( A, B )---2*30*2---( 1, 0 )( 0, 1 )
用网络分类A和B,让A是(0,1)(0,0),让B是(1,0)(0,0)。测试集为(0,0)(0,1)(1,0)(1,1).记为网络1020.固定收敛误差统计迭代次数和分类准确率,得到表格
0 | 1 | 1 | 0 | 1b | 1 | ||||
0 | 0 | 0 | 0 | 0 | 0 | ||||
1020 | |||||||||
f2[0] | f2[1] | 迭代次数n | 平均准确率p-ave | 1-0 | 0-1 | δ | 耗时ms/次 | 耗时ms/199次 | 耗时 min/199 |
0.502508 | 0.4975 | 22643.39 | 0.5 | 0.5879 | 0.41206 | 9.00E-04 | 151.32 | 30112 | 0.5019 |
0.547662 | 0.4523 | 24963.84 | 0.5 | 0.5879 | 0.41206 | 8.00E-04 | 165.13 | 32861 | 0.5477 |
0.517563 | 0.4824 | 27871.17 | 0.5 | 0.5716 | 0.428392 | 7.00E-04 | 189.36 | 37683 | 0.6281 |
0.517567 | 0.4824 | 31813.46 | 0.5 | 0.593 | 0.407035 | 6.00E-04 | 212.35 | 42273 | 0.7046 |
0.467369 | 0.5326 | 37092.37 | 0.5 | 0.5817 | 0.418342 | 5.00E-04 | 244.64 | 48684 | 0.8114 |
0.572806 | 0.4272 | 45074.93 | 0.5 | 0.5791 | 0.420854 | 4.00E-04 | 306.09 | 60913 | 1.0152 |
0.532644 | 0.4674 | 58061.95 | 0.5 | 0.5804 | 0.419598 | 3.00E-04 | 390.89 | 77787 | 1.2965 |
0.567812 | 0.4322 | 82587.38 | 0.5 | 0.5653 | 0.434673 | 2.00E-04 | 544.81 | 108418 | 1.807 |
0.452271 | 0.5477 | 154727.9 | 0.5 | 0.5829 | 0.417085 | 1.00E-04 | 1044.2 | 207797 | 3.4633 |
0.482415 | 0.5176 | 170173.2 | 0.5 | 0.5829 | 0.417085 | 9.00E-05 | 1146.4 | 228135 | 3.8023 |
0.497488 | 0.5025 | 189210.1 | 0.5 | 0.5716 | 0.428392 | 8.00E-05 | 1270 | 252733 | 4.2122 |
0.497488 | 0.5025 | 213974.4 | 0.5 | 0.5578 | 0.442211 | 7.00E-05 | 1436 | 285761 | 4.7627 |
0.542708 | 0.4573 | 244867.5 | 0.5 | 0.5766 | 0.423367 | 6.00E-05 | 1645.7 | 327488 | 5.4581 |
0.472365 | 0.5276 | 292013 | 0.5 | 0.5804 | 0.419598 | 5.00E-05 | 2070.8 | 412086 | 6.8681 |
0.477389 | 0.5226 | 358879.7 | 0.5 | 0.5628 | 0.437186 | 4.00E-05 | 2340.3 | 465719 | 7.762 |
0.527637 | 0.4724 | 465715 | 0.5 | 0.559 | 0.440955 | 3.00E-05 | 3053.4 | 607630 | 10.127 |
0.497488 | 0.5025 | 678376.4 | 0.5 | 0.5704 | 0.429648 | 2.00E-05 | 4422.4 | 880074 | 14.668 |
0.487437 | 0.5126 | 1292066 | 0.5 | 0.5616 | 0.438442 | 1.00E-05 | 8392.7 | 1670147 | 27.836 |
0.547738 | 0.4523 | 1428529 | 0.5 | 0.5578 | 0.442211 | 9.00E-06 | 9362.4 | 1863113 | 31.052 |
0.467337 | 0.5327 | 1594296 | 0.5 | 0.5791 | 0.420854 | 8.00E-06 | 12232 | 2434166 | 40.569 |
两个位的分类准确率趋向于稳定,但不是50%,50%。统计收敛误差为8e-6时的分类情况
A | 6 | B | A | 32 | B | |||||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||
1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | |||
2 | 1 | 0 | 2 | 1 | 0 | 2 | 1 | 0 | 2 | 1 | 0 | |||
3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | |||
A | 92 | B | A | 69 | B | |||||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||
1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | |||
2 | 1 | 0 | 2 | 1 | 0 | 2 | 1 | 0 | 2 | 1 | 0 | |||
3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 |
6 | 1 | 023 |
32 | 13 | 02 |
92 | 01 | 23 |
69 | 013 | 2 |
共收敛了199次,其中有6次,1被分类为A,023被分为B.32次13被分为A,02被分为B。92次01被分为A,23被分为B。69次013被分为A,2被分为B。
A | B | ||||
00 | 161 | 38 | 4.236842 | ||
11 | 101 | 98 | 1.03E+00 |
所以有161次(0,0)被分成A,38次被分成B,比例为4.23.而(1,1)被分成A和B的概率几乎相同。
所以有理由认为有80%的(0,0)被分类为A,有20%的(0,0)被分类为B。而(1,1)被分为A和B的概率相同。所以网络1020的峰值分类准确率
(1,0)位置为0.25*0.8+0.25+0.125=0.575
(0,1)位置为0.25*0.2+0.25+0.125=0.425
第二步
让A和B的位置调换,让A为(1,0)(0,0)让B为(0,1)(0,0)。测试集不变,得到表格
1 | 0 | 0 | 1 | 1 | 1b | ||||
0 | 0 | 0 | 0 | 0 | 0 | ||||
2010 | |||||||||
f2[0] | f2[1] | 迭代次数n | 平均准确率p-ave | 1-0 | 0-1 | δ | 耗时ms/次 | 耗时ms/199次 | 耗时 min/199 |
0.497492 | 0.5025 | 22657.76 | 0.5 | 0.5741 | 0.425879 | 9.00E-04 | 149.56 | 29762 | 0.496 |
0.457355 | 0.5426 | 24971.17 | 0.5 | 0.5842 | 0.415829 | 8.00E-04 | 162.87 | 32412 | 0.5402 |
0.5276 | 0.4724 | 27982.04 | 0.5 | 0.5678 | 0.432161 | 7.00E-04 | 182.14 | 36261 | 0.6044 |
0.482433 | 0.5176 | 31904.83 | 0.5 | 0.5854 | 0.414573 | 6.00E-04 | 205.76 | 40961 | 0.6827 |
0.51757 | 0.4824 | 37108.24 | 0.5 | 0.5704 | 0.429648 | 5.00E-04 | 238.67 | 47496 | 0.7916 |
统计收敛误差为5e-4时的分类情况
A | 16 | B | A | 22 | B | |||||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||
1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | |||
2 | 1 | 0 | 2 | 1 | 0 | 2 | 1 | 0 | 2 | 1 | 0 | |||
3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | |||
A | 89 | B | A | 72 | B | |||||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||
1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | |||
2 | 1 | 0 | 2 | 1 | 0 | 2 | 1 | 0 | 2 | 1 | 0 | |||
3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 |
16 | 2 | 013 |
22 | 23 | 01 |
89 | 02 | 13 |
72 | 023 | 1 |
有16次2被分为A,013被分为B。22次23被分为A,01被分为B。89次02被分为A,13被分为B。72次023被分为A,1被分为B。
00 | 161 | 38 | 4.236842 | |||
11 | 94 | 105 | 0.895238 |
所以(0,0)被161次分为A,38次被分为B。(1,1)被分类A和B的概率几乎相同。和网络1020 的情况是一致的。因此对网络1020和网络2010,(0,0)对A和B的相似性都是100%和50%。(1,1)对A和B的相似性也相同都是0,50%。所以(0,0)(1,1)被分为A和B的概率应该是一致的。但这个实验表明对(1,1)来说确实如此。但对(0,0)来说却取决于进样顺序,但即便顺序优先也只能被分到80%,而不是100%。
用同样的方法做网络0201
0 | 0 | 0 | 0 | 0 | 0 | ||||||||||||||||
1 | 0 | 0 | 1 | 1 | 1b | ||||||||||||||||
0201 | |||||||||||||||||||||
f2[0] | f2[1] | 迭代次数n | 平均准确率p-ave | 1-0 | 0-1 | δ | 耗时ms/次 | 耗时ms/199次 | |||||||||||||
0.4774 | 0.5226 | 22634 | 0.5 | 0.5691 | 0.430905 | 9.00E-04 | 149.2462 | 29700 | |||||||||||||
0.5176 | 0.4824 | 24983 | 0.5 | 0.5955 | 0.404523 | 8.00E-04 | 165.4422 | 32923 | |||||||||||||
0.5025 | 0.4975 | 27924 | 0.5 | 0.5967 | 0.403266 | 7.00E-04 | 180.196 | 35859 | |||||||||||||
0.4824 | 0.5176 | 31868 | 0.5 | 0.5917 | 0.408291 | 6.00E-04 | 205.2462 | 40859 | |||||||||||||
0.4724 | 0.5276 | 37290 | 0.5 | 0.5754 | 0.424623 | 5.00E-04 | 241.4271 | 48044 | |||||||||||||
A | 13 | B | A | 26 | B | ||||||||||||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||||||||
1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | ||||||||||
2 | 1 | 0 | 2 | 1 | 0 | 2 | 1 | 0 | 2 | 1 | 0 | ||||||||||
3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | ||||||||||
A | 87 | B | A | 73 | B | ||||||||||||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||||||||
1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | ||||||||||
2 | 1 | 0 | 2 | 1 | 0 | 2 | 1 | 0 | 2 | 1 | 0 | ||||||||||
3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | ||||||||||
13 | 2 | 013 |
26 | 23 | 01 |
87 | 02 | 13 |
73 | 023 | 1 |
有13次2被分为A,013被分为B。26次23被分为A,01被分为B。87次02被分为A,13被分为B。73次023被分为A,1被分为B。
00 | 160 | 39 | |
11 | 99 | 100 |
(0,0)被160次分为A,39次被分为B。(1,1)被分类A和B的概率几乎相同。
再用同样的方法做网络0102
0 | 0 | 0 | 0 | 0 | 0 | |||||||||||||||||
0 | 1 | 1 | 0 | 1 | 1b | |||||||||||||||||
0102 | ||||||||||||||||||||||
f2[0] | f2[1] | 迭代次数n | 平均准确率p-ave | 1-0 | 0-1 | δ | 耗时ms/次 | 耗时ms/199次 | ||||||||||||||
0.5226 | 0.477428 | 22665 | 0.5 | 0.598 | 0.402 | 9.00E-04 | 148.70352 | 29592 | ||||||||||||||
0.4975 | 0.502508 | 25023 | 0.5 | 0.5691 | 0.4309 | 8.00E-04 | 163.37186 | 32511 | ||||||||||||||
0.4875 | 0.512545 | 28031 | 0.5 | 0.5854 | 0.4146 | 7.00E-04 | 183.50754 | 36518 | ||||||||||||||
0.5075 | 0.492471 | 31693 | 0.5 | 0.5729 | 0.4271 | 6.00E-04 | 205.03015 | 40816 | ||||||||||||||
0.5075 | 0.49247 | 37077 | 0.5 | 0.5691 | 0.4309 | 5.00E-04 | 240.17085 | 47794 | ||||||||||||||
A | 18 | B | A | 24 | B | |||||||||||||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||||||||
1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | |||||||||||
2 | 1 | 0 | 2 | 1 | 0 | 2 | 1 | 0 | 2 | 1 | 0 | |||||||||||
3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | |||||||||||
A | 84 | B | A | 73 | B | |||||||||||||||||
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||||||||
1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | |||||||||||
2 | 1 | 0 | 2 | 1 | 0 | 2 | 1 | 0 | 2 | 1 | 0 | |||||||||||
3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | |||||||||||
18 | 1 | 023 |
24 | 13 | 02 |
84 | 01 | 23 |
73 | 013 | 2 |
有18次1被分为A,023被分为B。24次13被分为A,02被分为B。84次01被分为A,23被分为B。73次013被分为A,2被分为B。
00 | 157 | 42 | |
11 | 97 | 102 |
(0,0)被157次分为A,42次被分为B。(1,1)被分类A和B的概率几乎相同。
迭代次数n | 平均准确率p-ave | 1-0 | 0-1 | δ | |
1020 | 27871 | 0.5 | 0.5716 | 0.4284 | 7.00E-04 |
2010 | 27982 | 0.5 | 0.5678 | 0.4322 | 7.00E-04 |
0201 | 27924 | 0.5 | 0.5967 | 0.4033 | 7.00E-04 |
0102 | 28031 | 0.5 | 0.5854 | 0.4146 | 7.00E-04 |
观察这4组数据的迭代次数是很一致的。表明了差值结构
0 | 0 |
1 | 1b |
对于上下旋转和左右旋转这两种操作的对称性。也表明了这个结构无法区别(1,1),对(0,0)的分类有时序优先现象,但被分类为A或B的概率为4:1.