TRAINING的合并协方差矩阵必须为正定

问题描述

我知道这个问题已经被问过几次了，但是我找不到解决问题的方法.

I know this question has already been asked a couple of times, but I couldn't find a solution to my problem.

我的变量多于观察值，矩阵中没有NAN值.这是我的功能:

I don't have more variables than observations and I don't have NAN values in my matrix. Here's my function:

function [ind, idx_ran] = fselect(features_f, class_f, dir)

idx = linspace(1,size(features_f, 2), size(features_f, 2));

idx_ran = idx(:,randperm(size(features_f, 2)));

features_t_ran = features_f(:,idx_ran); % randomize colums

len = length(class_f);

r = randi(len, [1, round(len*0.15)]);

x = features_t_ran;
y = class_f;

xtrain = x;
ytrain = y;

xtrain(r,:) = [];
ytrain(r,:) = [];

xtest = x(r,:);
ytest = y(r,:);

f = @(xtrain, ytrain, xtest, ytest)(sum(~strcmp(ytest, classify(xtest, xtrain, ytrain))));
fs = sequentialfs(f, x, y, 'direction', dir);

ind = find(fs < 1);

end

这是我的测试和培训数据.

and here are my test and training data.

>> whos xtest
  Name         Size             Bytes  Class     Attributes

  xtest      524x42            176064  double

>> whos xtrain
  Name           Size              Bytes  Class     Attributes

  xtrain      3008x42            1010688  double

>> whos ytest
  Name         Size            Bytes  Class    Attributes

  ytest      524x1             32488  cell

>> whos ytrain
  Name           Size             Bytes  Class    Attributes

  ytrain      3008x1             186496  cell

>>

这是错误，

Error using crossval>evalFun (line 465)
The function
'@(xtrain,ytrain,xtest,ytest)(sum(~strcmp(ytest,classify(xtest,xtrain,ytrain))))' generated
the following error:
The pooled covariance matrix of TRAINING must be positive definite.

Error in crossval>getFuncVal (line 482)
funResult = evalFun(funorStr,arg(:));

Error in crossval (line 324)
    funResult = getFuncVal(1, nData, cvp, data, funorStr, []);

Error in sequentialfs>callfun (line 485)
    funResult = crossval(fun,x,other_data{:},...

Error in sequentialfs (line 353)
                crit(k) = callfun(fun,x,other_data,cv,mcreps,ParOptions);

Error in fselect (line 26)
fs = sequentialfs(f, x, y, 'direction', dir);

Error in workflow_forward (line 31)
    [ind, idx_ran] = fselect(features_f, class_f, 'forward');

昨天工作了. :/

推荐答案

如果检查函数classify，则会发现该错误是在程序检查从训练矩阵的QR分解获得的矩阵R的条件数时生成的.换句话说，它对您提供的培训矩阵不满意.它发现该矩阵是病态的，因此任何解都将是不稳定的(该函数执行的矩阵求逆等效，这将导致病态的训练矩阵除以非常小的数字).

If you inspect function classify you find that the error is generated when the program checks the condition number of the matrix R obtained from QR decomposition of your training matrix. In other words, it is unhappy with the training matrix you are providing. It finds that this matrix is ill-conditioned and therefore any solution would be unstable (the function performs the equivalent of a matrix inversion which would lead to the equivalent of division by a very small number for an ill-conditioned training matrix).

似乎通过缩小训练集的大小，稳定性降低了.我的建议是，如果可能的话，使用更大的训练集.

It seems that by shrinking the size of your training set the stability was reduced. My suggestion is to use a larger training set if possible.

修改

您可能想知道怎么可能有更多的观察结果而不是变量，并且仍然有病态的问题.答案是，不同的观察结果可以是彼此的线性组合.

You may be wondering how it is possible to have more observations than variables and still have an ill-conditioned problem. The answer is that different observations can be linear combinations of each other.

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