---- | ,<,
2, k=4,n=1,e=4, 33, 62, 144,|, 62, 111, 4551,>, --*---- | ,<,
2, k=2,n=1,e=1, 30, 63, 132,|, 63, 102, 7761,>, --*--- | ,<,
2, k=2,n=1,e=4, 32, 63, 132,|, 63, 100, 7761,>, --*--- | ,<,
2, k=2,n=1,e=2, 32, 64, 139,|, 64, 107, 7761,>, --*---- | ,<,
2, k=1,n=1,e=1, 37, 66, 108,|, 66, 71, 8926,>, --*-- | ,<,
2, k=1,n=1,e=2, 36, 66, 108,|, 66, 72, 8926,>, --*-- | ,<,
2, k=1,n=1,e=4, 36, 66, 107,|, 66, 71, 8926,>, --*-- | ,<,
----| /home/timm/tmp/desharnais.dash |----------------------
1, k=4,n=1,e=0, 11, 29, 55,|, 29, 44, 378,>,*- | ,<,
2, k=4,n=1,e=2, 20, 33, 68,|, 33, 48, 883,>,-*- | ,<,
2, k=4,n=1,e=4, 18, 33, 68,|, 33, 50, 883,>,-*- | ,<,
2, k=2,n=1,e=0, 16, 36, 59,|, 36, 43, 320,>,-* | ,<,
2, k=4,n=1,e=1, 16, 37, 69,|, 37, 53, 854,>,-*- | ,<,
2, k=1,n=1,e=0, 19, 41, 66,|, 41, 47, 387,>,-*- | ,<,
3, k=2,n=1,e=4, 15, 45, 77,|, 45, 62, 764,>,--*- | ,<,
3, k=2,n=1,e=2, 19, 47, 83,|, 47, 64, 764,>,--*- | ,<, 3, k=2,n=1,e=1, 19, 48, 79,|, 48, 60, 844,>,--*- | ,<,
3, k=1,n=1,e=2, 24, 48, 76,|, 48, 52, 655,>,--*- | ,<,
3, k=1,n=1,e=4, 25, 48, 78,|, 48, 53, 1220,>,--*- | ,<,
3, k=1,n=1,e=1, 24, 52, 85,|, 52, 61, 655,>,--*- | ,<,
----| /home/timm/tmp/miyazaki94.dash |----------------------
1, k=1,n=1,e=0, 29, 42, 75,|, 42, 46, 655,>,-*-- | ,<,
1, k=2,n=1,e=1, 17, 43, 88,|, 43, 71, 490,>,-*-- | ,<,
1, k=4,n=1,e=1, 25, 45, 95,|, 45, 70, 340,>,--*-- | ,<,
1, k=2,n=1,e=0, 27, 45, 88,|, 45, 61, 472,>,--*- | ,<,
1, k=1,n=1,e=2, 16, 45, 83,|, 45, 67, 648,>,--*- | ,<,
1, k=1,n=1,e=4, 16, 45, 83,|, 45, 67, 648,>,--*- | ,<,
1, k=4,n=1,e=0, 18, 45, 73,|, 45, 55, 370,>,--* | ,<,
1, k=4,n=1,e=2, 30, 51, 81,|, 51, 51, 602,>, -*- | ,<,
1, k=4,n=1,e=4, 30, 51, 81,|, 51, 51, 602,>, -*- | ,<,
1, k=2,n=1,e=2, 28, 57, 92,|, 57, 64, 472,>,--*-- | ,<,
1, k=2,n=1,e=4, 28, 57, 92,|, 57, 64, 472,>,--*-- | ,<,
1, k=1,n=1,e=1, 35, 60, 100,|, 60, 65, 648,>, --*- | ,<,
----| /home/timm/tmp/nasa93.dash |----------------------
1, k=2,n=1,e=0, 22, 52, 86,|, 52, 64, 2058,>,--*- | ,<,
1, k=1,n=1,e=0, 15, 50, 93,|, 50, 78, 900,>,--*-- | ,<,
1, k=1,n=1,e=1, 33, 54, 95,|, 54, 62, 4207,>, -*-- | ,<,
1, k=4,n=1,e=0, 27, 58, 104,|, 58, 77, 4029,>,--*-- | ,<, 1, k=1,n=1,e=2, 33, 62, 104,|, 62, 71, 4207,>, --*- | ,<,
1, k=1,n=1,e=4, 33, 63, 104,|, 63, 71, 4207,>, --*- | ,<,
1, k=4,n=1,e=1, 40, 73, 123,|, 73, 83, 1719,>, --*--- | ,<,
1, k=2,n=1,e=1, 29, 73, 123,|, 73, 94, 2443,>,---*--- | ,<,
1, k=2,n=1,e=4, 29, 74, 132,|, 74, 103, 2443,>,---*--- | ,<,
1, k=4,n=1,e=2, 40, 74, 129,|, 74, 89, 1719,>, --*--- | ,<,
1, k=2,n=1,e=2, 29, 75, 146,|, 75, 117, 2443,>,----*--- | ,<,
1, k=4,n=1,e=4, 40, 74, 126,|, 74, 86, 1719,>, --*--- | ,<,
----| /home/timm/tmp/china.dash |----------------------
1, k=4,n=1,e=0, 16, 30, 53,|, 30, 37, 1139,>,-* | ,<,
1, k=2,n=1,e=0, 14, 31, 49,|, 31, 35, 1609,>,-* | ,<,
1, k=1,n=1,e=0, 18, 36, 56,|, 36, 38, 1943,>,-* | ,<,
2, k=4,n=1,e=1, 35, 62, 159,|, 62, 124, 4551,>, --*-----| ,<,
2, k=4,n=1,e=2, 35, 62, 159,|, 62, 124, 4551,>, --*-----| ,<,
2, k=4,n=1,e=4, 35, 62, 159,|, 62, 124, 4551,>, --*-----| ,<,
2, k=2,n=1,e=1, 34, 65, 151,|, 65, 117, 7761,>, --*-----| ,<,
2, k=2,n=1,e=2, 34, 65, 151,|, 65, 117, 7761,>, --*-----| ,<,
2, k=2,n=1,e=4, 34, 65, 151,|, 65, 117, 7761,>, --*-----| ,<,
2, k=1,n=1,e=1, 37, 69, 115,|, 69, 78, 8926,>, --*-- | ,<,
2, k=1,n=1,e=2, 37, 69, 115,|, 69, 78, 8926,>, --*-- | ,<,
2, k=1,n=1,e=4, 37, 69, 115,|, 69, 78, 8926,>, --*-- | ,<,
----| /home/timm/tmp/finnish.dash |----------------------
1, k=1,n=1,e=0, 23, 36, 79,|, 36, 56, 950,>,-*-- | ,<,
1, k=1,n=1,e=1, 31, 50, 85,|, 50, 54, 1761,>, -*- | ,<,
1, k=1,n=1,e=2, 31, 50, 85,|, 50, 54, 1761,>, -*- | ,<,
1, k=1,n=1,e=4, 31, 50, 85,|, 50, 54, 1761,>, -*- | ,<,
1, k=4,n=1,e=0, 24, 51, 120,|, 51, 96, 1120,>,--*---- | ,<,
1, k=4,n=1,e=1, 28, 52, 121,|, 52, 93, 809,>,--*---- | ,<,
1, k=4,n=1,e=2, 28, 52, 121,|, 52, 93, 809,>,--*---- | ,<,
1, k=4,n=1,e=4, 28, 52, 121,|, 52, 93, 809,>,--*---- | ,<,
1, k=2,n=1,e=0, 23, 56, 81,|, 56, 58, 489,>,--*- | ,<,
1, k=2,n=1,e=1, 23, 58, 88,|, 58, 65, 1467,>,--*- | ,<,
1, k=2,n=1,e=2, 23, 58, 88,|, 58, 65, 1467,>,--*- | ,<,
1, k=2,n=1,e=4, 23, 58, 88,|, 58, 65, 1467,>,--*- | ,<,
----| /home/timm/tmp/coc81.dash |----------------------
1, k=2,n=1,e=0, 40, 76, 222,|, 76, 182, 3800,>, ---*----|--- ,<,
1, k=2,n=1,e=1, 46, 76, 262,|, 76, 216, 1286,>, --*----|------ ,<,
1, k=2,n=1,e=2, 46, 76, 262,|, 76, 216, 1286,>, --*----|------ ,<,
1, k=2,n=1,e=4, 46, 76, 262,|, 76, 216, 1286,>, --*----|------ ,<,
1, k=1,n=1,e=0, 39, 76, 163,|, 76, 124, 1240,>, ---*----| ,<,
1, k=4,n=1,e=1, 45, 80, 284,|, 80, 239, 977,>, --*----|------- ,<,
1, k=4,n=1,e=2, 45, 80, 284,|, 80, 239, 977,>, --*----|------- ,<,
1, k=4,n=1,e=4, 45, 80, 284,|, 80, 239, 977,>, --*----|------- ,<,
1, k=1,n=1,e=1, 56, 80, 160,|, 80, 104, 1523,>, --*----| ,<,
1, k=1,n=1,e=2, 56, 80, 160,|, 80, 104, 1523,>, --*----| ,<,
1, k=1,n=1,e=4, 56, 80, 160,|, 80, 104, 1523,>, --*----| ,<,
1, k=4,n=1,e=0, 36, 81, 224,|, 81, 188, 3188,>, ---*----|--- ,<,
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