In a more general sense, calculating the displacement distance and assumptions

(A,B)---m*n*k---(1,0)(0,1)

移位距离和假设

用神经网络分类A和B,把参与分类的A和B中的数字看作是组成A和B的粒子,分类的过程就是让A和B中的粒子互相交换位置,寻找最短移位路径的过程.而熵H与最短移位距离和成正比,迭代次数n与熵H成反比.

Summary of shift rules

每个粒子移位一次,位置重合不移位,Single shift distance if 1为底等于1-If the element value is 0The base is the element itself.

用神经网络分类8123.This picture starts with1为底,按照移位距离和假设8123The displacement distance and s为4-0.8-0.1-0.2-0.3=2.6

have been obtained in previous experiments

	771	122
δ	迭代次数n	迭代次数n
5.00E-04	28114.19	25862.05
4.00E-04	34375.59	31524.1
3.00E-04	44667.95	41011.36
2.00E-04	64534.3	59270.11
1.00E-04	123420.9	112397.9
S	2	3

If the shift distance is 2和3When the convergence error is 1e-4The average number of iterations when 123420和112397.According to the shift distance and inversely proportional to the number of iterations,8123The number of iterations should be in 123420和112397之间.

The experimental data is

	8123
δ	迭代次数n
5.00E-04	28525.63
4.00E-04	34343.1
3.00E-04	44964.48
2.00E-04	65561.12
1.00E-04	124472.5
s	2.6

The value is greater than the estimated value,This assumption can introduce errors when dealing with non-binarization problems,初略估算s=2.6The number of iterations may be 116806,Then the error brought by this algorithm is approx6.5%.

Go ahead and test this hypothesis

分类8114,8123和8222.因为这3The shift distance of the group and both are2.6,Then assume this3The number of iterations for groups should be the same.

得到的数据为

	8123	8222	8114
δ	迭代次数n	迭代次数n	迭代次数n
5.00E-04	28525.63	28458.6	28146.99
4.00E-04	34343.1	35125.9	34483.39
3.00E-04	44964.48	45007.68	44535.1
2.00E-04	65561.12	65602.42	64962.66
1.00E-04	124472.5	124651.6	123716.1
s	2.6	2.6	2.6

比较这3The lines are very consistent,This is quite hypothetical.

So use the shift distance and assumptions to estimate this3The number of iterations for group pictures,The estimated number of iterations is too small,约有7%的误差.

Compare this experimental data with the previous experimental data

	981	871	971	881	861	771	122	961	875
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	迭代次数n
5.00E-04	34219.01	34553.02	28229.22	27843.89	28270.21	28114.19	25862.05	25523.99	25117.39
4.00E-04	41899.68	41568.85	34548.15	34511.79	34803.25	34375.59	31524.1	30958.15	31102.23
3.00E-04	53474.56	54287.27	44497.27	44407.41	45065.05	44667.95	41011.36	40262.78	40239.05
2.00E-04	77797.83	78173.77	64693.36	64832.42	64707.93	64534.3	59270.11	59096.97	58618.7
1.00E-04	148175	146473.4	123601.3	122874.1	123288	123420.9	112397.9	113446.1	111994.6
s	1	1	2	2	2	2	3	3	3
	851	951	866	777	941	854	931	921	911
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	迭代次数n
5.00E-04	25288.76	23904.73	23868.01	23579.5	22959.57	22738.92	22166.65	22094.36	23575.86
4.00E-04	31347.55	28978.03	28820.87	28965.92	27774.2	27653.1	27290.48	27253.6	28991.81
3.00E-04	40549.93	38252.24	37659.14	37460.82	35993.35	36072.61	35639.73	35340.25	37399.98
2.00E-04	59255.58	55426.48	54661.18	54804.67	52950.71	53116.99	51890.25	52155.43	54335.16
1.00E-04	114094.8	106880.8	106599.8	106112.6	101146.2	100986.2	100158	98502.28	102787.2
s	3	4	4	4	5	5	6	7	8
	8123
δ	迭代次数n
5.00E-04	28525.63
4.00E-04	34343.1
3.00E-04	44964.48
2.00E-04	65561.12
1.00E-04	124472.5
s	2.6