用二分类神经网络估算多分类神经网络迭代次数的经验公式
神經(jīng)網(wǎng)絡(luò)的迭代次數(shù)n和收斂誤差δ總能滿足關(guān)系式
一個(gè)多分類網(wǎng)絡(luò)的參數(shù)a至少大于對應(yīng)二分類網(wǎng)絡(luò)的參數(shù)a的和，參數(shù)b的絕對值約等于對應(yīng)多個(gè)二分類網(wǎng)絡(luò)b的絕對值的最大值
本文再次驗(yàn)證這個(gè)關(guān)系式，這次用的13*13的圖片。
這次同樣統(tǒng)計(jì)了11個(gè)網(wǎng)絡(luò)，包括6個(gè)二分類網(wǎng)絡(luò)(0,1),(0,2),(0,3) ,(1,2) ,(1,3) ,(2,3),4個(gè)三分類網(wǎng)絡(luò)(0,1,2), (0,1,3), (0,2,3), (1,2,3)和1個(gè)4分類網(wǎng)絡(luò)(0,1,2,3).隱藏層節(jié)點(diǎn)數(shù)是30個(gè)，網(wǎng)絡(luò)結(jié)構(gòu)為
統(tǒng)計(jì)了0.5到1e-5共25個(gè)收斂誤差，每個(gè)收斂誤差測量199次，計(jì)算迭代次數(shù)的平均值，參數(shù)設(shè)置方案
static double ret=0.1; //學(xué)習(xí)率
static double weix=1000;
在收斂誤差一致的前提下得到數(shù)據(jù)為
| 0*1 | 0*2 | 0*3 | 1*2 | 1*3 | 2*3 | 0*1*2 | 0*1*3 | 0*2*3 | 1*2*3 | 0*1*2*3 | |
| δ | 迭代次數(shù)n | 迭代次數(shù)n | 迭代次數(shù)n | 迭代次數(shù)n | 迭代次數(shù)n | 迭代次數(shù)n | 迭代次數(shù)n | 迭代次數(shù)n | 迭代次數(shù)n | 迭代次數(shù)n | 迭代次數(shù)n |
| 0.5 | 6.733668 | 6.432161 | 7.934673 | 8.105528 | 6.547739 | 7.467337 | 109.2663 | 109.0603 | 140.809 | 140 | 286.9347 |
| 0.4 | 92.45226 | 130.2613 | 136.5025 | 137.2563 | 134.5025 | 157.0101 | 307.6884 | 316.1558 | 371.1407 | 422.5025 | 650.7136 |
| 0.3 | 127.5427 | 172.8995 | 182.9749 | 173.9648 | 173.4171 | 201.2362 | 363.2161 | 386.794 | 430.4874 | 507.8995 | 761.2261 |
| 0.2 | 164.5779 | 206.1508 | 215.9698 | 207.4975 | 228.5477 | 247 | 486.7789 | 526.3317 | 545.0754 | 601.2111 | 953.6181 |
| 0.1 | 212.9347 | 238.7638 | 273.7688 | 288.1307 | 289.2462 | 302.5427 | 725.7286 | 750.8492 | 666.0804 | 782.4573 | 1395.291 |
| 0.01 | 492.3568 | 499.1156 | 554.3065 | 577.5578 | 482.9045 | 709.6884 | 1537.714 | 1534.779 | 1748.864 | 1838.754 | 3527.402 |
| 0.001 | 1749.422 | 1239.317 | 1380.513 | 1259.834 | 1394.201 | 1586.437 | 5503.407 | 5288.035 | 5229.523 | 6207.176 | 13372.29 |
| 9.00E-04 | 1780.794 | 1269.829 | 1397.392 | 1301.698 | 1470.759 | 1627.312 | 6156.075 | 5747.99 | 5879.628 | 7184.457 | 14574.46 |
| 8.00E-04 | 1821.508 | 1300.221 | 1427.181 | 1365.206 | 1533.668 | 1651.271 | 7151.367 | 6412.387 | 6693.231 | 8668.538 | 15870.73 |
| 7.00E-04 | 1899.854 | 1343.427 | 1506.97 | 1473.92 | 1610.92 | 1687.844 | 7645.467 | 7032.508 | 7704.322 | 9852.95 | 17837.65 |
| 6.00E-04 | 2079.211 | 1429.427 | 1609.658 | 1579.015 | 1821.266 | 1718.256 | 8192.618 | 7752.04 | 8268.915 | 11306.83 | 20169.53 |
| 5.00E-04 | 2311.196 | 1606.09 | 1732.824 | 1725.075 | 2135.714 | 1819.724 | 9627.784 | 9097.573 | 8758.709 | 13330.59 | 23113.58 |
| 4.00E-04 | 2782.191 | 1866.683 | 1938.271 | 1922.266 | 2507.186 | 2001.879 | 12197.05 | 11707.81 | 9768.915 | 15206.4 | 27319.71 |
| 3.00E-04 | 3527.92 | 2105.075 | 2160.06 | 2119.327 | 2915.271 | 2356.864 | 14151.15 | 14440.69 | 11423.27 | 19837.41 | 32116.34 |
| 2.00E-04 | 4940.513 | 2290.633 | 2726.658 | 3916.864 | 4277.864 | 3197.91 | 18573.44 | 16839.37 | 14609.41 | 27853.5 | 42627.17 |
| 1.00E-04 | 6286.261 | 2953.437 | 4698.231 | 5288.95 | 6137.719 | 6983.533 | 28370.97 | 30612.63 | 21892.46 | 42267.14 | 65067.37 |
| 9.00E-05 | 6798.804 | 3054.482 | 4973.291 | 5504.528 | 7110.623 | 7555.291 | 30314.35 | 32981.02 | 22845.19 | 44865.28 | 70412.39 |
| 8.00E-05 | 8178.804 | 3228.673 | 5308.236 | 6164.126 | 8411.477 | 9249.191 | 32905.06 | 35526.37 | 24426.3 | 47631.96 | 73361.66 |
| 7.00E-05 | 9112.482 | 3473.719 | 5719.261 | 7559.583 | 9241.116 | 11221.53 | 34837.63 | 38546.76 | 26047.61 | 51185.5 | 78739.91 |
| 6.00E-05 | 11061.05 | 3819.296 | 6124.709 | 9005.462 | 9889.945 | 12914.13 | 37407.02 | 42679.86 | 27660.34 | 54867.78 | 84971.76 |
| 5.00E-05 | 13265.71 | 4103.749 | 6718.025 | 9591.985 | 10255.71 | 15455.26 | 40785.15 | 47235.65 | 29441.82 | 58825.92 | 94605.2 |
| 4.00E-05 | 15076.91 | 4494.03 | 7403.312 | 10655.01 | 11230.55 | 17489.82 | 46504.49 | 52647.85 | 31827.34 | 65334.03 | 106320.3 |
| 3.00E-05 | 15231.33 | 4951.95 | 8844.97 | 11024.6 | 15005 | 19989.93 | 53708.39 | 60466.93 | 36090.11 | 77109.76 | 122205.8 |
| 2.00E-05 | 15480.19 | 5992.995 | 11193.69 | 12763.09 | 20777.64 | 22714.18 | 63942.11 | 72226.67 | 42875.96 | 90485.73 | 150295.9 |
| 1.00E-05 | 25031.74 | 9386.864 | 18406.62 | 16025.06 | 32662.04 | 27580.57 | 84369.78 | 93154.76 | 51661.85 | 124660 | 206286.5 |
擬合得到
| 0*1 | 32.47802450723911*δ**-0.5831015031864778 | |||||||||
| 0.9686458706264336?? ******? 決定系數(shù) r**2 | ||||||||||
| 0*2 | 51.30919270911507*δ**-0.44791865995565994 | |||||||||
| 0.9886193583905813?? ******? 決定系數(shù) r**2 | ||||||||||
| 0*3 | 47.886005223510566*δ**-0.4951534676480396 | |||||||||
| 0.956391073533652?? ******? 決定系數(shù) r**2 | ||||||||||
| 1*2 | 44.770770031148054*δ**-0.5161391642217052 | |||||||||
| 0.9560196957829404?? ******? 決定系數(shù) r**2 | ||||||||||
| 1*3 | 39.14550161580376*δ**-0.5559753593232657 | |||||||||
| 0.9180999873192752?? ******? 決定系數(shù) r**2 | ||||||||||
| 2*3 | 43.241682284703*δ**-0.5540998301120651 | |||||||||
| 0.9002198444886652?? ******? 決定系數(shù) r**2 | ||||||||||
| a | 計(jì)算值/實(shí)驗(yàn)值 | b | 計(jì)算值/實(shí)驗(yàn)值 | |||||||
| 13*13 | 0*1*2 | 144.2610575835931*δ**-0.5632352720039274 | 127 | 0.881944 | 0.58 | 1.035714 | ||||
| 0.9851774619520932?? ******? 決定系數(shù) r**2 | ||||||||||
| 0*1*3 | 141.49290439392576*δ**-0.5701088860390905 | 118 | 0.836879 | 0.58 | 1.017544 | |||||
| 0.976530648984943?? ******? 決定系數(shù) r**2 | ||||||||||
| 0*2*3 | 188.3901208060544*δ**-0.5060309899441509 | 141 | 0.75 | 0.55 | 1.1 | |||||
| 0.9658468622014262?? ******? 決定系數(shù) r**2 | ||||||||||
| 1*2*3 | 173.6071390053005*δ**-0.5788764903846232 | 126 | 0.728324 | 0.55 | 0.964912 | |||||
| 0.9822308629582532?? ******? 決定系數(shù) r**2 | ||||||||||
| 0*1*2*3 | 310.10754292910167*δ**-0.5713600303084961 | 256 | 0.825806 | 0.58 | 1.017544 | |||||
| 0.9922829022306022?? ******? 決定系數(shù) r**2 | ||||||||||
| 平均 | 0.8 | 1.02 | ||||||||
如計(jì)算
計(jì)算得到a的值是實(shí)驗(yàn)值的0.82，b的值是實(shí)驗(yàn)值的1.01.
整體平均a的計(jì)算值是實(shí)驗(yàn)值的0.8，b的計(jì)算值是實(shí)驗(yàn)值的1.02.
11*11的網(wǎng)絡(luò)，a的計(jì)算值是實(shí)驗(yàn)值的約0.78，b的計(jì)算值約為實(shí)驗(yàn)值的0.98。
9*9的網(wǎng)絡(luò)，a的計(jì)算值是實(shí)驗(yàn)值的約0.9，b的計(jì)算值是實(shí)驗(yàn)值的約0.96。
總結(jié)
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