matlab - 在MATLAB中使用自动编码器进行函数逼近

我有一个简单的非线性函数y = x。^ 2，其中x和y是n维向量，而正方形是逐分量正方形。我想使用Matlab中的自动编码器以低维向量近似y。问题是即使低维空间设置为n-1，重建y也会失真。我的训练数据看起来像
this，这是从低维空间重构的典型result。我的Matlab代码如下。

%% Training data
inputSize=100;
hiddenSize1 = 80;

epo=1000;
dataNum=6000;
rng(123);
y=rand(2,dataNum);
xTrain=zeros(inputSize,dataNum);
for i=1:dataNum
    xTrain(:,i)=linspace(y(1,i),y(2,i),inputSize).^2;
end

%scaling the data to [-1,1]
for i=1:inputSize
    meanX=0.5; %mean(xTrain(i,:));
    sd=max(xTrain(i,:))-min(xTrain(i,:));
    xTrain(i,:) = (xTrain(i,:)- meanX)./sd;
end

%% Training the first Autoencoder

% Create the network.
autoenc1 = feedforwardnet(hiddenSize1);
autoenc1.trainFcn = 'trainscg';
autoenc1.trainParam.epochs = epo;

% Do not use process functions at the input or output
autoenc1.inputs{1}.processFcns = {};
autoenc1.outputs{2}.processFcns = {};

% Set the transfer function for both layers to the logistic sigmoid
autoenc1.layers{1}.transferFcn = 'tansig';
autoenc1.layers{2}.transferFcn = 'tansig';

% Use all of the data for training
autoenc1.divideFcn = 'dividetrain';
autoenc1.performFcn = 'mae';
%% Train the autoencoder
autoenc1 = train(autoenc1,xTrain,xTrain);
%%
% Create an empty network
autoEncoder = network;

% Set the number of inputs and layers
autoEncoder.numInputs = 1;
autoEncoder.numlayers = 1;

% Connect the 1st (and only) layer to the 1st input, and also connect the
% 1st layer to the output
autoEncoder.inputConnect(1,1) = 1;
autoEncoder.outputConnect = 1;

% Add a connection for a bias term to the first layer
autoEncoder.biasConnect = 1;

% Set the size of the input and the 1st layer
autoEncoder.inputs{1}.size = inputSize;
autoEncoder.layers{1}.size = hiddenSize1;

% Use the logistic sigmoid transfer function for the first layer
autoEncoder.layers{1}.transferFcn = 'tansig';

% Copy the weights and biases from the first layer of the trained
% autoencoder to this network
autoEncoder.IW{1,1} = autoenc1.IW{1,1};
autoEncoder.b{1,1} = autoenc1.b{1,1};


%%
% generate the features
feat1 = autoEncoder(xTrain);

%%
% Create an empty network
autoDecoder = network;

% Set the number of inputs and layers
autoDecoder.numInputs = 1;
autoDecoder.numlayers = 1;

% Connect the 1st (and only) layer to the 1st input, and also connect the
% 1st layer to the output
autoDecoder.inputConnect(1,1) = 1;
autoDecoder.outputConnect(1) = 1;

% Add a connection for a bias term to the first layer
autoDecoder.biasConnect(1) = 1;

% Set the size of the input and the 1st layer
autoDecoder.inputs{1}.size = hiddenSize1;
autoDecoder.layers{1}.size = inputSize;

% Use the logistic sigmoid transfer function for the first layer
autoDecoder.layers{1}.transferFcn = 'tansig';

% Copy the weights and biases from the first layer of the trained
% autoencoder to this network

autoDecoder.IW{1,1} = autoenc1.LW{2,1};
autoDecoder.b{1,1} = autoenc1.b{2,1};

%% Reconstruction
desired=xTrain(:,50);
input=feat1(:,50);
output = autoDecoder(input);

figure
plot(output)
hold on
plot(desired,'r')

最佳答案

我不是Matlab用户，但是您的代码让我觉得您有一个标准的浅层自动编码器。您不能真正使用单个自动编码器来近似非线性，因为它不会比纯粹的线性PCA重构具有更好的最优性（如果您需要，我可以提供更详尽的数学推理，尽管这不是math.stackexchange）。。您需要构建一个深层网络，以通过几层线性变换来近似非线性。然后，当您对自动编码器进行去噪时，自动编码器是一个不好的模型（今天几乎没有人在实践中使用它们），它们倾向于通过尝试从嘈杂的版本中重建先验来学习更重要的表示形式。尝试构建深度降噪的自动编码器。 This video引入了去噪自动编码器的概念。该课程还提供了有关深度降噪自动编码器的视频。

关于matlab - 在MATLAB中使用自动编码器进行函数逼近，我们在Stack Overflow上找到一个类似的问题：https://stackoverflow.com/questions/34703372/