比较搜索难度曲线5s1-4和4s1
在行列可自由变换的条件下，平面上的5点结构只有34个,4点结构有16个
(A,B)---6*n*2---(0,1)(1,0)
让B全是0。当收敛误差为7e-4，收敛199次取迭代次数平均值。让隐藏层节点数n分别为10，15，20，25，30，40，50，60，70，80，90，100.测5s1和4s1和4s2的迭代次数。
如当n=30时得到迭代次数为
| 4s1 | 4s2 | 5s1 | ||||
| 4202.005 | 5532.598 | 1 | 3741.754 | 18 | 22838.29 | |
| 10464.07 | 13538.93 | 2 | 3931.854 | 19 | 23604.21 | |
| 12464.74 | 16116.55 | 3 | 4698.186 | 20 | 24190.2 | |
| 12975.07 | 16497.91 | 4 | 8242.307 | 21 | 25271.88 | |
| 24480.26 | 20072.22 | 5 | 9316.829 | 22 | 25362.72 | |
| 27187.2 | 22153.55 | 6 | 9595.523 | 23 | 25830.95 | |
| 27969.19 | 23041.28 | 7 | 9881.854 | 24 | 26147.98 | |
| 33727.32 | 28303.47 | 8 | 11477.18 | 25 | 27140.27 | |
| 23485.43 | 29617.7 | 9 | 11842.01 | 26 | 28920.35 | |
| 26175.72 | 31989.87 | 10 | 12293.91 | 27 | 29236.75 | |
| 27994.4 | 35060.94 | 11 | 13314.01 | 28 | 29119.55 | |
| 31024.71 | 39153.08 | 12 | 13784.47 | 29 | 32283.36 | |
| 42767.27 | 39544.08 | 13 | 16289.34 | 30 | 33423.06 | |
| 35176.25 | 44463.89 | 14 | 19031.78 | 31 | 33575.85 | |
| 41257.21 | 51943.55 | 15 | 19999.14 | 32 | 40765.7 | |
| 55639.52 | 70138.06 | 16 | 21272.81 | 33 | 46256.03 | |
| 17 | 22932.26 | 34 | 66022.36 |
将5s1归一化，通过结构加法
得到5s1-4
| 30 | ||
| 5s1-4 | 4s1 | 4s2 |
| 1.98 | 1 | 1 |
| 3.52 | 2.49 | 2.45 |
| 3.38 | 2.97 | 2.91 |
| 4.04 | 3.09 | 2.98 |
| 5.61 | 5.83 | 3.63 |
| 6.55 | 6.47 | 4 |
| 6.04 | 6.66 | 4.16 |
| 6.1 | 8.03 | 5.12 |
| 6.33 | 5.59 | 5.35 |
| 6.99 | 6.23 | 5.78 |
| 5.56 | 6.66 | 6.34 |
| 5.34 | 7.38 | 7.08 |
| 9.21 | 10.2 | 7.15 |
| 6.47 | 8.37 | 8.04 |
| 9.1 | 9.82 | 9.39 |
| 14.1 | 13.2 | 12.7 |
比较这3条搜索难度曲线，显然5s1-4和4s1非常相似。
其他各组数据
| 10 | 15 | 20 | 25 | ||||||||||||
| 5s1-4 | 4s1 | 4s2 | 5s1-4 | 4s1 | 4s2 | 5s1-4 | 4s1 | 4s2 | 5s1-4 | 4s1 | 4s2 | ||||
| 1 | 1.71 | 1 | 1 | 1.88 | 1 | 1 | 1.94 | 1 | 1 | 1.99 | 1 | 1 | |||
| 2 | 2.41 | 1.82 | 1.81 | 2.92 | 2.14 | 2.07 | 3.21 | 2.32 | 2.22 | 3.42 | 2.43 | 2.37 | |||
| 3 | 2.53 | 2.2 | 2.18 | 2.99 | 2.58 | 2.45 | 3.2 | 2.81 | 2.71 | 3.37 | 2.93 | 2.82 | |||
| 4 | 3.15 | 2.61 | 2.6 | 3.63 | 2.88 | 2.75 | 3.86 | 3.02 | 2.94 | 4.01 | 3.1 | 2.96 | |||
| 5 | 3.29 | 3.53 | 2.19 | 4.25 | 4.43 | 2.68 | 4.85 | 5.06 | 3.16 | 5.34 | 5.58 | 3.4 | |||
| 6 | 4.02 | 3.95 | 2.41 | 5.12 | 4.98 | 2.99 | 5.78 | 5.69 | 3.48 | 6.29 | 6.2 | 3.78 | |||
| 7 | 3.42 | 3.65 | 2.36 | 4.47 | 4.84 | 2.98 | 5.16 | 5.66 | 3.53 | 5.72 | 6.25 | 3.92 | |||
| 8 | 3.36 | 4.42 | 2.78 | 4.44 | 5.78 | 3.66 | 5.17 | 6.89 | 4.33 | 5.76 | 7.58 | 4.76 | |||
| 9 | 3.46 | 2.98 | 2.93 | 4.6 | 3.94 | 3.73 | 5.36 | 4.65 | 4.48 | 5.97 | 5.22 | 4.92 | |||
| 10 | 4.27 | 3.7 | 3.57 | 5.4 | 4.67 | 4.39 | 6.12 | 5.34 | 5.02 | 6.71 | 5.88 | 5.44 | |||
| 11 | 3.28 | 3.63 | 3.57 | 4.22 | 4.81 | 4.61 | 4.84 | 5.62 | 5.43 | 5.31 | 6.31 | 5.94 | |||
| 12 | 3.73 | 4.47 | 4.41 | 4.53 | 5.71 | 5.36 | 4.95 | 6.53 | 6.2 | 5.21 | 7.08 | 6.7 | |||
| 13 | 4.69 | 5.07 | 3.45 | 6.44 | 6.95 | 4.65 | 7.61 | 8.38 | 5.73 | 8.64 | 9.47 | 6.49 | |||
| 14 | 4.3 | 4.74 | 4.74 | 5.31 | 6.13 | 5.88 | 5.86 | 7.14 | 6.85 | 6.29 | 7.94 | 7.55 | |||
| 15 | 5.21 | 5.16 | 5.14 | 6.81 | 6.9 | 6.55 | 7.82 | 8.14 | 7.82 | 8.66 | 9.12 | 8.66 | |||
| 16 | 9.19 | 8.29 | 8.23 | 11.4 | 10.3 | 9.79 | 12.7 | 11.7 | 11.2 | 13.6 | 12.8 | 12 |
| 30 | 40 | 50 | 60 | ||||||||||||
| 5s1-4 | 4s1 | 4s2 | 5s1-4 | 4s1 | 4s2 | 5s1-4 | 4s1 | 4s2 | 5s1-4 | 4s1 | 4s2 | ||||
| 1.98 | 1 | 1 | 1.98 | 1 | 1 | 1 | 1.97 | 1 | 1 | 1.94 | 1 | 1 | |||
| 3.52 | 2.49 | 2.45 | 3.65 | 2.52 | 2.48 | 2 | 3.73 | 2.58 | 2.52 | 3.76 | 2.59 | 2.51 | |||
| 3.38 | 2.97 | 2.91 | 3.42 | 3.02 | 2.91 | 3 | 3.45 | 3.05 | 2.96 | 3.42 | 3.03 | 2.93 | |||
| 4.04 | 3.09 | 2.98 | 4.1 | 3.06 | 2.97 | 4 | 4.12 | 3.06 | 3 | 4.11 | 3.02 | 2.95 | |||
| 5.61 | 5.83 | 3.63 | 6.05 | 6.29 | 3.81 | 5 | 6.39 | 6.66 | 3.97 | 6.63 | 6.93 | 4.03 | |||
| 6.55 | 6.47 | 4 | 7.02 | 6.85 | 4.19 | 6 | 7.38 | 7.23 | 4.37 | 7.65 | 7.44 | 4.38 | |||
| 6.04 | 6.66 | 4.16 | 6.56 | 7.26 | 4.47 | 7 | 6.96 | 7.74 | 4.72 | 7.27 | 8.1 | 4.81 | |||
| 6.1 | 8.03 | 5.12 | 6.66 | 8.67 | 5.46 | 8 | 7.12 | 9.27 | 5.74 | 7.48 | 9.65 | 5.82 | |||
| 6.33 | 5.59 | 5.35 | 6.93 | 6.11 | 5.88 | 9 | 7.38 | 6.63 | 6.4 | 7.7 | 6.94 | 6.78 | |||
| 6.99 | 6.23 | 5.78 | 7.53 | 6.69 | 6.19 | 10 | 7.94 | 7.13 | 6.66 | 8.26 | 7.46 | 6.89 | |||
| 5.56 | 6.66 | 6.34 | 5.95 | 7.12 | 6.73 | 11 | 6.2 | 7.45 | 6.99 | 6.36 | 7.58 | 7.04 | |||
| 5.34 | 7.38 | 7.08 | 5.43 | 7.75 | 7.38 | 12 | 5.47 | 8.03 | 7.68 | 5.43 | 8.08 | 7.76 | |||
| 9.21 | 10.2 | 7.15 | 10.3 | 11.2 | 8.02 | 13 | 11.1 | 12.1 | 8.86 | 11.7 | 12.7 | 9.43 | |||
| 6.47 | 8.37 | 8.04 | 6.74 | 9.01 | 8.68 | 14 | 6.91 | 9.52 | 9.26 | 6.98 | 9.86 | 9.57 | |||
| 9.1 | 9.82 | 9.39 | 9.85 | 10.7 | 10.3 | 15 | 10.5 | 11.5 | 11.2 | 10.9 | 12.1 | 11.8 | |||
| 14.1 | 13.2 | 12.7 | 14.9 | 14 | 13.4 | 16 | 15.5 | 14.7 | 14.2 | 16 | 15.2 | 14.6 |
| 70 | 80 | 90 | 100 | |||||||||||
| 5s1-4 | 4s1 | 4s2 | 5s1-4 | 4s1 | 4s2 | 5s1-4 | 4s1 | 4s2 | 5s1-4 | 4s1 | 4s2 | |||
| 1.91 | 1 | 1 | 1.88 | 1 | 1 | 1.84 | 1 | 1 | 1.8 | 1 | 1 | |||
| 3.77 | 2.59 | 2.51 | 3.77 | 2.59 | 2.5 | 3.74 | 2.59 | 2.48 | 3.7 | 2.57 | 2.46 | |||
| 3.37 | 3.03 | 2.91 | 3.34 | 3.01 | 2.89 | 3.27 | 2.98 | 2.85 | 3.21 | 2.96 | 2.81 | |||
| 4.09 | 2.98 | 2.96 | 4.09 | 2.95 | 2.93 | 4.05 | 2.94 | 2.93 | 4.02 | 2.91 | 2.91 | |||
| 6.82 | 7.14 | 4.06 | 7.01 | 7.35 | 4.05 | 7.15 | 7.57 | 4.03 | 7.29 | 7.76 | 3.99 | |||
| 7.84 | 7.65 | 4.41 | 8.07 | 7.83 | 4.4 | 8.24 | 8.01 | 4.35 | 8.43 | 8.2 | 4.3 | |||
| 7.49 | 8.36 | 4.88 | 7.73 | 8.67 | 4.91 | 7.9 | 8.95 | 4.92 | 8.08 | 9.23 | 4.9 | |||
| 7.75 | 9.99 | 5.91 | 8.06 | 10.3 | 5.93 | 8.29 | 10.6 | 5.89 | 8.53 | 10.9 | 5.85 | |||
| 7.97 | 7.22 | 7.11 | 8.24 | 7.49 | 7.45 | 8.43 | 7.75 | 7.77 | 8.61 | 8 | 8.1 | |||
| 8.52 | 7.67 | 7.19 | 8.8 | 7.98 | 7.47 | 9.02 | 8.25 | 7.73 | 9.22 | 8.48 | 7.99 | |||
| 6.47 | 7.64 | 7.05 | 6.58 | 7.66 | 6.99 | 6.62 | 7.62 | 6.89 | 6.66 | 7.53 | 6.76 | |||
| 5.36 | 8.08 | 7.85 | 5.29 | 8.07 | 7.87 | 5.19 | 8.03 | 7.86 | 5.06 | 7.96 | 7.81 | |||
| 12.2 | 13.3 | 9.99 | 12.7 | 13.8 | 10.5 | 13.2 | 14.3 | 11 | 13.6 | 14.7 | 11.4 | |||
| 7.04 | 10.2 | 9.96 | 7.11 | 10.4 | 10.3 | 7.1 | 10.7 | 10.6 | 7.08 | 10.9 | 10.8 | |||
| 11.3 | 12.5 | 12.4 | 11.7 | 13 | 12.9 | 12 | 13.5 | 13.5 | 12.2 | 13.9 | 14 | |||
| 16.4 | 15.5 | 15.1 | 16.8 | 15.8 | 15.6 | 17.1 | 16.3 | 16.1 | 17.5 | 16.6 | 16.6 |
所有这些数据5s1-4和4s1之间都有这样的相似性，如n=10
n=100
所以这意味这由5s1-4近似4s1的可行性，如果这个假设成立也就意味这由（n+1）s1-n近似ns1的可行性。比较n=30时，4s1-3和3s1的数据
| 3s1 | 4s1-3 |
| 1 | 4.84 |
| 2.03 | 5.78 |
| 2.02 | 5.58 |
| 1.83 | 6.99 |
| 2.89 | 7.52 |
| 3.37 | 10.4 |
（n+1）s1-n≈ns1 ，n越大两条曲线的近似性越好
因此有
| … | ||
| ↓ | ||
| 6s1 | ⇋ | 6s2 |
| ↓ | ||
| 5s1 | ⇋ | 5s2 |
| ↓ | ||
| 4s1 | ⇋ | 4s2 |
| ↓ | ||
| 3s1 | ⇋ | 3s2 |
| ↓ | ||
| 2s1 | ⇋ | 2s2 |
横向，ns1⇋ns2，ns1和ns2可通过归一化严格相互转化
纵向，（n+1）s1-n≈ns1 ，n越大两条曲线的近似性越好
原文地址：https://blog.csdn.net/georgesale/article/details/142715356
免责声明：本站文章内容转载自网络资源，如本站内容侵犯了原著者的合法权益，可联系本站删除。更多内容请关注自学内容网（zxcms.com）！