The influence of the number of non-zero values in the picture on Classification

( 0 , 7)---m*n*2---(1,0)(0,1)

take mnist The picture of is reduced to 9*9, Statistics of non 0 Number of points

0	1	2	3	4	5	6	7	8	9
44.4698	27.7134	41.7294	17.9278	15.9034	16.9892	17.8176	14.0056	19.4652	15.9438

It turns out that 0 At most non 0 spot , The average is about 44.5 individual . and 7 least , stay 81 Only about 14 Values are non-zero . Now change the form 7 Compare the number of zeros in Central Africa and how the number of iterations changes .

	0*7
	f2[0]	f2[1]	The number of iterations n	Average accuracy p-ave	1-0	0-1	δ	Time consuming ms/ Time	Time consuming ms/199 Time
44.4698-14.0056	8.55E-06	0.999991	7822.01	0.992943	0.995795	0.990223	1.00E-05	270.7437	53889
44.4698-14.0056*0.9	8.43E-06	0.999992	5539.92	0.989532	0.989457	0.989603	1.00E-05	174.8241	34797
44.4698-14.0056*0.8	7.11E-06	0.999993	4698.231	0.984982	0.980028	0.989705	1.00E-05	169.3769	33842
44.4698-14.0056*0.7	8.02E-06	0.999992	5672.623	0.99049	0.985627	0.995126	1.00E-05	184.3367	36689
44.4698-14.0056*0.6	6.43E-06	0.999994	4257.085	0.991707	0.991888	0.991534	1.00E-05	156.2965	31117
44.4698-14.0056*0.5	6.36E-06	0.999994	5994.452	0.994202	0.994862	0.993572	1.00E-05	197.5276	39319
44.4698-14.0056*0.4	8.39E-06	0.999992	8845.538	0.995017	0.995929	0.994149	1.00E-05	260.4221	51840
44.4698-14.0056*0.3	9.09E-06	0.999991	15703.26	0.998956	0.997862	1	1.00E-05	447.2864	89020
44.4698-14.0056*0.2	8.97E-06	0.999991	28967.59	0.99965	1	0.999316	1.00E-05	895.5377	178223

For example, the last set of data 44.4698-14.0056*0.2 indicate , form 7 Only randomly reserved 20% Non - 0 spot , It's just 2-3 There are white dots, and the rest are all black . Experimental results show that even so, the network can achieve convergence , And the classification accuracy is all 10 The highest in the Group .

Compare the number of iterations

The number of iterations decreases first and then increases , The lowest point is about 60%. According to the inverse relationship between the number of iterations and entropy

It shows that the entropy of these two groups of pictures increases first and then decreases .

With non 0 The decrease of value and the decrease of entropy are well explained , But how to explain 60% before , With non 0 The phenomenon of decreasing value and increasing entropy ？ Because it's white on black , So the difference between the two groups of pictures should be 4 Kind of

0	white	7	white
0	white	7	black
0	black	7	black
0	black	7	white

It should be this 4 These differences jointly determine the result of classification , If 7 White dots decrease , Then the black dot increases ,

0	white	7	white	Reduce
0	black	7	white	Reduce

form 0 relative 7 The difference in white should be smaller , It becomes less obvious . and

0	white	7	black	increase
0	black	7	black	increase

relative 7 The difference in the black part of should be bigger .

So with 7 Decrease of white dot , Just assume that 60% The former difference increases more than the former difference decreases , And in the 60% In the future, the increase of the difference is less than the decrease of the difference , It can explain the inflection point of the curve .