(2**0.5,3**0.5)—100*10*2—(1,0)(0,1)
(2**0.5,5**0.5)—100*10*2—(1,0)(0,1)
(2**0.5,e)—100*10*2—(1,0)(0,1)
(2**0.5,pi)—100*10*2—(1,0)(0,1)
(2**0.5,6**0.5)—100*10*2—(1,0)(0,1)
(2**0.5,7**0.5)—100*10*2—(1,0)(0,1)
(2**0.5,8**0.5)—100*10*2—(1,0)(0,1)
(2**0.5,10**0.5)—100*10*2—(1,0)(0,1)
做了8個網絡分別用來分類2**0.5和3**0.5，5**0.5，e，pi，6**0.5，7**0.5，8**0.5，10**0.5.
每個無理數保留3萬位有效數字，10個數字一張圖片，前2500張用於訓練後500張用於測試。比較這幾個無理數之間的差異有什麼不同。
首先統計平均分類準確率pave
|
2500-3000 |
2**0.5 |
|||||||
|
3**0.5 |
5**0.5 |
e |
pi |
6**0.5 |
7**0.5 |
8**0.5 |
10**0.5 |
|
|
δ |
平均準確率p-ave |
平均準確率p-ave |
平均準確率p-ave |
平均準確率p-ave |
平均準確率p-ave |
平均準確率p-ave |
平均準確率p-ave |
平均準確率p-ave |
|
0.5 |
0.500452261 |
0.500140704 |
0.499537688 |
0.49918593 |
0.499919598 |
0.499728643 |
0.500271357 |
0.499974874 |
|
0.4 |
0.517994975 |
0.514286432 |
0.483246231 |
0.513592965 |
0.516512563 |
0.528879397 |
0.485668342 |
0.522889447 |
|
0.3 |
0.519864322 |
0.524417085 |
0.498226131 |
0.517949749 |
0.519909548 |
0.526909548 |
0.491758794 |
0.523060302 |
|
0.2 |
0.513638191 |
0.509175879 |
0.486874372 |
0.509286432 |
0.519301508 |
0.52119598 |
0.491236181 |
0.518477387 |
|
0.1 |
0.512447236 |
0.513547739 |
0.493236181 |
0.509276382 |
0.51518593 |
0.511758794 |
0.491582915 |
0.516567839 |
|
0.01 |
0.504768844 |
0.510100503 |
0.491236181 |
0.502487437 |
0.502869347 |
0.504517588 |
0.49521608 |
0.509271357 |
|
0.001 |
0.506643216 |
0.508743719 |
0.49361809 |
0.498085427 |
0.502261307 |
0.506427136 |
0.497633166 |
0.505562814 |
|
9.00E-04 |
0.504467337 |
0.509894472 |
0.492979899 |
0.499030151 |
0.502321608 |
0.505979899 |
0.49598995 |
0.506663317 |
|
8.00E-04 |
0.504919598 |
0.507306533 |
0.491341709 |
0.49938191 |
0.503160804 |
0.50440201 |
0.495321608 |
0.507899497 |
|
7.00E-04 |
0.504733668 |
0.509356784 |
0.492432161 |
0.499482412 |
0.502025126 |
0.505592965 |
0.497889447 |
0.506592965 |
|
6.00E-04 |
0.506145729 |
0.510477387 |
0.492135678 |
0.500778894 |
0.501924623 |
0.506211055 |
0.497115578 |
0.507733668 |
|
5.00E-04 |
0.506638191 |
0.508623116 |
0.494291457 |
0.501095477 |
0.501969849 |
0.505361809 |
0.497437186 |
0.505005025 |
|
4.00E-04 |
0.507050251 |
0.507512563 |
0.491351759 |
0.499376884 |
0.501497487 |
0.504653266 |
0.496472362 |
0.506386935 |
|
3.00E-04 |
0.504934673 |
0.508844221 |
0.491201005 |
0.499226131 |
0.501934673 |
0.505407035 |
0.49638191 |
0.505763819 |
|
2.00E-04 |
0.506919598 |
0.508211055 |
0.492668342 |
0.498939698 |
0.501844221 |
0.505346734 |
0.497130653 |
0.506899497 |
|
1.00E-04 |
0.504577889 |
0.507728643 |
0.493246231 |
0.499738693 |
0.503150754 |
0.50679397 |
0.498025126 |
0.507075377 |
畫成圖
可以看到pave分成兩類，一類是小於50%的有pi，8**0.5和e。pi的pave略小於50%，表明2**0.5和pi的數字分佈差異最小，最不易區分。另一類是pave顯著大於50%，有6**0.5，5**0.5，和7**0.5，10**0.5，3**0.5.其中5**0.5的值最大，而7**0.5，10**0.5，3**0.5這3條線幾乎纏繞在一起。表明這3個數，數字的分佈規律接近。
再比較迭代次數的差異
|
2500-3000 |
2**0.5 |
|||||||
|
3**0.5 |
5**0.5 |
e |
pi |
6**0.5 |
7**0.5 |
8**0.5 |
10**0.5 |
|
|
δ |
迭代次數n |
迭代次數n |
迭代次數n |
迭代次數n |
迭代次數n |
迭代次數n |
迭代次數n |
迭代次數n |
|
0.5 |
19.33668342 |
21.46231156 |
17.51758794 |
19.78894472 |
19.83919598 |
18.32160804 |
18.30150754 |
18.15075377 |
|
0.4 |
11770.69849 |
10664.17085 |
11189.55779 |
13534.35678 |
12302.9799 |
11250.29648 |
14480.20603 |
12549.19095 |
|
0.3 |
57086.41709 |
30062.04523 |
34580.47236 |
60393.05528 |
46272.32663 |
27982.51256 |
82839.9799 |
37837.63317 |
|
0.2 |
135191.0503 |
120788.809 |
116589.8241 |
155078.8492 |
144089.191 |
138026.407 |
149974.5226 |
143811.2462 |
|
0.1 |
188887.3668 |
188465.4372 |
178663.6633 |
223942.9347 |
204056.1357 |
193853.9497 |
215478.4573 |
202345.005 |
|
0.01 |
301379.1156 |
301602.6281 |
299744.0854 |
331224.8744 |
303747.5226 |
309335.9899 |
330023.4724 |
313953.8342 |
|
0.001 |
421724.9246 |
426455.4925 |
427566.1055 |
454390.4271 |
426886.8844 |
432921.1508 |
471719.2412 |
443662.1759 |
|
9.00E-04 |
422781.603 |
427780.2462 |
423875.9045 |
463541.8593 |
432401.9849 |
450963.1407 |
486230.7136 |
445343.2412 |
|
8.00E-04 |
430972.1859 |
436584.196 |
452748.3869 |
469522.0704 |
438084.6633 |
463982.2513 |
493815.2764 |
459795.2462 |
|
7.00E-04 |
442785.7789 |
448578.2864 |
452554.5729 |
478613.8342 |
448150.6734 |
470797.5126 |
503312.9095 |
469001.3166 |
|
6.00E-04 |
455381.5578 |
463744.0653 |
459869.4724 |
499163.2211 |
466124.7437 |
481626.995 |
519613.5628 |
474531.4271 |
|
5.00E-04 |
467498.3266 |
485689.8392 |
466761.0905 |
507353.9698 |
489677.3568 |
503013.1407 |
544202.0251 |
495688.9698 |
|
4.00E-04 |
488769.1357 |
502967.1859 |
489836.603 |
536803.005 |
502668.8794 |
517509.5075 |
568515.9347 |
514145.794 |
|
3.00E-04 |
508326.191 |
523964.7186 |
528504.8643 |
564641.9497 |
518025.1709 |
556086.8894 |
606002.7236 |
552131.4673 |
|
2.00E-04 |
564547.0955 |
567855.5276 |
569002.3518 |
606663.7236 |
562929.1206 |
607040.6281 |
658516.7538 |
600759.8191 |
|
1.00E-04 |
646090.0402 |
660761.2312 |
660039.6482 |
703975.5025 |
655903.1106 |
706416.8894 |
793831.5176 |
655716.3869 |
只有8**0.5的迭代次數顯著的大些，而其他的網絡的迭代次數相差很小，區別不大。完全相同的兩個對象無法被分成兩類，迭代次數越大表明二者差異越小，表明2**0.5和8**0.5的差異是最小的。
無理數的數據來源
https://www.wolframalpha.com/input/?i=x%5E2-1
N[sqr(2),30000]