Matlab 多项式回归的10倍交叉验证

我想使用10倍交叉验证方法，测试多项式形式（第一、第二或第三） 第三级）更适合。我想将我的数据集划分为10个子集，并从10个数据集中删除1个子集。导出不含此子集的回归模型，使用导出的回归模型预测此子集的输出值，并计算残差。最后，对每个子集重复计算程序，并将所得残差的平方和。 我已经在Matlab2013b上编写了以下代码，对数据进行采样，并在训练数据上测试回归。我被困在如何对每个子集重复这个问题上，以及如何比较哪种多项式形式更适合

% Sample the data
parm = [AT];
n = length(parm);
k = 10;                 % how many parts to use
allix = randperm(n);    % all data indices, randomly ordered
numineach = ceil(n/k);  % at least one part must have this many data points
allix = reshape([allix NaN(1,k*numineach-n)],k,numineach);
for p=1:k
testix = allix(p,:);            % indices to use for testing
testix(isnan(testix)) = [];     % remove NaNs if necessary
trainix = setdiff(1:n,testix);  % indices to use for training
%train = parm(trainix); %gives the training data
%test = parm(testix);  %gives the testing data
end 

% Derive regression on the training data 
Sal = Salinity(trainix);
Temp = Temperature(trainix);
At = parm(trainix);

xyz =[Sal Temp At];
% Fit a Polynomial Surface
surffit = fit([xyz(:,1), xyz(:,2)],xyz(:,3), 'poly11');
% Shows equation, rsquare, rmse 
[b,bint,r] = fit([xyz(:,1), xyz(:,2)],xyz(:,3), 'poly11');

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关于为每个子集执行代码，您可以将fit放入循环中并存储结果，例如

% Sample the data
parm = [AT];
n = length(parm);
k = 10;                 % how many parts to use
allix = randperm(n);    % all data indices, randomly ordered
numineach = ceil(n/k);  % at least one part must have this many data points
allix = reshape([allix NaN(1,k*numineach-n)],k,numineach);

bAll = []; bintAll = []; rAll = [];

for p=1:k
    testix = allix(p,:);            % indices to use for testing
    testix(isnan(testix)) = [];     % remove NaNs if necessary
    trainix = setdiff(1:n,testix);  % indices to use for training
    %train = parm(trainix); %gives the training data
    %test = parm(testix);  %gives the testing data

    % Derive regression on the training data 
    Sal = Salinity(trainix);
    Temp = Temperature(trainix);
    At = parm(trainix);

    xyz =[Sal Temp At];
    % Fit a Polynomial Surface
    surffit = fit([xyz(:,1), xyz(:,2)],xyz(:,3), 'poly11');
    % Shows equation, rsquare, rmse 
    [b,bint,r] = fit([xyz(:,1), xyz(:,2)],xyz(:,3), 'poly11');

    bAll = [bAll, coeffvalues(b)]; bintAll = [bintAll,bint]; rAll = [rAll,r]; 
end 

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关于最佳拟合，您可能可以选择rmse最低的拟合。

不允许使用fittype/horzcat（第7行）串联双对象的错误。哦，我明白了。从b开始，您可能只需要保存系数。如果是，您可以尝试bAll=[bAll，coeffvalues（b）]而不是bAll=[bAll，b]。抱歉，无法自行测试，因为未安装曲线拟合工具箱