Matlab：利用1D-CNN（一维卷积神经网络），分析高光谱曲线数据或时序数据

1DCNN 简介：

1D-CNN（一维卷积神经网络）是一种特殊类型的卷积神经网络，设计用于处理一维序列数据。这种网络结构通常由多个卷积层和池化层交替组成，最后使用全连接层将提取的特征映射到输出。

以下是1D-CNN的主要组成部分和特点：

输入层：接收一维序列数据作为模型的输入。
卷积层：使用一系列可训练的卷积核在输入数据上滑动并提取特征。卷积操作能够有效地提取局部信息，从而捕捉输入序列的局部模式。
激活函数：对卷积层的输出进行非线性变换，增强模型的表达能力。
池化层：通过对卷积层输出进行降维，减少计算量，同时提高模型的鲁棒性和泛化能力。
全连接层：将池化层的输出映射到模型的输出，通常用于分类、回归等任务。

在使用1D-CNN时，通常需要设置一些超参数，如卷积核的大小、卷积层的个数、池化操作的方式、激活函数的选择等。

与传统机器学习对比：

首先，1D-CNN是一种深度学习模型，它使用卷积层来自动提取一维序列数据（如音频、文本等）中的特征。这种方式与传统机器学习中的特征提取方法不同，传统机器学习通常需要手动设计和选择特征。通过自动提取特征，1D-CNN能够减少人工特征提取的工作量，并有可能发现更复杂的特征表示。其次，1D-CNN在处理序列数据时能够更好地捕捉局部关系。卷积操作通过在输入数据上滑动固定大小的窗口来提取局部特征，这使得1D-CNN在语音识别、自然语言处理、时间序列预测等任务中表现出色。而传统机器学习模型，如支持向量机（SVM）或决策树，通常不具备这种处理局部关系的能力。

需要注意的是，在数据尺度较小的时候，如只有100多个参数，相较于传统机器学习模型，1D-CNN并没有优势，表现性能一般和机器学习表现无明显差距。鉴于卷积对于目标特征的提取及压缩的特点，数据长度（参数）越高，1D-CNN就越发有优势。因此在时序回归、高光谱分析、股票预测、音频分析上1D-CNN的表现可圈可点。此外，利用1D-CNN做回归和分类对样本量有较高的要求，因为卷积结构本身对噪声就比较敏感，数据集较少时，特别容易发生严重的过拟合现象，建议样本量800+有比较好的应用效果。

三种不同结构的自定义的1D-CNN

基于VGG结构的1D-CNN（VNet）

基于 VGG 主干网络设计的 VNet 参考了陈庆等的优化结构，卷积核大小为 4，包含 6 个卷积深度，并在每个平均池化层后引入一个比例为 0.3 的随机失活层（dropout layer）防止过拟合,参数量为342K。

matlab构建代码：

function layers=creatCNN2D_VGG(inputsize)
filter=16;
layers = [imageInputLayer([inputsize],"Name","imageinput")convolution2dLayer([1 4],filter,"Name","conv","Padding","same")convolution2dLayer([1 4],filter,"Name","conv_1","Padding","same")maxPooling2dLayer([1 2],"Name","maxpool","Padding","same","Stride",[1 2])convolution2dLayer([1 4],filter*2,"Name","conv_2","Padding","same")convolution2dLayer([1 4],filter*2,"Name","conv_3","Padding","same")maxPooling2dLayer([1 2],"Name","maxpool_1","Padding","same","Stride",[1 2])fullyConnectedLayer(filter*8,"Name","fc")fullyConnectedLayer(1,"Name","fc_1")regressionLayer("Name","regressionoutput")];

基于EfficienNet结构的1D-CNN （ENet）

ENet 采用 Swish 激活函数，引入了跳跃连接与 SE（squeeze and excitation）注意力机制，其不仅能有效实现更深的卷积深度，还能对通道方向上的数据特征进行感知，在数据尺度较大时，有一定优势。参数量170.4K

生成代码：

function lgraph=creatCNN2D_EffiPlus2(inputsize)filter=8;
lgraph = layerGraph();tempLayers = [imageInputLayer([1 1293 1],"Name","imageinput")convolution2dLayer([1 3],filter,"Name","conv_11","Padding","same","Stride",[1 2])%'DilationFactor',[1,2]batchNormalizationLayer("Name","batchnorm_8")swishLayer("Name","swish_1_1_1")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [convolution2dLayer([1 3],filter,"Name","conv_1_1","Padding","same","Stride",[1 1])%%batchNormalizationLayer("Name","batchnorm_1_1")swishLayer("Name","swish_1_5")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [globalAveragePooling2dLayer("Name","gapool_1_1")convolution2dLayer([1 1],2,"Name","conv_2_1_1","Padding","same")swishLayer("Name","swish_2_1_1")convolution2dLayer([1 1],filter,"Name","conv_3_1_1","Padding","same")sigmoidLayer("Name","sigmoid_1_1")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [multiplicationLayer(2,"Name","multiplication_3")convolution2dLayer([1 3],filter*2,"Name","conv","Padding","same","Stride",[1 2])batchNormalizationLayer("Name","batchnorm")swishLayer("Name","swish_1_1")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [convolution2dLayer([1 3],filter*2,"Name","conv_1","Padding","same","Stride",[1 1])%%batchNormalizationLayer("Name","batchnorm_1")swishLayer("Name","swish_1")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [globalAveragePooling2dLayer("Name","gapool_1")convolution2dLayer([1 1],4,"Name","conv_2_1","Padding","same")swishLayer("Name","swish_2_1")convolution2dLayer([1 1],filter*2,"Name","conv_3_1","Padding","same")sigmoidLayer("Name","sigmoid_1")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [multiplicationLayer(2,"Name","multiplication")convolution2dLayer([1 3],filter*4,"Name","conv_9","Padding","same","Stride",[1 2])batchNormalizationLayer("Name","batchnorm_6")swishLayer("Name","swish_1_4")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [convolution2dLayer([1 3],filter*4,"Name","conv_10","Padding","same","Stride",[1 1])%%batchNormalizationLayer("Name","batchnorm_7")swishLayer("Name","swish_1_3")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [globalAveragePooling2dLayer("Name","gapool_2")convolution2dLayer([1 1],8,"Name","conv_2_2","Padding","same")swishLayer("Name","swish_2_2")convolution2dLayer([1 1],filter*4,"Name","conv_3_2","Padding","same")sigmoidLayer("Name","sigmoid_2")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [multiplicationLayer(2,"Name","multiplication_2")convolution2dLayer([1 3],filter*8,"Name","conv_5","Padding","same","Stride",[1 2])batchNormalizationLayer("Name","batchnorm_2")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [convolution2dLayer([1 1],filter*8,"Name","conv_6","Padding","same")batchNormalizationLayer("Name","batchnorm_3")swishLayer("Name","swish")convolution2dLayer([1 3],filter*8,"Name","conv_7","Padding","same")batchNormalizationLayer("Name","batchnorm_4")swishLayer("Name","swish_1_2")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [globalAveragePooling2dLayer("Name","gapool")convolution2dLayer([1 1],12,"Name","conv_2","Padding","same")swishLayer("Name","swish_2")convolution2dLayer([1 1],filter*8,"Name","conv_3","Padding","same")sigmoidLayer("Name","sigmoid")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [multiplicationLayer(2,"Name","multiplication_1")convolution2dLayer([1 3],filter*8,"Name","conv_8","Padding","same")batchNormalizationLayer("Name","batchnorm_5")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [additionLayer(2,"Name","addition")convolution2dLayer([1 3],1,"Name","conv_4","Padding","same")swishLayer("Name","swish_3")averagePooling2dLayer([1 3],"Name","avgpool2d","Padding","same")fullyConnectedLayer(1,"Name","fc")regressionLayer("Name","regressionoutput")];
lgraph = addLayers(lgraph,tempLayers);lgraph = connectLayers(lgraph,"swish_1_1_1","conv_1_1");
lgraph = connectLayers(lgraph,"swish_1_1_1","gapool_1_1");
lgraph = connectLayers(lgraph,"swish_1_5","multiplication_3/in1");
lgraph = connectLayers(lgraph,"sigmoid_1_1","multiplication_3/in2");
lgraph = connectLayers(lgraph,"swish_1_1","conv_1");
lgraph = connectLayers(lgraph,"swish_1_1","gapool_1");
lgraph = connectLayers(lgraph,"swish_1","multiplication/in1");
lgraph = connectLayers(lgraph,"sigmoid_1","multiplication/in2");
lgraph = connectLayers(lgraph,"swish_1_4","conv_10");
lgraph = connectLayers(lgraph,"swish_1_4","gapool_2");
lgraph = connectLayers(lgraph,"swish_1_3","multiplication_2/in1");
lgraph = connectLayers(lgraph,"sigmoid_2","multiplication_2/in2");
lgraph = connectLayers(lgraph,"batchnorm_2","conv_6");
lgraph = connectLayers(lgraph,"batchnorm_2","addition/in2");
lgraph = connectLayers(lgraph,"swish_1_2","gapool");
lgraph = connectLayers(lgraph,"swish_1_2","multiplication_1/in1");
lgraph = connectLayers(lgraph,"sigmoid","multiplication_1/in2");
lgraph = connectLayers(lgraph,"batchnorm_5","addition/in1");

基于ResNet结构的1D-CNN （RNet）

RNet 由 3 层残差网络模块构成，其结构相较于 ENet 较为精简，模型容量更少，个人感觉性能比较综合。参数量33.7K

function lgraph=creatCNN2D_ResNet(inputsize)
lgraph = layerGraph();
filter=16;tempLayers = [imageInputLayer([inputsize],"Name","imageinput")convolution2dLayer([1 3],filter,"Name","conv","Padding","same","Stride",[1 2])batchNormalizationLayer("Name","batchnorm")reluLayer("Name","relu")maxPooling2dLayer([1 3],"Name","maxpool","Padding",'same',"Stride",[1 2])];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [convolution2dLayer([1 3],filter,"Name","conv_1","Padding","same")batchNormalizationLayer("Name","batchnorm_1")reluLayer("Name","relu_1")convolution2dLayer([1 3],filter,"Name","conv_2","Padding","same")batchNormalizationLayer("Name","batchnorm_2")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [additionLayer(2,"Name","addition")reluLayer("Name","relu_3")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [convolution2dLayer([1 3],filter*2,"Name","conv_3","Padding","same","Stride",[1 2])batchNormalizationLayer("Name","batchnorm_3")reluLayer("Name","relu_2")convolution2dLayer([1 3],filter*2,"Name","conv_4","Padding","same")batchNormalizationLayer("Name","batchnorm_4")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [convolution2dLayer([1 3],filter*2,"Name","conv_8","Padding","same","Stride",[1 2])batchNormalizationLayer("Name","batchnorm_8")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [additionLayer(2,"Name","addition_1")reluLayer("Name","relu_5")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [convolution2dLayer([1 3],filter*4,"Name","conv_5","Padding","same","Stride",[1 2])batchNormalizationLayer("Name","batchnorm_5")reluLayer("Name","relu_4")convolution2dLayer([1 3],filter*4,"Name","conv_6","Padding","same")batchNormalizationLayer("Name","batchnorm_6")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [convolution2dLayer([1 3],filter*4,"Name","conv_7","Padding","same","Stride",[1 2])batchNormalizationLayer("Name","batchnorm_7")];
lgraph = addLayers(lgraph,tempLayers);tempLayers = [additionLayer(2,"Name","addition_2")reluLayer("Name","res3a_relu")globalMaxPooling2dLayer("Name","gmpool")fullyConnectedLayer(1,"Name","fc")regressionLayer("Name","regressionoutput")];
lgraph = addLayers(lgraph,tempLayers);lgraph = connectLayers(lgraph,"maxpool","conv_1");
lgraph = connectLayers(lgraph,"maxpool","addition/in2");
lgraph = connectLayers(lgraph,"batchnorm_2","addition/in1");
lgraph = connectLayers(lgraph,"relu_3","conv_3");
lgraph = connectLayers(lgraph,"relu_3","conv_8");
lgraph = connectLayers(lgraph,"batchnorm_4","addition_1/in1");
lgraph = connectLayers(lgraph,"batchnorm_8","addition_1/in2");
lgraph = connectLayers(lgraph,"relu_5","conv_5");
lgraph = connectLayers(lgraph,"relu_5","conv_7");
lgraph = connectLayers(lgraph,"batchnorm_6","addition_2/in1");
lgraph = connectLayers(lgraph,"batchnorm_7","addition_2/in2");

ENet和RNet的结构示意图

训练代码与案例：

训练代码

我们基于RNet采用1293长度的数据对样本进行训练，做回归任务，代码如下：

clear allload("TestData2.mat");%数据分割
%[AT,AP]=ks(Alltrain,588);
num_div=1;%直接载入数据[numsample,sampleSize]=size(AT);
for i=1:numsampleXTrain(:,:,1,i)=AT(i,1:end-num_div);YTrain(i,1)=AT(i,end);
end
[numtest,~]=size(AP)
for i=1:numtestXTest(:,:,1,i)=AP(i,1:end-num_div);YTest(i,1)=AP(i,end);
end%Ytrain=inputData(:,end);
figure
histogram(YTrain)
axis tight
ylabel('Counts')
xlabel('TDS')options = trainingOptions('adam', ...'MaxEpochs',150, ...'MiniBatchSize',64, ...'InitialLearnRate',0.008, ...'GradientThreshold',1, ...'Verbose',false,...'Plots','training-progress',...'ValidationData',{XTest,YTest});layerN=creatCNN2D_ResNet([1,1293,1]);%创建网络，根据自己的需求改函数名称[Net, traininfo] = trainNetwork(XTrain,YTrain,layerN,options);YPredicted = predict(Net,XTest);
predictionError = YTest- YPredicted;
squares = predictionError.^2;
rmse = sqrt(mean(squares))
[R P] = corrcoef(YTest,YPredicted)
scatter(YPredicted,YTest,'+')
xlabel("Predicted Value")
ylabel("True Value")
R2=R(1,2)^2;
hold on
plot([0 2000], [-0 2000],'r--')

训练数据输入如下：最后一列为预测值：

训练过程如下：

训练数据分享

源数据分享：TestData2.mat

链接：https://pan.baidu.com/s/1B1o2xB4aUFOFLzZbwT-7aw?pwd=1xe5
提取码：1xe5

训练建议

以个人经验来说，VNet结构最为简单，但是综合表现最差。对于800-3000长度的数据，容量较小的RNet的表现会比ENet好，对于长度超过的3000的一维数据，ENet的表现更好。

关于超参数的设计：首先最小批次minibatch设置小于64会好一点，确保最终结果会比较好，反正一维卷积神经网络训练很快。第二，与图片不同，一维数据常常数值精度比较高（图片一般就uint8或16格式），因此学习率不宜太高，要不表现会有所下降。我自己尝试的比较好的学习率是0.008.总体来说0.015-0.0005之间都OK，0.05以上结果就开始下降了。

其他引用函数

KS数据划分

Kennard-Stone（KS）方法是一种常用于数据集划分的方法，尤其适用于化学计量学等领域。其主要原理是保证训练集中的样本按照空间距离分布均匀。

function [XSelected,XRest,vSelectedRowIndex]=ks(X,Num) %Num=三分之二的数值
%  ks selects the samples XSelected which uniformly distributed in the exprimental data X's space 
%  Input  
%         X:the matrix of the sample spectra 
%         Num:the number of the sample spectra you want select  
%  Output 
%         XSelected:the sample spectras was sel   ected from the X 
%         XRest:the sample spectras remain int the X after select 
%         vSelectedRowIndex:the row index of the selected sample in the X matrix      
%  Programmer: zhimin zhang @ central south university on oct 28 ,2007 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% start of the kennard-stone step one 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% [nRow,nCol]=size(X); % obtain the size of the X matrix 
mDistance=zeros(nRow,nRow); %dim a matrix for the distance storage 
vAllofSample=1:nRow; for i=1:nRow-1 vRowX=X(i,:); % obtain a row of X for j=i+1:nRow vRowX1=X(j,:); % obtain another row of X         mDistance(i,j)=norm(vRowX-vRowX1); % calc the Euclidian distance end end [vMax,vIndexOfmDistance]=max(mDistance); [nMax,nIndexofvMax]=max(vMax); %vIndexOfmDistance(1,nIndexofvMax) 
%nIndexofvMax 
vSelectedSample(1)=nIndexofvMax; 
vSelectedSample(2)=vIndexOfmDistance(nIndexofvMax); 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% end of the kennard-stone step one 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% start of the kennard-stone step two 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for i=3:Num vNotSelectedSample=setdiff(vAllofSample,vSelectedSample); vMinDistance=zeros(1,nRow-i + 1); for j=1:(nRow-i+1) nIndexofNotSelected=vNotSelectedSample(j); vDistanceNew = zeros(1,i-1); for k=1:(i-1) nIndexofSelected=vSelectedSample(k); if(nIndexofSelected<=nIndexofNotSelected) vDistanceNew(k)=mDistance(nIndexofSelected,nIndexofNotSelected); else vDistanceNew(k)=mDistance(nIndexofNotSelected,nIndexofSelected);     end                        end vMinDistance(j)=min(vDistanceNew); end [nUseless,nIndexofvMinDistance]=max(vMinDistance); vSelectedSample(i)=vNotSelectedSample(nIndexofvMinDistance); 
end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%%%% end of the kennard-stone step two 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%%%% start of export the result 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
vSelectedRowIndex=vSelectedSample; for i=1:length(vSelectedSample) XSelected(i,:)=X(vSelectedSample(i),:); 
end vNotSelectedSample=setdiff(vAllofSample,vSelectedSample); 
for i=1:length(vNotSelectedSample) XRest(i,:)=X(vNotSelectedSample(i),:); 
end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%%%% end of export the result 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%