在行列可自由变换的条件下,平面上的4点结构只有16个

(A,B)---6*30*2---(0,1)(1,0)
让A分别是4a1,2,…,16,让B全是0。当收敛误差为7e-4,收敛199次取迭代次数平均值,得到
| 迭代次数 | 搜索难度 | ||
| 1 | 6830.8492 | 1 | |
| 2 | 16272.286 | 2.382176 | |
| 3 | 19248.146 | 2.817826 | |
| 4 | 19952.196 | 2.920895 | |
| 5 | 23455.864 | 3.433814 | |
| 6 | 25988.859 | 3.804631 | |
| 7 | 27253.231 | 3.989728 | |
| 8 | 33256.528 | 4.868579 | |
| 9 | 36521.251 | 5.346517 | |
| 10 | 38757.945 | 5.673957 | |
| 11 | 41967.322 | 6.143793 | |
| 12 | 46774.467 | 6.847533 | |
| 13 | 49417.533 | 7.234464 | |
| 14 | 53409.02 | 7.818797 | |
| 15 | 62999.894 | 9.22285 | |
| 16 | 84650.839 | 12.39243 |
3点结构有6个

按照结构加法有

13(3a1+1)=2*4a1+4a2+2*4a3+2*4a4+4*4a12+2*4a14
| a | b | |||||||||||
| - | - | - | - | - | - | - | - | - | - | - | - | |
| - | 1 | 1 | - | - | - | - | 1 | 1 | - | - | - | |
| - | 1 | - | - | - | - | - | - | - | - | - | - | |
| - | - | - | - | - | - | - | - | 1 | - | - | - | |
| - | - | - | - | - | - | - | - | - | - | - | - | |
| - | - | - | - | - | - | - | - | - | - | - | - |
严格的4a1-1得到4个结构其中只有a,b两个结构是需要的,a就是3a1迭代次数为28392,但是b的迭代次数为29721,b的迭代次数要比a大4.6%。所以2(4a1-1)=3a1+1.046*3a1
如果认为训练集A-B矩阵的行可自由变换2(4a1-1)=2*3a1给这项带来4.6%的误差,但简化了计算。
| a | b | |||||||||||
| - | - | - | - | - | - | - | - | - | 1 | - | - | |
| - | - | - | - | - | - | - | - | - | - | - | - | |
| - | - | - | - | - | - | - | - | - | - | - | - | |
| - | 1 | - | 1 | - | - | - | 1 | - | 1 | - | - | |
| - | - | - | 1 | - | - | - | - | - | - | - | - | |
| - | - | - | - | - | - | - | - | - | - | - | - |
4a3减一得到a,b两个需要的结构,因为训练集A-B矩阵的列可自由变换,对迭代次数没有影响,因此结构a就是3a1.,结构b的迭代次数为30472,比3a1要大7%。出于简化计算的考虑也忽略了这个误差。
如果结构的搜索难度有简单的加和关系则3a1的搜索难度为
(2*1+2.38+2*2.81+2*2.92+4*6.84+2*7.81)/13=4.52
3a2

6(3a2+1)=4a3+4a5+4*4a6
(2.81+3.43+4*3.8)/6=3.57
3a3

15(3a3+1)=2*4a1+4a2+4a3+3*4a5+2*4a7+4*4a8+2*4a11
(2*1+2.38+2.81+3*3.43+2*3.99+4*4.87+2*6.14)/15=3.81
3a4

15(3a4+1)=4a2+4a4+2*4a9+3*4a10+2*4a11+2*4a14+4*4a15
(2.38+2.92+2*5.35+3*5.67+2*6.14+2*7.82+4*9.22)/15=6.52
3a5

9(3a5+1)=4a2+2*4a7+2*4a9+4*4a13
(2.38+2*3.99+2*5.35+4*7.23)/9=5.55
3a6

6(3a6+1)=4a4+4a10+4*4a16
(2.92+5.67+4*12.39)/6=6.69
| 搜索难度 | 搜索难度 | 迭代次数 | |
| 1 | (2*1+2.38+2*2.81+2*2.92+4*6.84+2*7.81)/13 | 4.52461538 | 28392.17 |
| 2 | (2.81+3.43+4*3.8)/6 | 3.57333333 | 36372.48 |
| 3 | (2*1+2.38+2.81+3*3.43+2*3.99+4*4.87+2*6.14)/15 | 3.81466667 | 36629.86 |
| 4 | (2.38+2.92+2*5.35+3*5.67+2*6.14+2*7.82+4*9.22)/15 | 6.52066667 | 51425.59 |
| 5 | (2.38+2*3.99+2*5.35+4*7.23)/9 | 5.55333333 | 61047.4 |
| 6 | (2.92+5.67+4*12.39)/6 | 9.69166667 | 91182.79 |
把6个搜索难度画成图

整体上是增的



















