分类9个无理数并比较他们之间的分布差异

(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个网络分别用来分类2**0.5和3**0.5,5**0.5,e,pi,6**0.5,7**0.5,8**0.5,10**0.5.

每个无理数保留3万位有效数字,10个数字一张图片,前2500张用于训练后500张用于测试。比较这几个无理数之间的差异有什么不同。

 

首先统计平均分类准确率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

平均准确率p-ave

平均准确率p-ave

平均准确率p-ave

平均准确率p-ave

平均准确率p-ave

平均准确率p-ave

平均准确率p-ave

平均准确率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

 

画成图

可以看到pave分成两类,一类是小于50%的有pi,8**0.5和e。pi的pave略小于50%,表明2**0.5和pi的数字分布差异最小,最不易区分。另一类是pave显著大于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这3条线几乎缠绕在一起。表明这3个数,数字的分布规律接近。

 

再比较迭代次数的差异

 

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

迭代次数n

迭代次数n

迭代次数n

迭代次数n

迭代次数n

迭代次数n

迭代次数n

迭代次数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的迭代次数显著的大些,而其他的网络的迭代次数相差很小,区别不大。完全相同的两个对象无法被分成两类,迭代次数越大表明二者差异越小,表明2**0.5和8**0.5的差异是最小的。

 

无理数的数据来源

https://www.wolframalpha.com/input/?i=x%5E2-1

N[sqr(2),30000]

 

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