神经网络训练集的数量最少可以是多少个？

(mnist 0 ,2)---81*30*2---(1,0)(0,1)

用81*30*2的网络分类mnist的0和2。让训练集的数量n分别等于5000,4500,4000,3500,3000,2500,2000,1500,1000,500,400,300,200,100,50,40,30,20,10,5,4,3,2，共22个值。看看训练集的大小对分类结果到底有什么影响。

让收敛标准δ等于0.5到1e-5的25个值，每个值收敛199次，取平均值。因此共收敛了25*199*22次，首先比较迭代次数

	5000	4500	4000	3500	3000	2500	2000	1500	1000	500	400	300	200	100	50	40	30	20	10	5	4	3	2
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	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	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
0.5	8.8140704	9.1909548	8.8190955	8.4572864	10.462312	8.7035176	9.5175879	8.6582915	7.6582915	7.8743719	8.2562814	8.5678392	8.3919598	8.6633166	9.9145729	9.6432161	8.9949749	8.8994975	8.7135678	7.8643216	8.9346734	8.1155779	9.5778894
0.4	212.50251	211.55779	212.45226	212.45729	211.60804	211.91457	210.79899	210.69347	211.86935	211.48744	211.85427	211.43719	212.01508	210.1809	224.24121	233.84422	211.24121	189.16583	165.1809	147.88442	117.20101	91.221106	119.82412
0.3	267.47739	267.42714	268.35176	268.56784	267.55779	269.72362	266.93467	268.24121	268.46231	267.29146	268.93467	269.24623	269.44724	281.8794	295.1005	298.44724	268.88945	242.32161	211.32161	188.78894	153.60302	121.27136	156.47236
0.2	326.42714	326.14573	327.85427	327.41709	325.33166	325.94472	324.11558	324.00503	324.77387	326.1206	326.42211	323.15578	328.9196	321.23116	349.75879	343.45226	320.94975	290.57286	257.50251	230.33668	190.32161	151.46734	194.96482
0.1	412.12563	411.66834	412.71859	410.34673	410.65327	410.30653	411.80402	410.62814	412.46734	408.71859	409.21608	411.61307	407.94975	394.58291	419	418.37186	393.68844	358.02513	320.76884	296.84925	254.45226	208.36181	261.35176
0.01	687.25126	687.90452	688.32161	687.19095	687.64824	688.83417	688.84422	688.79899	687.38693	690.05528	687.34673	746.40704	658.22111	718.0402	776.55276	789.8794	801.15075	677.35678	668.50754	833.62312	841.84925	750.77387	895.1407
0.001	1432.1206	1434.809	1441.7588	1434.9146	1442.1206	1436.9548	1434.4925	1436.6633	1439.6432	1381.8291	1351.3769	1382.3518	1439.1457	1734.9648	1956.9548	1823	2014.5628	1685.5377	1984.206	4369.7337	5041.6734	4713.5025	5422.1608
9.00E-04	1456.1608	1460.7035	1451.5025	1447.8794	1450.7638	1451.6382	1455.809	1444.603	1446.0503	1433.6281	1400.4221	1446.2764	1478.4422	1850.0201	2017.0603	1923.8794	2103.8693	1782.3216	2089.8543	4776.5578	5523.2915	5151.5779	5912.6583
8.00E-04	1476.2613	1492.6734	1478.2111	1486.1206	1486.3518	1477.9899	1484.794	1490.6734	1486.2714	1503.6583	1462.2111	1503.4372	1508.5628	1926.8543	2131.3467	2013.9397	2179.4322	1878.5628	2247.1206	5199.6935	6138.7889	5759.2764	6572.0251
7.00E-04	1562.4925	1578.1809	1524.7538	1562.9548	1556.1608	1526.4623	1569.2261	1572.1508	1570.8241	1552.3719	1535.598	1539.4573	1623.6683	2041.7839	2241.4874	2113.6131	2288.2261	2009.7437	2436.6281	5852.8593	6856.0302	6487.9548	7382.8392
6.00E-04	1739.8291	1716.8945	1745.4774	1733.9598	1718.3116	1754.9849	1721.1156	1699.397	1714.6734	1623.407	1632.6834	1626.1709	1741.9899	2227.2714	2385.3819	2282.7186	2426.2462	2200.0302	2700.0251	6668.9397	7915.3166	7379.3266	8446.5829
5.00E-04	1973.005	1991.0854	1968.3417	1962	1989.9196	1976.9749	1995.7688	1994.6131	2007.6884	1738.794	1787.8191	1736.4925	1850.9849	2408.9146	2565.0653	2418.397	2598.3417	2403.1859	3030.9598	7778.8342	9280.5276	8705.9397	9959.9749
4.00E-04	2199.6985	2193.7286	2195.7588	2192.794	2184.9045	2189.3869	2191.4975	2193.0352	2201.9598	1940.0804	1865.8492	1871.5176	1984.8342	2651.4824	2796.8392	2655.2764	2810.8945	2701.7035	3445.3518	9422.6482	11411.593	10665.794	12130.487
3.00E-04	2357.8593	2367.0251	2301.6683	2364.794	2349.7487	2354.7035	2351.6784	2351.1558	2301.7688	2177.2362	2005.8693	2060.0804	2207.9397	2942.4322	3126.8141	2977.7337	3145.4523	3169.4975	4142.6784	12117.422	14843.985	13859.246	15798.899
2.00E-04	2720.0704	2721.3166	2717.8593	2737.2362	2737.4372	2715.6683	2713.7085	2732.9548	2527.1859	2447.2764	2347.0352	2390.0101	2499.3266	3416.6834	3686.5126	3535.0704	3741.2864	4028.8191	5430.0754	17564.221	21180.206	20099.714	22702.196
1.00E-04	3232.2312	3191.9095	3224.3719	3190.7437	3248.3216	3148.5427	3200.6935	3304.2915	3395.0653	3193.397	2914.0704	3068.1508	3079.5779	4259.1256	4887.2161	4723.9045	4932.3518	6167.8593	8921.2915	32454.814	40394.704	38274.864	43284.08
9.00E-05	3349.2261	3476.3116	3344.7538	3373.3668	3361.7286	3324.5126	3373.2161	3428.5327	3499.7186	3322.9146	3007.0754	3188.1206	3188.6332	4415.5879	5132.4824	4889.8342	5198.3869	6468.3417	9665.5729	36499.598	44655.573	42241.442	47656.889
8.00E-05	3504.804	3539.9899	3547.4472	3479.1859	3502.3317	3529.0352	3541.2161	3583.8392	3615.9598	3445.8593	3137.7688	3344.6533	3257.5779	4584.7839	5404.0704	5146.9397	5539.6683	7175.2663	10511.402	40534.156	49344.457	47385.558	53222.025
7.00E-05	3653.1156	3726.9246	3729.2261	3702.8442	3707.4874	3714.6734	3705.407	3880.5628	3774.4221	3564.2111	3340.1407	3468.0905	3436.4523	4746.5226	5731.8693	5404.6935	5891.3467	7878.804	11638.96	45481.166	56305.769	53515.744	60549.729
6.00E-05	3929.4673	3915.0854	3890.6834	3941.4774	3911.0854	3927.5075	3873.5075	4095.3065	4017.4673	3833.4372	3450.1106	3639.8593	3599.5879	4975.2362	6067.2362	5844.7387	6293.2462	8663.5678	13157.673	52073.91	64788.075	61990.95	69664.422
5.00E-05	4192.794	4190.3719	4227.0352	4170.392	4180.2211	4163.2261	4207.1759	4520.6633	4331.5678	4129.7889	3613.4673	3988.2814	3755.5176	5264.3819	6548.7538	6378.5025	6874.4372	9644.2513	14924.668	62609.307	77956.347	73659.774	82517.106
4.00E-05	4523.6181	4493.3668	4508.0302	4535.5276	4529.1859	4519.6784	4620.0302	5113.2563	4856.0603	4433.5176	3885.9095	4225.0653	3962.5025	5648.9246	7172.7688	7061.9447	7608.0553	11173.799	17715.101	76565.05	95891.744	91528.302	102076.31
3.00E-05	5188.9347	5054.4322	5068.2915	5110.2714	5073.4472	5049.0955	5369.0754	5866.1307	5367.0352	4857.8492	4231.0251	4689.5276	4313.9397	6265.4874	8135.8241	8043.603	8751.8191	13786.422	22453.111	100730.41	124742.73	119835.06	133002.63
2.00E-05	6466.5226	6381.6181	6361.9196	6518.8241	6220.7437	5920.0905	6424.4724	7012.2814	6266.6131	5553.2764	4841.196	5318.4824	4772.1206	7124.3417	9987.8442	9547.4975	10778.769	17824.211	30159.804	145903.06	184341.3	175563.38	196519.59
1.00E-05	8313.608	8557.6583	8151.3869	8708.9548	8502.7638	8496.1608	8866.8945	10567.688	8471.8291	7002.201	5876.4221	6555.9296	5697.799	9080.402	13627.683	13488.05	15949.482	29974.482	52077.955	282663.62	352860.69	340905.93	379743.73

神经网络训练集的数量最少可以是多少个？

迭代次数的最大值出现在训练集n的数量等于2的时候，而迭代次数最小的值出现在约n=200的位置。

神经网络训练集的数量最少可以是多少个？

训练集n=5000到n=200的图。也就是迭代次数随着训练集n的数量的减小，是先减小后增大的。

再比较分类准确率的平均值pave

	5000	4500	4000	3500	3000	2500	2000	1500	1000	500	400	300	200	100	50	40	30	20	10	5	4	3	2
δ	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave	平均准确率p-ave
0.5	0.5155649	0.525283	0.5210321	0.520093	0.5255652	0.521097	0.5150104	0.5187518	0.5122981	0.524776	0.5280403	0.5248309	0.5243039	0.523722	0.5199432	0.5311897	0.5173657	0.5246111	0.5198907	0.5094933	0.5161269	0.5139115	0.5116212
0.4	0.8702259	0.8703283	0.8691944	0.869599	0.8684126	0.8697913	0.8704881	0.8753984	0.8709801	0.8724812	0.8622461	0.87115	0.8711874	0.8905262	0.8999221	0.9151123	0.8909333	0.85563	0.7201589	0.6832597	0.7042044	0.724747	0.701045
0.3	0.9501983	0.9508327	0.951532	0.9504206	0.9501284	0.951572	0.9504631	0.9496488	0.9508926	0.950006	0.9508951	0.9504031	0.950523	0.9517768	0.9544742	0.9534576	0.9351954	0.925817	0.8779859	0.8195625	0.7918144	0.7487862	0.7802931
0.2	0.9389767	0.9381375	0.9372059	0.9383623	0.9387095	0.9376455	0.9366689	0.9383198	0.9367114	0.9389867	0.9369037	0.9382724	0.9366589	0.9600188	0.9585602	0.9548138	0.9395711	0.9407425	0.9132167	0.8531924	0.8086731	0.7302766	0.7802856
0.1	0.9583904	0.9579258	0.9581856	0.9580707	0.9582555	0.9572265	0.9584978	0.9581281	0.9584553	0.9574363	0.9574513	0.957726	0.9537399	0.9612876	0.9627936	0.9591421	0.94327	0.9456952	0.9260842	0.863435	0.815996	0.7155809	0.7760547
0.01	0.9391315	0.9406251	0.9364716	0.9399083	0.9398683	0.9383048	0.9351254	0.9357748	0.9394762	0.9359072	0.9373458	0.9760807	0.9610952	0.9697194	0.9739678	0.9645219	0.9532828	0.9512448	0.9403479	0.8682778	0.8176419	0.7053233	0.7745886
0.001	0.9764778	0.9764953	0.97679	0.9765552	0.9767476	0.9764379	0.9766227	0.9765253	0.976303	0.9784359	0.9784809	0.9774619	0.9771372	0.9752415	0.9703662	0.9667323	0.9532254	0.9541695	0.9419088	0.868023	0.8182713	0.7041944	0.7746361
9.00E-04	0.9766651	0.9767625	0.9765078	0.9767625	0.9767476	0.976775	0.9766477	0.9766477	0.9766626	0.9780388	0.9785358	0.977829	0.9770148	0.9751266	0.9703588	0.9668596	0.9534052	0.9541495	0.9418164	0.8680305	0.8181189	0.7039971	0.7756801
8.00E-04	0.9767076	0.9768525	0.9766352	0.9766352	0.9767775	0.9767451	0.9766027	0.9766152	0.9767625	0.9780263	0.9785108	0.978326	0.9772795	0.9749593	0.970139	0.9671069	0.953098	0.954147	0.9418739	0.8677857	0.818601	0.7049487	0.7757101
7.00E-04	0.9770747	0.97685	0.9767625	0.9768949	0.9770448	0.9765627	0.9770373	0.9769549	0.9771946	0.9782361	0.9782786	0.9784234	0.9768574	0.9749593	0.9700266	0.967007	0.9527109	0.9542444	0.9419863	0.8676359	0.818004	0.7039322	0.7746886
6.00E-04	0.9778315	0.9774019	0.9778265	0.9775543	0.9777091	0.9775218	0.9777516	0.9774244	0.9780788	0.978366	0.9781537	0.9782436	0.9767001	0.9748069	0.9700615	0.9668072	0.9525136	0.9545041	0.9420537	0.868565	0.8179566	0.7024212	0.7743814
5.00E-04	0.9779913	0.9779564	0.9777816	0.977789	0.9777341	0.9779289	0.977844	0.9780288	0.9798645	0.9785408	0.9784959	0.97942	0.9776317	0.9748169	0.970144	0.9667572	0.9521364	0.9543867	0.9419488	0.8679206	0.8176968	0.7041595	0.776282
4.00E-04	0.9758235	0.9757036	0.9754838	0.9756137	0.9755687	0.9754663	0.9754188	0.9752165	0.9796597	0.9784784	0.9788205	0.9797596	0.9777865	0.9745172	0.970104	0.9665899	0.9519891	0.9544492	0.9419588	0.8673886	0.8183837	0.7037024	0.7755627
3.00E-04	0.9739328	0.9744073	0.9725991	0.9745047	0.9739752	0.9737255	0.9740377	0.9741701	0.9783885	0.9784409	0.9780363	0.9779139	0.977272	0.9737779	0.970069	0.9667073	0.9518892	0.9546165	0.9418714	0.8676484	0.8183762	0.70363	0.775238
2.00E-04	0.9794125	0.9797247	0.979872	0.9798995	0.9798745	0.9797821	0.9794449	0.979887	0.9790753	0.9769998	0.9784509	0.9773645	0.975726	0.973688	0.9695346	0.9666973	0.9515245	0.9547514	0.9421211	0.8683377	0.8177743	0.7033727	0.7759498
1.00E-04	0.980926	0.9810084	0.9808411	0.9809834	0.980951	0.9811283	0.980976	0.9806862	0.9790953	0.9768275	0.9756112	0.9740677	0.9746621	0.9729987	0.9682158	0.9665325	0.9513247	0.9548663	0.9421311	0.8678857	0.8183762	0.703635	0.7747785
9.00E-05	0.9806463	0.9803166	0.9806488	0.9809085	0.9807562	0.9806712	0.9806712	0.9806338	0.9789904	0.9763954	0.9749268	0.9736655	0.9745222	0.9728239	0.9681709	0.96646	0.9513797	0.9549712	0.9421112	0.8677458	0.8177518	0.7053533	0.774786
8.00E-05	0.9804839	0.9805938	0.9803815	0.9804664	0.9806563	0.9805364	0.9805264	0.9806663	0.9791327	0.9758684	0.9756361	0.9733683	0.9743973	0.972689	0.9682183	0.96649	0.9512373	0.9549837	0.9419963	0.868048	0.8178817	0.7029681	0.7755202
7.00E-05	0.9804015	0.9804864	0.9807237	0.9807312	0.9805788	0.9805988	0.980444	0.9805414	0.9792951	0.9754888	0.9756261	0.972719	0.9742325	0.9725916	0.9680984	0.9664276	0.9512573	0.9549837	0.942221	0.8683652	0.8182063	0.703123	0.7754153
6.00E-05	0.9813256	0.9811508	0.9811833	0.9813231	0.9813456	0.9812132	0.9805289	0.9806737	0.9784434	0.9753514	0.9749568	0.9721295	0.9740502	0.9724942	0.968086	0.96649	0.9511774	0.9549187	0.9421311	0.8678682	0.8182213	0.7048163	0.7757975
5.00E-05	0.9822272	0.9822472	0.9823596	0.9822123	0.982432	0.9821248	0.9808885	0.9808036	0.9782511	0.9748844	0.974185	0.9717849	0.9738304	0.9726041	0.9682658	0.9664376	0.95099	0.9551635	0.9422735	0.8676359	0.8176843	0.7048213	0.7754603
4.00E-05	0.9829091	0.9828691	0.9828117	0.9828092	0.9827642	0.9825619	0.9811333	0.980916	0.9781787	0.9747295	0.9733459	0.9712279	0.9735731	0.9727364	0.9681684	0.9665125	0.9510125	0.9550011	0.9422935	0.8679631	0.8180465	0.7020091	0.7761796
3.00E-05	0.9830414	0.9828966	0.983009	0.9822947	0.9825419	0.9817352	0.9812832	0.9813955	0.9792751	0.9737704	0.9723743	0.9703413	0.9730412	0.9730012	0.9682633	0.9665574	0.9508901	0.9549437	0.9420787	0.868008	0.8183937	0.7037798	0.7758599
2.00E-05	0.9835609	0.9836109	0.9834286	0.980424	0.9821698	0.9811833	0.9812607	0.9813231	0.9788006	0.9728014	0.9720346	0.9697419	0.9723718	0.9730511	0.9684231	0.9665974	0.9508152	0.9549187	0.9422061	0.8680455	0.8184411	0.7033278	0.7753179
1.00E-05	0.9823371	0.982442	0.980971	0.9800469	0.9825145	0.9821198	0.9801493	0.9805389	0.9776916	0.9709732	0.9717599	0.9697269	0.9712654	0.9724792	0.9684156	0.9664176	0.9500659	0.9547589	0.9423259	0.8676908	0.8181664	0.7034527	0.7754153

神经网络训练集的数量最少可以是多少个？

随着训练集n的减小分类准确率是减小的（不考虑n=2），

神经网络训练集的数量最少可以是多少个？

训练集数量n=5000到n=500的图像，

	5000	500	500/5000
5.00E-05	0.982227239	0.974884362	0.992524258
4.00E-05	0.982909078	0.974729513	0.991678207
3.00E-05	0.98304145	0.973770443	0.990569058
2.00E-05	0.983560946	0.972801383	0.989060603
1.00E-05	0.982337133	0.970973156	0.988431693

比较n=500和n=5000的数据，虽然将训练集的数量减小到原来的1/10，但分类准确率只下降了约1%。

再比较n=5000和n=2500的数据

	5000	2500	2500/5000
5.00E-05	0.982227239	0.982124839	0.999895746
4.00E-05	0.982909078	0.982561915	0.9996468
3.00E-05	0.98304145	0.981735217	0.998671233
2.00E-05	0.983560946	0.981183252	0.997582566
1.00E-05	0.982337133	0.982119844	0.999778804

训练集数量下降到一半，分类准确率下降约1‰，也就表明对这个网络完全可以将训练集的数量减到一半，分类差异不大。

Mnist的数据集的图片是从1开头，因此训练集的数量n=2意味着可以用1张图片实现分类。尽管分类准确率损失比较大。

因此对这个网络来说，从实用角度训练集数量的最小值可以是原来的50%，但如果仅让网络保持基本的分类能力，训练集数量的最小值是1个。

神经网络训练集的数量最少可以是多少个？

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