用分类映射的方法分类两条直线y=n和y=x*tanθ+n-n* tanθ，两条直线的交点是（n，n）
设r为0到1之间的随机数，两个训练集为
A:[r+n][(r+n)*tanθ+n-n*tanθ]
B:[r+n][n]
训练集有5000个，测试集初始化方式相同，有1000个。
网络结构为
(A,B)—2*2*2—(1,0)(0,1)（有java代码）
让n=0，0.1，0.2---3.75共28个值收敛了28*16*199次，观察网络的分辨准确率和迭代次数是如何随着n的变化而变化的。
迭代次数数据
|
0 |
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
1 |
1.1 |
1.2 |
1.3 |
1.4 |
1.5 |
1.6 |
1.7 |
1.8 |
1.9 |
2 |
2.25 |
2.5 |
2.75 |
3 |
3.25 |
3.5 |
3.75 |
|
|
δ |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
迭代次数 |
|
0.5 |
162.8894 |
164.5126 |
173.7337 |
198.1256 |
151.4171 |
184.6332 |
197.0603 |
184.8844 |
193.2663 |
175.4673 |
172.1256 |
175.7588 |
191.0553 |
161.809 |
185.3668 |
185.2915 |
186.8392 |
180.6332 |
212.7035 |
158.3216 |
174.5226 |
162.8744 |
164.0101 |
161.9196 |
193.392 |
163.4673 |
216.6683 |
190.3216 |
|
0.4 |
6704.146 |
6490.226 |
6637.407 |
6727.462 |
6666.809 |
6844.698 |
6890.98 |
6392.296 |
6630.437 |
6781.975 |
6724.075 |
6616.377 |
6766.497 |
7085.342 |
6754.156 |
6720.367 |
6939.161 |
6785.312 |
7147.201 |
6915.965 |
6956.347 |
6895.995 |
7057.633 |
7232.457 |
7232.839 |
7136.367 |
7247 |
7292.357 |
|
0.3 |
7304.402 |
7001.166 |
7157.362 |
7156.93 |
7105.06 |
7459.372 |
7378.92 |
7158.045 |
7264.367 |
7366.598 |
7364.347 |
7562.859 |
7572.146 |
7742.256 |
7471.291 |
7671.844 |
7575.231 |
7815.322 |
8015.533 |
7648.286 |
8000.166 |
7636.608 |
7947.472 |
8032.357 |
8395.513 |
8250.397 |
7990.447 |
8218.568 |
|
0.2 |
7750.874 |
7688.97 |
7370.518 |
7612.598 |
7611.251 |
7923.603 |
7961.864 |
7657.07 |
7935.432 |
8124.327 |
8062.548 |
7867.101 |
8206.246 |
8153.925 |
8253.754 |
8416.206 |
8411.191 |
8543.322 |
8621.211 |
8253.462 |
8485.382 |
8432.497 |
8614.719 |
8880.698 |
9131.281 |
8943.894 |
8946.136 |
9060.166 |
|
0.1 |
8472.106 |
8269.894 |
8233.03 |
8181.714 |
8494.276 |
8572.849 |
8661.09 |
8662.186 |
8944.789 |
8864.166 |
8999.623 |
9102.93 |
9174.759 |
9436.246 |
9369.492 |
9359 |
9500.759 |
9490.005 |
9876.015 |
9440.065 |
10039.34 |
9581.281 |
10087.47 |
10232.95 |
10197.8 |
9932.055 |
9785.603 |
10498.63 |
|
0.01 |
11047.28 |
10357.41 |
10170.2 |
10556.95 |
10806.76 |
11853.69 |
12115.44 |
12264.74 |
12383.84 |
13008.01 |
13273.24 |
13742.86 |
13567.55 |
14700.41 |
15082.85 |
14469.93 |
15302.01 |
14963.52 |
15488.99 |
15585.62 |
15674.84 |
16024.77 |
17250.85 |
17635.41 |
17885.5 |
18331.95 |
19037.56 |
20527.45 |
|
0.001 |
15949.57 |
13360.87 |
13337.84 |
14327.5 |
15936.8 |
17060.02 |
18192.05 |
19825.59 |
19596.83 |
20945.23 |
21276.32 |
21661.59 |
21949.58 |
24102.88 |
24715.26 |
23972.36 |
25780.18 |
25750.23 |
25414.93 |
26795.01 |
26204.04 |
28462.87 |
31650.29 |
32803 |
37622.27 |
43100.07 |
47126.66 |
57652.27 |
|
9.00E-04 |
16385.22 |
13499.85 |
13523.93 |
14469.42 |
16208.01 |
17673.69 |
18811 |
20234.31 |
20429.3 |
21318.24 |
22062.96 |
22064.83 |
22265.53 |
24699.91 |
25443.71 |
24799.55 |
26532.65 |
26398.36 |
26273.75 |
27044.83 |
27157.91 |
29405.29 |
32223.79 |
35087.71 |
38718.29 |
45488.8 |
50564.61 |
62426.83 |
|
8.00E-04 |
16601.06 |
13576.7 |
13715.1 |
14830.07 |
16641.85 |
18125.7 |
19234.12 |
20670.59 |
21194.7 |
21667.38 |
23042.04 |
23027.08 |
22527.95 |
25541.54 |
25938.52 |
25060.44 |
27449.43 |
26978.64 |
27324.3 |
27376.21 |
27996.3 |
30659.38 |
32953.21 |
37565.75 |
39376.84 |
48518.29 |
53240.52 |
65967.03 |
|
7.00E-04 |
17169.87 |
13883.84 |
13797.62 |
14899.34 |
17045.29 |
18856.1 |
19680.52 |
22193.4 |
21753.6 |
22407.31 |
23864.82 |
24536.36 |
23337.46 |
26046.39 |
26326.63 |
25560.93 |
27915.89 |
27531.1 |
28906.37 |
28171.08 |
29449.63 |
31405.35 |
35119.82 |
39227.15 |
41040.77 |
51903.32 |
56343.2 |
70393.14 |
|
6.00E-04 |
17630.13 |
14085.33 |
14188.31 |
15252.83 |
17450.99 |
19841.57 |
20499.53 |
23464.46 |
22198.68 |
23100.08 |
24294.18 |
26045.34 |
24460.28 |
26721.26 |
27214.22 |
26123.77 |
28717.94 |
28185.94 |
30359.12 |
29353.96 |
31017.12 |
33431.16 |
37184.17 |
41485.41 |
44786.97 |
55527.96 |
61752.95 |
75898.69 |
|
5.00E-04 |
18631.19 |
14388.16 |
14477.67 |
15726.37 |
17931.69 |
21092.81 |
22039.63 |
23668.38 |
23273.93 |
23881.55 |
24841.09 |
26595.17 |
26450.83 |
27433.14 |
28729.05 |
27917.58 |
30113.31 |
29585.7 |
31671.36 |
31237.32 |
32934.65 |
34993.06 |
39004.11 |
42952.99 |
48441.56 |
60128.41 |
67817.84 |
86082.6 |
|
4.00E-04 |
19211.79 |
15077.17 |
14814.17 |
16235.16 |
18329.16 |
22687.1 |
24020.57 |
24152.28 |
24492.99 |
25529.53 |
26503.18 |
27330.49 |
29037.46 |
28277.25 |
30392.92 |
29703.87 |
31772.11 |
31210.92 |
32733.55 |
33470.89 |
35026.24 |
36856.95 |
42045.15 |
48070.57 |
52605.37 |
68022.45 |
76196.3 |
100852.2 |
|
3.00E-04 |
20484.61 |
15611.52 |
15433.74 |
17325.13 |
19516.9 |
26777.29 |
24841.73 |
25445.11 |
26230.2 |
30014.73 |
28002.16 |
29787.73 |
30969.93 |
30879.2 |
32052.68 |
32102.71 |
33974.42 |
34156.33 |
34362.58 |
36398.18 |
36508.85 |
40252.59 |
46247.39 |
52562.23 |
59314.3 |
78189.45 |
89947.53 |
125496.4 |
|
2.00E-04 |
22011.69 |
16338.01 |
16139.57 |
18703.34 |
21618.41 |
41873.07 |
27040.85 |
32110.6 |
29440.69 |
31735.22 |
30168.13 |
30484.64 |
31615.09 |
34439.91 |
35552.24 |
34938.9 |
37857.3 |
37220.8 |
38770.76 |
38741.2 |
41366.44 |
45719.87 |
52403.1 |
61832.09 |
70750.4 |
93253.14 |
110715.5 |
174654.9 |
|
1.00E-04 |
25422.17 |
17953.08 |
17744.19 |
21308.99 |
29550.53 |
52630.72 |
55579.81 |
61412.06 |
63599.88 |
60190.26 |
37802.84 |
38143.55 |
40581.46 |
38721.73 |
41285.62 |
40976.03 |
43785.39 |
45300.44 |
44978.88 |
47526.23 |
50649.24 |
57475.61 |
67941.38 |
81746.42 |
97458.47 |
137821 |
175270.3 |
283332.6 |
将迭代次数曲线画出来
随着n的增加迭代次数变大。
但在0<n<1区间内明显的有一个精细结构。如果将迭代次数理解成两个分类对象相似性的量度，至少对这个实验来说神经网络的分类特征并没有平移不变性，因为显然随着交点的移动两条线在夹角不变的情况下，迭代次数是变化的。
再观察分类准确率
|
0 |
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
1 |
1.1 |
1.2 |
1.3 |
1.4 |
1.5 |
1.6 |
1.7 |
1.8 |
1.9 |
2 |
2.25 |
2.5 |
2.75 |
3 |
3.25 |
3.5 |
3.75 |
|
|
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 |
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 |
0.5 |
0.500168 |
0.501088 |
0.503161 |
0.5 |
0.5 |
0.500045 |
0.500518 |
0.502467 |
0.501231 |
0.500475 |
0.500201 |
0.500515 |
0.500681 |
0.501731 |
0.500116 |
0.50051 |
0.502304 |
0.501513 |
0.5 |
0.5 |
0.500515 |
0.501116 |
0.499452 |
0.5 |
0.501327 |
0.50058 |
0.49998 |
|
0.4 |
0.957869 |
0.977578 |
0.97105 |
0.90903 |
0.894774 |
0.90857 |
0.875766 |
0.877445 |
0.805384 |
0.762892 |
0.702799 |
0.705457 |
0.680593 |
0.652741 |
0.640955 |
0.644138 |
0.605332 |
0.605302 |
0.589528 |
0.586397 |
0.570553 |
0.578211 |
0.540676 |
0.537329 |
0.517352 |
0.50748 |
0.502638 |
0.500362 |
|
0.3 |
0.971862 |
0.970947 |
0.929477 |
0.883749 |
0.863563 |
0.882053 |
0.855505 |
0.852641 |
0.779399 |
0.745588 |
0.703852 |
0.701636 |
0.686553 |
0.654799 |
0.653935 |
0.646427 |
0.617766 |
0.613528 |
0.606055 |
0.606093 |
0.589357 |
0.593688 |
0.554809 |
0.558967 |
0.532472 |
0.53649 |
0.514462 |
0.506146 |
|
0.2 |
0.979193 |
0.95744 |
0.911907 |
0.874852 |
0.850244 |
0.87049 |
0.847236 |
0.838807 |
0.766857 |
0.740912 |
0.695636 |
0.704965 |
0.697485 |
0.659724 |
0.656048 |
0.650952 |
0.623116 |
0.617668 |
0.610575 |
0.609475 |
0.600492 |
0.59854 |
0.563857 |
0.571884 |
0.548038 |
0.559166 |
0.530445 |
0.524211 |
|
0.1 |
0.982327 |
0.947603 |
0.905553 |
0.875038 |
0.846186 |
0.869992 |
0.845495 |
0.831565 |
0.765972 |
0.748377 |
0.701344 |
0.708613 |
0.700545 |
0.668085 |
0.66305 |
0.650289 |
0.632068 |
0.621859 |
0.62059 |
0.612055 |
0.608332 |
0.60203 |
0.567736 |
0.576804 |
0.555261 |
0.567857 |
0.534442 |
0.536394 |
|
0.01 |
0.988756 |
0.952832 |
0.91201 |
0.891525 |
0.870299 |
0.879344 |
0.850583 |
0.826445 |
0.751681 |
0.728264 |
0.701734 |
0.706425 |
0.679043 |
0.67695 |
0.667736 |
0.653842 |
0.654736 |
0.629834 |
0.632 |
0.645771 |
0.611487 |
0.607435 |
0.612827 |
0.619899 |
0.570138 |
0.601211 |
0.574626 |
0.597598 |
|
0.001 |
0.996405 |
0.964633 |
0.932636 |
0.906053 |
0.8835 |
0.899764 |
0.865658 |
0.844407 |
0.745668 |
0.741776 |
0.686271 |
0.663558 |
0.688392 |
0.669399 |
0.673802 |
0.662962 |
0.677317 |
0.657183 |
0.637181 |
0.644671 |
0.612857 |
0.63753 |
0.651198 |
0.627198 |
0.625786 |
0.609553 |
0.630442 |
0.623148 |
|
9.00E-04 |
0.996824 |
0.964917 |
0.934178 |
0.907068 |
0.885435 |
0.899344 |
0.869289 |
0.844736 |
0.74995 |
0.733319 |
0.677359 |
0.671236 |
0.688397 |
0.670967 |
0.667729 |
0.664513 |
0.67948 |
0.665751 |
0.647467 |
0.643588 |
0.616623 |
0.64355 |
0.653437 |
0.638618 |
0.616397 |
0.632156 |
0.616141 |
0.653997 |
|
8.00E-04 |
0.997048 |
0.965945 |
0.934329 |
0.907698 |
0.88648 |
0.899357 |
0.866264 |
0.845678 |
0.751236 |
0.726769 |
0.674475 |
0.689661 |
0.674791 |
0.664877 |
0.664764 |
0.65645 |
0.675447 |
0.669296 |
0.659864 |
0.648704 |
0.619827 |
0.65098 |
0.650967 |
0.648367 |
0.583264 |
0.632573 |
0.629704 |
0.657317 |
|
7.00E-04 |
0.99704 |
0.96648 |
0.934844 |
0.909035 |
0.887626 |
0.899289 |
0.868028 |
0.837136 |
0.75157 |
0.71643 |
0.660467 |
0.704183 |
0.676897 |
0.656266 |
0.665842 |
0.648575 |
0.67041 |
0.664234 |
0.677075 |
0.656013 |
0.634209 |
0.65002 |
0.647812 |
0.650299 |
0.585691 |
0.629558 |
0.636736 |
0.651603 |
|
6.00E-04 |
0.996932 |
0.967181 |
0.935857 |
0.909925 |
0.888209 |
0.900008 |
0.866352 |
0.797761 |
0.751291 |
0.711008 |
0.642073 |
0.70999 |
0.686857 |
0.642362 |
0.670942 |
0.634975 |
0.672726 |
0.662917 |
0.686161 |
0.661035 |
0.64356 |
0.643028 |
0.648354 |
0.643435 |
0.619736 |
0.642437 |
0.639352 |
0.669822 |
|
5.00E-04 |
0.996126 |
0.967651 |
0.937043 |
0.911432 |
0.890095 |
0.90355 |
0.853683 |
0.791015 |
0.75393 |
0.716387 |
0.645565 |
0.685917 |
0.711445 |
0.637666 |
0.682631 |
0.65753 |
0.675312 |
0.665153 |
0.681186 |
0.671309 |
0.651648 |
0.637364 |
0.655839 |
0.641198 |
0.628485 |
0.63905 |
0.661015 |
0.676178 |
|
4.00E-04 |
0.995583 |
0.968357 |
0.938407 |
0.911842 |
0.892201 |
0.906319 |
0.823583 |
0.763857 |
0.755709 |
0.729048 |
0.657246 |
0.674035 |
0.726543 |
0.653108 |
0.700279 |
0.679008 |
0.671118 |
0.662771 |
0.644756 |
0.674078 |
0.633399 |
0.644289 |
0.666319 |
0.655201 |
0.613146 |
0.645874 |
0.673776 |
0.680877 |
|
3.00E-04 |
0.995128 |
0.968734 |
0.939907 |
0.913837 |
0.894005 |
0.927018 |
0.877756 |
0.713412 |
0.741427 |
0.747173 |
0.66607 |
0.63645 |
0.702221 |
0.671319 |
0.689377 |
0.677945 |
0.666106 |
0.664033 |
0.643045 |
0.658608 |
0.634779 |
0.660864 |
0.660284 |
0.652264 |
0.626405 |
0.658291 |
0.688226 |
0.686947 |
|
2.00E-04 |
0.995739 |
0.969513 |
0.942269 |
0.918008 |
0.905364 |
0.952254 |
0.849525 |
0.696739 |
0.744857 |
0.726035 |
0.667138 |
0.636917 |
0.696892 |
0.674111 |
0.672764 |
0.673736 |
0.677528 |
0.674673 |
0.67347 |
0.662181 |
0.643133 |
0.65544 |
0.671563 |
0.65405 |
0.628261 |
0.669284 |
0.675073 |
0.690221 |
|
1.00E-04 |
0.996427 |
0.971389 |
0.944603 |
0.919837 |
0.911176 |
0.964452 |
0.952053 |
0.909025 |
0.764367 |
0.71694 |
0.662932 |
0.654244 |
0.704907 |
0.658744 |
0.699683 |
0.689033 |
0.669729 |
0.686043 |
0.65209 |
0.670425 |
0.64908 |
0.665603 |
0.684518 |
0.667935 |
0.67653 |
0.691078 |
0.694033 |
0.683332 |
分类准确率随着n的增加不断的下降，这个现象也表明了平移对分类是有影响的。
因此这个实验表明神经网络的被分类特征并没有在二维平面内的平移不变性，分类特征对坐标的选择是高度敏感的。标尺的选择对分类效果有非常大的影响。这里所谓的标尺就是一种数值的大小比例，将数值理解成是二维空间的密度，这个结论就等价于表明空间的形状对分类有影响。