构造一个81*30*3的网络和一个有5个3*3卷积核的网络,分类mnist的0,1,2通过分类准确率数据比较卷积核的作用。
数据集是mnist的0,1,2将图片变成9*9,
无卷积核的裸网络的结构是
Mnist(0,1,2)---81---30---3----(1,0,0) || (0,1,0) || (0,0,1)
5个卷积核的网络的结构是
Mnist(0,1,2)---con3*3*5---7*7*5---30---3----(1,0,0) || (0,1,0) || (0,0,1)
用网络输出值与目标值的差值作为网络的收敛结束标准
|输出值-目标值|=δ
让δ分别等于1e-4到1e-8.每个δ收敛199次取平均值,共收敛了2*17*199次。分别记录对应每个δ的平均准确率,最大准确率,迭代次数和收敛时间和199测分类准确率的标准差。
无核网路的数据
无核 |
||||||||||
f2[0] |
f2[1] |
f2[2] |
迭代次数n |
平均准确率p-ave |
δ |
耗时ms/次 |
耗时ms/199次 |
耗时 min/199 |
最大值p-max |
标准差 |
7.44E-05 |
0.196045 |
0.803986 |
27833.26 |
0.982809 |
1.00E-04 |
547.1005 |
108896 |
1.814933 |
0.986336 |
0.00211 |
6.83E-05 |
0.175937 |
0.824082 |
29340.49 |
0.982986 |
9.00E-05 |
573.1156 |
114054 |
1.9009 |
0.986336 |
0.00188 |
5.85E-05 |
0.155833 |
0.844184 |
31737.18 |
0.983441 |
8.00E-05 |
618.3266 |
123052 |
2.050867 |
0.986336 |
0.001577 |
5.28E-05 |
0.140752 |
0.859263 |
35173.1 |
0.983954 |
7.00E-05 |
683.9799 |
136117 |
2.268617 |
0.986972 |
0.00156 |
4.35E-05 |
0.125671 |
0.874342 |
39840.33 |
0.984409 |
6.00E-05 |
768.4221 |
152917 |
2.548617 |
0.986972 |
0.001206 |
3.62E-05 |
0.145763 |
0.854247 |
44351.31 |
0.984731 |
5.00E-05 |
852.5075 |
169655 |
2.827583 |
0.987925 |
0.001112 |
2.74E-05 |
0.020133 |
0.979874 |
50897.51 |
0.985356 |
4.00E-05 |
983.9598 |
195809 |
3.263483 |
0.987607 |
0.000962 |
2.08E-05 |
0.050275 |
0.949732 |
58540.31 |
0.985867 |
3.00E-05 |
1116.874 |
222260 |
3.704333 |
0.988561 |
0.000888 |
1.38E-05 |
0.025142 |
0.974863 |
75020.01 |
0.986892 |
2.00E-05 |
1426.417 |
283873 |
4.731217 |
0.989514 |
0.000979 |
6.59E-06 |
0.030159 |
0.969844 |
105302.8 |
0.988173 |
1.00E-05 |
1998.704 |
397760 |
6.629333 |
0.990467 |
0.000959 |
5.49E-06 |
0.025133 |
0.97487 |
112076.2 |
0.988353 |
9.00E-06 |
2110.879 |
420065 |
7.001083 |
0.990149 |
0.000943 |
5.04E-06 |
0.010057 |
0.989946 |
117964.6 |
0.988484 |
8.00E-06 |
1685.663 |
335447 |
5.590783 |
0.990149 |
0.000934 |
4.40E-06 |
0.005031 |
0.994971 |
121447.5 |
0.988562 |
7.00E-06 |
2273.709 |
452468 |
7.541133 |
0.990467 |
0.000869 |
3.57E-06 |
0.00503 |
0.994972 |
131816.6 |
0.988819 |
6.00E-06 |
2486.296 |
494773 |
8.246217 |
0.990467 |
0.000776 |
3.06E-06 |
0.00503 |
0.994972 |
139246.6 |
0.988963 |
5.00E-06 |
2608.704 |
519148 |
8.652467 |
0.990785 |
0.000846 |
2.38E-06 |
3.57E-06 |
0.999998 |
151750.2 |
0.989309 |
4.00E-06 |
2832.452 |
563658 |
9.3943 |
0.991103 |
0.000704 |
1.69E-06 |
2.61E-06 |
0.999998 |
171937 |
0.989515 |
3.00E-06 |
3367.844 |
670218 |
11.1703 |
0.991738 |
0.00071 |
1.17E-06 |
1.70E-06 |
0.999999 |
192145.3 |
0.989838 |
2.00E-06 |
3892.382 |
774592 |
12.90987 |
0.992374 |
0.000737 |
5.27E-07 |
8.49E-07 |
0.999999 |
239406.2 |
0.990485 |
1.00E-06 |
4200.975 |
836004 |
13.9334 |
0.992056 |
0.00071 |
4.82E-07 |
7.58E-07 |
0.999999 |
242219.7 |
0.990493 |
9.00E-07 |
4819.492 |
959087 |
15.98478 |
0.992056 |
0.000757 |
4.10E-07 |
6.94E-07 |
1 |
252592.7 |
0.990489 |
8.00E-07 |
4682.965 |
931916 |
15.53193 |
0.992374 |
0.000747 |
3.61E-07 |
6.05E-07 |
1 |
264546.9 |
0.990627 |
7.00E-07 |
4006.704 |
797340 |
13.289 |
0.992374 |
0.000802 |
3.01E-07 |
5.15E-07 |
1 |
270883.3 |
0.990676 |
6.00E-07 |
4904.412 |
975989 |
16.26648 |
0.992691 |
0.000774 |
2.40E-07 |
4.36E-07 |
1 |
288360.4 |
0.990876 |
5.00E-07 |
5213.447 |
1037490 |
17.2915 |
0.992374 |
0.000763 |
1.96E-07 |
3.47E-07 |
1 |
298620.9 |
0.990921 |
4.00E-07 |
5504.915 |
1095486 |
18.2581 |
0.992691 |
0.000761 |
1.40E-07 |
2.64E-07 |
1 |
321430.4 |
0.991157 |
3.00E-07 |
5984.598 |
1190954 |
19.84923 |
0.992691 |
0.000749 |
9.61E-08 |
1.74E-07 |
1 |
352910.5 |
0.991388 |
2.00E-07 |
6380.844 |
1269793 |
21.16322 |
0.993327 |
0.00081 |
4.34E-08 |
8.83E-08 |
1 |
400271.1 |
0.991641 |
1.00E-07 |
7226.673 |
1438111 |
23.96852 |
0.993327 |
0.000805 |
3.55E-08 |
8.02E-08 |
1 |
418117.3 |
0.991618 |
9.00E-08 |
7554.206 |
1503293 |
25.05488 |
0.993327 |
0.000814 |
3.17E-08 |
7.15E-08 |
1 |
422921 |
0.991623 |
8.00E-08 |
7639.899 |
1520351 |
25.33918 |
0.993645 |
0.000817 |
2.78E-08 |
6.30E-08 |
1 |
431914.3 |
0.991701 |
7.00E-08 |
7826.965 |
1557578 |
25.95963 |
0.993963 |
0.000806 |
2.50E-08 |
5.31E-08 |
1 |
450995.3 |
0.99169 |
6.00E-08 |
8424.93 |
1676577 |
27.94295 |
0.993327 |
0.000812 |
1.92E-08 |
4.46E-08 |
1 |
451507.8 |
0.991741 |
5.00E-08 |
7867.839 |
1565708 |
26.09513 |
0.993327 |
0.000764 |
1.51E-08 |
3.63E-08 |
1 |
477393.6 |
0.991709 |
4.00E-08 |
8821.698 |
1755519 |
29.25865 |
0.993645 |
0.000898 |
1.07E-08 |
2.68E-08 |
1 |
500028.4 |
0.991799 |
3.00E-08 |
8999.995 |
1791000 |
29.85 |
0.993645 |
0.000833 |
7.50E-09 |
1.79E-08 |
1 |
525958.1 |
0.991767 |
2.00E-08 |
10181.58 |
2026156 |
33.76927 |
0.99428 |
0.000815 |
4.07E-09 |
8.80E-09 |
1 |
576699 |
0.991812 |
1.00E-08 |
10419.82 |
2073544 |
34.55907 |
0.993963 |
0.000785 |
5个卷积核网络的数据
5 |
||||||||||
f2[0] |
f2[1] |
f2[2] |
迭代次数n |
平均准确率p-ave |
δ |
耗时ms/次 |
耗时ms/199次 |
耗时 min/199 |
最大值p-max |
标准差 |
0.698479 |
0.286469 |
0.015158 |
35781.01 |
0.98182 |
1.00E-04 |
9274.779 |
1845703 |
30.76172 |
0.990149 |
0.005496 |
0.71355 |
0.251294 |
0.035248 |
37055.27 |
0.98186 |
9.00E-05 |
10043.37 |
1998647 |
33.31078 |
0.990785 |
0.005262 |
0.743701 |
0.231193 |
0.025191 |
39660.05 |
0.98263 |
8.00E-05 |
10321.43 |
2053985 |
34.23308 |
0.991103 |
0.005188 |
0.723605 |
0.251285 |
0.025183 |
43073.96 |
0.983444 |
7.00E-05 |
11203.3 |
2229457 |
37.15762 |
0.99142 |
0.004914 |
0.743706 |
0.226156 |
0.030199 |
48387.61 |
0.984043 |
6.00E-05 |
12841.87 |
2555539 |
42.59232 |
0.990785 |
0.00463 |
0.788931 |
0.165856 |
0.045265 |
54111.62 |
0.984663 |
5.00E-05 |
14461.2 |
2877799 |
47.96332 |
0.991738 |
0.003962 |
0.839182 |
0.110578 |
0.050282 |
58390.81 |
0.984872 |
4.00E-05 |
15125.22 |
3009936 |
50.1656 |
0.992056 |
0.004193 |
0.819085 |
0.125647 |
0.055299 |
69861.23 |
0.986394 |
3.00E-05 |
18088.98 |
3599726 |
59.99543 |
0.993645 |
0.003836 |
0.934664 |
0.025141 |
0.040216 |
84607.48 |
0.987275 |
2.00E-05 |
21809.21 |
4340032 |
72.33387 |
0.992691 |
0.003321 |
0.884417 |
0.040209 |
0.075384 |
113518.7 |
0.989006 |
1.00E-05 |
29023.62 |
5775703 |
96.26172 |
0.993009 |
0.002595 |
0.884418 |
0.035183 |
0.080408 |
116764.5 |
0.989011 |
9.00E-06 |
31420.88 |
6252772 |
104.2129 |
0.993645 |
0.002452 |
0.924619 |
0.030157 |
0.045232 |
121199.8 |
0.988969 |
8.00E-06 |
32736.33 |
6514563 |
108.5761 |
0.993963 |
0.002788 |
0.864318 |
0.015081 |
0.120607 |
127616.1 |
0.989206 |
7.00E-06 |
33793.67 |
6724962 |
112.0827 |
0.993009 |
0.002299 |
0.874369 |
0.035181 |
0.090456 |
133287.6 |
0.989308 |
6.00E-06 |
35072.14 |
6979369 |
116.3228 |
0.993963 |
0.002649 |
0.844219 |
0.03518 |
0.120606 |
148576.1 |
0.989966 |
5.00E-06 |
38453.66 |
7652282 |
127.538 |
0.99428 |
0.002038 |
0.909546 |
0.010054 |
0.080405 |
153811.6 |
0.990119 |
4.00E-06 |
40236.49 |
8007064 |
133.4511 |
0.993645 |
0.001917 |
0.783919 |
0.020103 |
0.195981 |
174867 |
0.989859 |
3.00E-06 |
45900.82 |
9134269 |
152.2378 |
0.99428 |
0.002644 |
0.778894 |
0.020102 |
0.201006 |
191543.2 |
0.990271 |
2.00E-06 |
50249.96 |
9999758 |
166.6626 |
0.993963 |
0.002102 |
0.758794 |
0.010051 |
0.231156 |
230501 |
0.990403 |
1.00E-06 |
59820.19 |
11904219 |
198.4037 |
0.993963 |
0.002415 |
0.653266 |
0.015076 |
0.331659 |
240200.4 |
0.990157 |
9.00E-07 |
62553.32 |
12448114 |
207.4686 |
0.994598 |
0.00262 |
0.663317 |
0.010051 |
0.326633 |
248517.1 |
0.990466 |
8.00E-07 |
64427.78 |
12821141 |
213.6857 |
0.99428 |
0.002311 |
0.678392 |
0.020101 |
0.301508 |
257205 |
0.990272 |
7.00E-07 |
68003.96 |
13532795 |
225.5466 |
0.993963 |
0.002239 |
0.723618 |
0.015076 |
0.261307 |
263480.2 |
0.990697 |
6.00E-07 |
67587.88 |
13450013 |
224.1669 |
0.995234 |
0.002069 |
0.61809 |
4.36E-07 |
0.38191 |
275964 |
0.99074 |
5.00E-07 |
71423.62 |
14213308 |
236.8885 |
0.994916 |
0.002054 |
0.59799 |
0.025126 |
0.376885 |
293300.9 |
0.990467 |
4.00E-07 |
75939.62 |
15111996 |
251.8666 |
0.99428 |
0.002173 |
0.562814 |
2.61E-07 |
0.437186 |
310972.9 |
0.990822 |
3.00E-07 |
80267.45 |
15973228 |
266.2205 |
0.994916 |
0.002226 |
0.547739 |
0.01005 |
0.442211 |
336482.8 |
0.990976 |
2.00E-07 |
87635.89 |
17439546 |
290.6591 |
0.995234 |
0.002104 |
0.532663 |
0.015075 |
0.452261 |
382286.8 |
0.990991 |
1.00E-07 |
99956.42 |
19891345 |
331.5224 |
0.994598 |
0.002179 |
0.492462 |
0.005025 |
0.502513 |
388770.6 |
0.990823 |
9.00E-08 |
101827 |
20263594 |
337.7266 |
0.994916 |
0.002112 |
0.462312 |
0.005025 |
0.532663 |
390518.9 |
0.990989 |
8.00E-08 |
102264.8 |
20350700 |
339.1783 |
0.994598 |
0.002224 |
0.452261 |
0.005025 |
0.542714 |
400328.2 |
0.990715 |
7.00E-08 |
104427.7 |
20781121 |
346.352 |
0.994916 |
0.002378 |
0.40201 |
0.015075 |
0.582915 |
423798.3 |
0.991336 |
6.00E-08 |
111411.3 |
22170863 |
369.5144 |
0.995234 |
0.002112 |
0.417085 |
0.015075 |
0.567839 |
437013.5 |
0.991344 |
5.00E-08 |
113981.6 |
22682349 |
378.0392 |
0.994916 |
0.002024 |
0.407035 |
0.01005 |
0.582915 |
459736.3 |
0.991328 |
4.00E-08 |
120307.9 |
23941283 |
399.0214 |
0.994598 |
0.001805 |
0.407035 |
0.005025 |
0.58794 |
470944.5 |
0.991096 |
3.00E-08 |
122076.8 |
24293292 |
404.8882 |
0.995869 |
0.001853 |
0.356784 |
0.015075 |
0.628141 |
502589.2 |
0.991781 |
2.00E-08 |
131185.6 |
26105935 |
435.0989 |
0.994916 |
0.001486 |
0.346734 |
0.005025 |
0.648241 |
572687 |
0.991658 |
1.00E-08 |
150921.6 |
30033399 |
500.5567 |
0.994598 |
0.001607 |
将平均准确率和最大准确率以及标准差列出来
无核 |
5个核 |
无核 |
5个核 |
无核 |
5个核 |
||||
δ |
平均准确率p-ave |
平均准确率p-ave |
最大值p-max |
最大值p-max |
标准差 |
标准差 |
|||
1.00E-04 |
0.982809 |
0.98182 |
0.986336 |
0.990149 |
0.00211 |
0.005496 |
0.383995 |
||
9.00E-05 |
0.982986 |
0.98186 |
0.986336 |
0.990785 |
0.00188 |
0.005262 |
0.357206 |
||
8.00E-05 |
0.983441 |
0.98263 |
0.986336 |
0.991103 |
0.001577 |
0.005188 |
0.303999 |
||
7.00E-05 |
0.983954 |
0.983444 |
0.986972 |
0.99142 |
0.00156 |
0.004914 |
0.31742 |
||
6.00E-05 |
0.984409 |
0.984043 |
0.986972 |
0.990785 |
0.001206 |
0.00463 |
0.260549 |
||
5.00E-05 |
0.984731 |
0.984663 |
0.987925 |
0.991738 |
0.001112 |
0.003962 |
0.280694 |
||
4.00E-05 |
0.985356 |
0.984872 |
0.987607 |
0.992056 |
0.000962 |
0.004193 |
0.229515 |
||
3.00E-05 |
0.985867 |
0.986394 |
0.988561 |
0.993645 |
0.000888 |
0.003836 |
0.23158 |
||
2.00E-05 |
0.986892 |
0.987275 |
0.989514 |
0.992691 |
0.000979 |
0.003321 |
0.294673 |
||
1.00E-05 |
0.988173 |
0.989006 |
0.990467 |
0.993009 |
0.000959 |
0.002595 |
0.369499 |
||
9.00E-06 |
0.988353 |
0.989011 |
0.990149 |
0.993645 |
0.000943 |
0.002452 |
0.384622 |
||
8.00E-06 |
0.988484 |
0.988969 |
0.990149 |
0.993963 |
0.000934 |
0.002788 |
0.334908 |
||
7.00E-06 |
0.988562 |
0.989206 |
0.990467 |
0.993009 |
0.000869 |
0.002299 |
0.378022 |
||
6.00E-06 |
0.988819 |
0.989308 |
0.990467 |
0.993963 |
0.000776 |
0.002649 |
0.293088 |
||
5.00E-06 |
0.988963 |
0.989966 |
0.990785 |
0.99428 |
0.000846 |
0.002038 |
0.41509 |
||
4.00E-06 |
0.989309 |
0.990119 |
0.991103 |
0.993645 |
0.000704 |
0.001917 |
0.367068 |
||
3.00E-06 |
0.989515 |
0.989859 |
0.991738 |
0.99428 |
0.00071 |
0.002644 |
0.268445 |
||
2.00E-06 |
0.989838 |
0.990271 |
0.992374 |
0.993963 |
0.000737 |
0.002102 |
0.350831 |
||
1.00E-06 |
0.990485 |
0.990403 |
0.992056 |
0.993963 |
0.00071 |
0.002415 |
0.293812 |
||
9.00E-07 |
0.990493 |
0.990157 |
0.992056 |
0.994598 |
0.000757 |
0.00262 |
0.28912 |
||
8.00E-07 |
0.990489 |
0.990466 |
0.992374 |
0.99428 |
0.000747 |
0.002311 |
0.323109 |
||
7.00E-07 |
0.990627 |
0.990272 |
0.992374 |
0.993963 |
0.000802 |
0.002239 |
0.358189 |
||
6.00E-07 |
0.990676 |
0.990697 |
0.992691 |
0.995234 |
0.000774 |
0.002069 |
0.374171 |
||
5.00E-07 |
0.990876 |
0.99074 |
0.992374 |
0.994916 |
0.000763 |
0.002054 |
0.371331 |
||
4.00E-07 |
0.990921 |
0.990467 |
0.992691 |
0.99428 |
0.000761 |
0.002173 |
0.35034 |
||
3.00E-07 |
0.991157 |
0.990822 |
0.992691 |
0.994916 |
0.000749 |
0.002226 |
0.336619 |
||
2.00E-07 |
0.991388 |
0.990976 |
0.993327 |
0.995234 |
0.00081 |
0.002104 |
0.384796 |
||
1.00E-07 |
0.991641 |
0.990991 |
0.993327 |
0.994598 |
0.000805 |
0.002179 |
0.369567 |
||
9.00E-08 |
0.991618 |
0.990823 |
0.993327 |
0.994916 |
0.000814 |
0.002112 |
0.385203 |
||
8.00E-08 |
0.991623 |
0.990989 |
0.993645 |
0.994598 |
0.000817 |
0.002224 |
0.367109 |
||
7.00E-08 |
0.991701 |
0.990715 |
0.993963 |
0.994916 |
0.000806 |
0.002378 |
0.338951 |
||
6.00E-08 |
0.99169 |
0.991336 |
0.993327 |
0.995234 |
0.000812 |
0.002112 |
0.384475 |
||
5.00E-08 |
0.991741 |
0.991344 |
0.993327 |
0.994916 |
0.000764 |
0.002024 |
0.377483 |
||
4.00E-08 |
0.991709 |
0.991328 |
0.993645 |
0.994598 |
0.000898 |
0.001805 |
0.497674 |
||
3.00E-08 |
0.991799 |
0.991096 |
0.993645 |
0.995869 |
0.000833 |
0.001853 |
0.449515 |
||
2.00E-08 |
0.991767 |
0.991781 |
0.99428 |
0.994916 |
0.000815 |
0.001486 |
0.548764 |
||
1.00E-08 |
0.991812 |
0.991658 |
0.993963 |
0.994598 |
0.000785 |
0.001607 |
0.488578 |
观察平均准确率
可以看到无核的裸网络和含卷积核的网络的平均性能其实相差不大,
在δ>1e-6的区间含卷积核的网络的平均性能>无核的裸网络;
在δ<1e-6的区间无核的裸网络的平均性能>含卷积核的网络;
第二步比较标准差
这个很明显,网络增加了卷积核只是使网络平均性能的标准差变大了,也就是无核的裸网络的性能要比增加了卷积核的网络要稳定。裸网络的标准差只有含卷积核网络的1/3左右。
最后比较最大性能
因为裸网络和含有卷积核的网络的平均性能差不多,但是含卷积核网路的标准差更大显然使得含卷积核网络的最大性能也更大。
因此,卷积核只是增加了网络的性能的标准差,让网络变得更不稳定,增加了得到更大准确率的概率当然也增加了得到更差准确率的概率。但就平均性能而言和无核的裸网络平均性能相差不大,但却慢的多。
至少对这个实验而言一个结构简单的网络的性能要远好于含有多个卷积核的复杂网络。
***这篇文的实验数据已经上传到我的资源