标题:
卷积神经网络算法的一个实现（3）
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作者:
yuyang911220
时间:
2015-10-22 21:07
标题:
卷积神经网络算法的一个实现（3）
为了描述清楚对卷积核旋转180与卷积层的残差的卷积所关联的权重与单元，正是前向计算所关联的权重与单元，我们选一个稍微大一点的卷积核，即假设卷积层采用用3*3的卷积核，其上一层采样层的输出map的大小是5*5，那么前向传输由采样层得到卷积层的过程如下：
图8
这里我们采用自己实现的convn（即内部不会对卷积核旋转），并假定上面的矩阵A、B下标都从1开始，那么有：
B11 = A11*K11 + A12*K12 + A13*K13 + A21*K21 + A22*K22 + A23*K23 + A31*K31 + A32*K32 + A33*
K33
B12
= A12*K11 + A13*K12 + A14*K13 + A22*K21 + A23*K22 + A24*K23 + A32*K31 + A33*K32 + A34*
K33
B13
= A13*K11 + A14*K12 + A15*K13 + A23*K21 + A24*K22 + A25*K23 + A33*K31 + A34*K32 + A35*
K33
B21
= A21*K11 + A22*K12 + A23*K13 + A31*K21 + A32*K22 + A33*K23 + A41*K31 + A42*K32 + A43*
K33
B22
= A22*K11 + A23*K12 + A24*K13 + A32*K21 + A33*K22 + A34*K23 + A42*K31 + A43*K32 + A44*
K33
B23
= A23*K11 + A24*K12 + A25*K13 + A33*K21 + A34*K22 + A35*K23 + A43*K31 + A44*K32 + A45*
K33
B31
= A31*K11 + A32*K12 + A33*K13 + A41*K21 + A42*K22 + A43*K23 + A51*K31 + A52*K32 + A53*
K33
B32
= A32*K11 + A33*K12 + A34*K13 + A42*K21 + A43*K22 + A44*K23 + A52*K31 + A53*K32 + A54*
K33
B33
= A33*K11 + A34*K12 + A35*K13 + A43*K21 + A44*K22 + A45*K23 + A53*K31 + A54*K32 + A55*K33 我们可以得到B矩阵每个单元与哪些卷积核单元和哪些A矩阵的单元之间有关联：
A11 [K11] [B11]
A12 [K12, K11] [B12, B11]A13 [K13, K12, K11] [B12, B13, B11]A14 [K13, K12] [B12, B13]A15 [K13] [B13]A21 [K21, K11] [B21, B11]A22 [K22, K21, K12, K11] [B12, B22, B21, B11]A23 [K23, K22, K21, K13, K12, K11] [B23, B22, B21, B12, B13, B11]
A24 [K23, K22, K13, K12] [B23, B12, B13, B22]
A25 [K23, K13] [B23, B13]A31 [K31, K21, K11] [B31, B21, B11]A32 [K32, K31, K22, K21, K12, K11] [B31, B32, B22, B12, B21, B11]A33 [K33, K32, K31, K23, K22, K21, K13, K12, K11] [B23, B22, B21, B31, B12, B13, B11, B33, B32]A34 [K33, K32, K23, K22, K13, K12] [B23, B22, B32, B33, B12, B13]A35 [K33, K23, K13] [B23, B13, B33]A41 [K31, K21] [B31, B21]A42 [K32, K31, K22, K21] [B32, B22, B21, B31]A43 [K33, K32, K31, K23, K22, K21] [B31, B23, B22, B32, B33, B21]A44 [K33, K32, K23, K22] [B23, B22, B32, B33]A45 [K33, K23] [B23, B33]A51 [K31] [B31]A52 [K32, K31] [B31, B32]A53 [K33, K32, K31] [B31, B32, B33]A54 [K33, K32] [B32, B33]A55 [K33] [B33]
然后再用matlab的convn(内部会对卷积核进行180度旋转)进行一次convn(B,K,'full')，结合图7，看红色部分，除去0，A11=B'33*K'33=B11*K11，发现A11正好与K11、B11关联对不对；我们再看一个A24=B'34*K'21+B'35*K'22+B'44*K'31+B'45*K'32=B12*K23+B13*K22+B22*K13+B23*K12，发现参与A24计算的卷积核单元与B矩阵单元，正好是前向计算时关联的单元，所以我们可以通过旋转卷积核后进行卷积而得到采样层的残差。
残差计算出来后，剩下的就是用更新权重和偏置，这和BP是一样的，因此不再细究，有问题欢迎交流。
5、代码实现
详细的代码不再这里贴了，我依旧放在了
github
，欢迎参考和指正。我又是在重造车轮了，没有使用任何第三方的库类，这里贴一下调用代码：
public
static
void
runCnn() {
//
创建一个卷积神经网络
LayerBuilder builder =
new
LayerBuilder();
builder.addLayer(Layer.buildInputLayer(
new
Size(28, 28
)));
builder.addLayer(Layer.buildConvLayer(
6,
new
Size(5, 5
)));
builder.addLayer(Layer.buildSampLayer(
new
Size(2, 2
)));
builder.addLayer(Layer.buildConvLayer(
12,
new
Size(5, 5
)));
builder.addLayer(Layer.buildSampLayer(
new
Size(2, 2
)));
builder.addLayer(Layer.buildOutputLayer(
10
));
CNN cnn
=
new
CNN(builder, 50
);
//
导入数据集
String fileName = "dataset/train.format"
;
Dataset dataset
= Dataset.load(fileName, ",", 784
);
cnn.train(dataset,
3);
//
String modelName = "model/model.cnn"
;
cnn.saveModel(modelName);
dataset.clear();
dataset
=
null
;
//
预测
//
CNN cnn = CNN.loadModel(modelName);
Dataset testset = Dataset.load("dataset/test.format", ",", -1
);
cnn.predict(testset,
"dataset/test.predict"
); }
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