不同类的Matlab协方差矩阵计算

Question

我有 2 个不同的文件，其中一个是具有 3823*63 个元素（3823 个输入和 63 个特征）的输入矩阵 (X)，另一个是具有 3823*1 的类向量 (R)元素；这些元素的值从 0 到 9（有 10 个类）。

我必须为每个类计算协方差矩阵。到目前为止，我只能为每个具有这么多嵌套循环的类计算平均向量。然而，它导致我脑死亡。

还有其他简单的方法吗？

---

有我的目的的代码（感谢 Sam Roberts）：

xTra = importdata('optdigits.tra');
xTra = xTra(:,2:64); % first column's inputs are all zero

rTra = importdata('optdigits.tra');
rTra = rTra(:,65); % classes of the data

c = numel(unique(rTra));

for i = 1:c
    rTrai = (rTra==i-1); % Get indices of the elements from the ith class
    meanvect{i} = mean(xTra(rTrai,:)); % Calculate their mean
    covmat{i} = cov(xTra(rTrai,:)); % Calculate their covariance
end

Answer 1

这能满足你的需要吗？

X = rand(3263,63);
R = randi(10,3263,1)-1;

numClasses = numel(unique(R));

for i = 1:numClasses
    Ri = (R==i); % Get indices of the elements from the ith class
    meanvect{i} = mean(X(Ri,:)); % Calculate their mean
    covmat{i} = cov(X(Ri,:)); % Calculate their covariance
end

此代码循环遍历每个类，选择 R 中与该类中的观察相对应的行，然后从 X 中获取相同的行并计算它们的均值和协方差。它将它们存储在一个元胞数组中，因此您可以像这样访问结果：

% Display the mean vector of class 1
meanvect{1}

% Display the covariance matrix of class 2
covmat{2}

希望有帮助！

Answer 2

不要使用mean 和sum 作为变量名，因为它们是有用的Matlab 内置函数的名称。 （输入doc mean或doc sum获取使用帮助）

cov 还会为您计算协方差矩阵。

您可以使用逻辑索引来提取示例。

covarianceMatrices = cell(m,1);
for k=0:m-1
    covarianceMatrices{k} = cov(xTra(rTra==k,:));
end

单线

covarianceMatrices = arrayfun(@(k) cov(xTra(rTra==k,:)), 0:m-1, 'UniformOutput', false);

Answer 3

首先为每个类构造数据矩阵。 其次计算每个数据矩阵的协方差。

下面的代码就是这样做的。

% assume allData contains all the data you've read in, each row is one data point
% assume classVector contains the class of each data point
numClasses = 10;
data = cell(10,1);       %use cells to store each of the data matrices
covariance = cell(10,1); %store each of the class covariance matrices
[numData dummy] = size(allData);

%get the data out of allData and into each class' data matrix
%there is probably a nice matrix way to do this, but this is hopefully clearer
for i = 1:numData
  currentClass = classVector(i) + 1; %Matlab indexes from 1
  currentData = allData(i,:);
  data{currentClass} = [data{currentClass}; currentData];
end

%calculate the covariance matrix for each class
for i = 1:numClasses
  covariance{i} = cov(data{i});
end