作一個5分類網絡分類mnist的0，1，2，3，4.用3*3的卷積核，卷積核數量從1個到36個，收斂標準爲1e-4，每個網絡收斂199次，共收斂了36*199次。比較平均分類準確率，來判斷這個網絡到底應該用多少個卷積核。
實驗得到的數據
|
con |
f2[0] |
f2[1] |
f2[2] |
f2[3] |
f2[4] |
迭代次數n |
平均準確率p-ave |
δ |
耗時ms/次 |
耗時ms/199次 |
耗時 min/199 |
最大值p-max |
平均值標準差 |
|
1 |
0.3969992 |
3.98E-05 |
0.0503128 |
0.4673393 |
0.0854662 |
104470.93 |
0.9590255 |
1.00E-04 |
7423.3367 |
1477250 |
24.620833 |
0.9680872 |
0.0043556 |
|
2 |
0.5326588 |
4.04E-05 |
0.0603636 |
0.371877 |
0.0352327 |
91750.819 |
0.9702316 |
1.00E-04 |
12125.719 |
2413018 |
40.216967 |
0.9780113 |
0.0035651 |
|
3 |
0.6381764 |
0.0100856 |
0.0452943 |
0.2713923 |
0.035238 |
86584.065 |
0.9738819 |
1.00E-04 |
16815.226 |
3346247 |
55.770783 |
0.9820977 |
0.0040536 |
|
4 |
0.6381738 |
4.73E-05 |
0.1106123 |
0.2211455 |
0.0302111 |
86691.578 |
0.9767782 |
1.00E-04 |
22660.191 |
4509378 |
75.1563 |
0.9832652 |
0.0037532 |
|
5 |
0.6331478 |
0.0100947 |
0.075442 |
0.2512897 |
0.0302126 |
86251.307 |
0.9778187 |
1.00E-04 |
28140.724 |
5600006 |
93.333433 |
0.9844328 |
0.0038567 |
|
6 |
0.663292 |
0.0201439 |
0.0804656 |
0.2110933 |
0.0251883 |
87147.04 |
0.9782626 |
1.00E-04 |
34999.673 |
6964940 |
116.08233 |
0.9856003 |
0.0049456 |
|
7 |
0.6431916 |
0.0352167 |
0.1055901 |
0.1809471 |
0.0352373 |
88852.809 |
0.979523 |
1.00E-04 |
40875.286 |
8134201 |
135.57002 |
0.9875462 |
0.0036779 |
|
8 |
0.5929492 |
0.030195 |
0.1357355 |
0.2211434 |
0.0201619 |
89753.98 |
0.9798262 |
1.00E-04 |
47459.693 |
9444484 |
157.40807 |
0.9873516 |
0.0041034 |
|
9 |
0.7034819 |
0.0301944 |
0.0854927 |
0.1608519 |
0.0201675 |
87998.749 |
0.9798575 |
1.00E-04 |
54462.874 |
10838112 |
180.6352 |
0.9867679 |
0.0034211 |
|
10 |
0.6130412 |
0.0603421 |
0.1457836 |
0.1759217 |
0.0050887 |
89349.714 |
0.9803728 |
1.00E-04 |
59108.151 |
11762539 |
196.04232 |
0.9857949 |
0.0035238 |
|
11 |
0.5879192 |
0.0402465 |
0.1407561 |
0.2060706 |
0.0251908 |
90482.065 |
0.9803962 |
1.00E-04 |
67296.894 |
13392090 |
223.2015 |
0.9865733 |
0.0038802 |
|
12 |
0.6331418 |
0.0502906 |
0.0955387 |
0.2161208 |
0.0050907 |
89244.975 |
0.9797597 |
1.00E-04 |
70763.487 |
14081940 |
234.699 |
0.9875462 |
0.0044283 |
|
13 |
0.592942 |
0.0955135 |
0.1508071 |
0.1407538 |
0.020162 |
89329.613 |
0.9808901 |
1.00E-04 |
75231.442 |
14971057 |
249.51762 |
0.9869624 |
0.0033256 |
|
14 |
0.6230928 |
0.0804369 |
0.0854918 |
0.1909943 |
0.0201645 |
90552.005 |
0.9797753 |
1.00E-04 |
84153.206 |
16746520 |
279.10867 |
0.987157 |
0.0045751 |
|
15 |
0.5929442 |
0.0754167 |
0.1156359 |
0.1909996 |
0.0251897 |
93018.387 |
0.9802105 |
1.00E-04 |
91327.648 |
18174212 |
302.90353 |
0.9865733 |
0.0039654 |
|
16 |
0.5627995 |
0.0904876 |
0.1658809 |
0.1558236 |
0.0251893 |
92548.422 |
0.9797861 |
1.00E-04 |
94837.101 |
18872624 |
314.54373 |
0.9867679 |
0.0057113 |
|
17 |
0.5376756 |
0.1005396 |
0.1307096 |
0.1909953 |
0.0402658 |
94034.508 |
0.9804715 |
1.00E-04 |
102810.7 |
20459334 |
340.9889 |
0.98813 |
0.0039014 |
|
18 |
0.5226047 |
0.1055641 |
0.16588 |
0.1759218 |
0.0302125 |
93370.829 |
0.9794135 |
1.00E-04 |
108527.4 |
21596970 |
359.9495 |
0.9865733 |
0.0057292 |
|
19 |
0.4773845 |
0.1055662 |
0.1457795 |
0.2311939 |
0.040265 |
92563.859 |
0.9798262 |
1.00E-04 |
114088.12 |
22703535 |
378.39225 |
0.9865733 |
0.004553 |
|
20 |
0.5376743 |
0.1156157 |
0.1106088 |
0.1909971 |
0.0452859 |
93299.754 |
0.9796404 |
1.00E-04 |
121038.73 |
24086713 |
401.44522 |
0.987157 |
0.0045705 |
|
21 |
0.5226023 |
0.1206402 |
0.1357329 |
0.1960206 |
0.0251851 |
97356.729 |
0.9799376 |
1.00E-04 |
134315.59 |
26728803 |
445.48005 |
0.9867679 |
0.004487 |
|
22 |
0.5075321 |
0.1005449 |
0.1206582 |
0.2261668 |
0.045284 |
96326.749 |
0.9803376 |
1.00E-04 |
137166.5 |
27296139 |
454.93565 |
0.9869624 |
0.0044399 |
|
23 |
0.5025043 |
0.1507855 |
0.115633 |
0.1909954 |
0.0402654 |
97184.352 |
0.9800403 |
1.00E-04 |
145956.26 |
29045295 |
484.08825 |
0.9865733 |
0.0036915 |
|
24 |
0.4824062 |
0.1357126 |
0.1658767 |
0.2010443 |
0.015138 |
99128.06 |
0.9799279 |
1.00E-04 |
153790.74 |
30604360 |
510.07267 |
0.9867679 |
0.0040233 |
|
25 |
0.5276279 |
0.1507869 |
0.1156348 |
0.165873 |
0.040264 |
100264.15 |
0.9801645 |
1.00E-04 |
161833.56 |
32204878 |
536.74797 |
0.9869624 |
0.0039724 |
|
26 |
0.4924545 |
0.1206439 |
0.1457783 |
0.196021 |
0.0452845 |
99471.93 |
0.9799572 |
1.00E-04 |
168385.3 |
33508709 |
558.47848 |
0.9875462 |
0.0041268 |
|
27 |
0.4874312 |
0.1407408 |
0.1608527 |
0.1859737 |
0.0251922 |
102755.69 |
0.9799474 |
1.00E-04 |
178808.95 |
35582981 |
593.04968 |
0.9867679 |
0.0041321 |
|
28 |
0.4623089 |
0.1759113 |
0.1457781 |
0.1759214 |
0.0402655 |
100270.1 |
0.97939 |
1.00E-04 |
187493.72 |
37311250 |
621.85417 |
0.9859895 |
0.0049753 |
|
29 |
0.4723593 |
0.165862 |
0.1457793 |
0.1708976 |
0.0452927 |
104338.68 |
0.9799953 |
1.00E-04 |
197608.21 |
39324034 |
655.40057 |
0.9861841 |
0.0038264 |
|
30 |
0.4321601 |
0.1658635 |
0.1709047 |
0.1909934 |
0.040261 |
103310.58 |
0.979434 |
1.00E-04 |
201993.4 |
40196709 |
669.94515 |
0.987157 |
0.0040633 |
|
31 |
0.4673351 |
0.155815 |
0.1457778 |
0.1658707 |
0.0653866 |
102941.5 |
0.9791524 |
1.00E-04 |
208387.09 |
41469030 |
691.1505 |
0.9877408 |
0.0045501 |
|
32 |
0.517581 |
0.1105933 |
0.1055844 |
0.236215 |
0.0302168 |
101947.78 |
0.9791221 |
1.00E-04 |
213261.81 |
42439106 |
707.31843 |
0.9861841 |
0.0041763 |
|
33 |
0.4371863 |
0.1507924 |
0.1759286 |
0.1809449 |
0.0553372 |
107287.02 |
0.9798115 |
1.00E-04 |
231864.87 |
46141110 |
769.0185 |
0.9861841 |
0.0041173 |
|
34 |
0.4924578 |
0.1306948 |
0.1106064 |
0.2161159 |
0.0503128 |
107965.09 |
0.9797509 |
1.00E-04 |
236180.71 |
46999979 |
783.33298 |
0.9865733 |
0.0039793 |
|
35 |
0.5075315 |
0.1206431 |
0.1256796 |
0.150798 |
0.0955321 |
107841.65 |
0.9792522 |
1.00E-04 |
246869.31 |
41097532 |
684.95887 |
0.9859895 |
0.0047116 |
|
36 |
0.5125546 |
0.1457666 |
0.1307065 |
0.1608499 |
0.0503141 |
107752.64 |
0.9797509 |
1.00E-04 |
255624.7 |
50869316 |
847.82193 |
0.9867679 |
0.0042543 |
將pave畫成圖
網絡峯值性能出現在con=13，峯值性能爲0.9808901.當con<13時隨着卷積核數量的增加網絡性能迅速增加，當con>13隨着卷積核數量的增加網絡性能持續的減弱。
這張圖是con=10到con=36的圖片，當con=36時平均性能只有峯值性能的99.88%，但是耗時確是峯值耗時3.39倍，也就是用了3.39倍的時間但性能卻下降了0.12%。
這個實驗再次清晰的表明了卷積核數量存在最優值，卷積核數量超過最優值以後，繼續增加捲積核會導致網絡性能下降。
再比較前面的實驗數據，用3*3的卷積核二分類0和2的卷積核最優值是4個，而10分類是最優值是47個，這次實驗的5分類最優值13個。
可以用這3組數據得到一個近似的估算卷積核數量最優值的方法
Con=0.475*x**2-0.3250000000000002*x+2.7500000000000004
- ****** 決定係數 r**2
|
con |
分類數x |
|
|
|
||
|
2 |
4 |
|
|
3 |
6.05 |
|
|
4 |
9.05 |
|
|
5 |
13 |
|
|
6 |
17.9 |
|
|
7 |
23.75 |
|
|
8 |
30.55 |
|
|
9 |
38.3 |
|
|
10 |
47 |
用這個方法估算一個6分類網絡的卷積核數量的最優值大約爲18個。