( 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 |
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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.