MATLAB: PCA (dimension reduction) in embedded matlab

dimension reductionpca

I have a 22×22 matrix 'Y' which needs to be dimension reduced to 10 principal values (The principal values are chosen by choosing the top 10 eigenvectors of 'Y') and the remaining rows should be filled with zeros all the while maintaining the order.

I am quite new to matlab so it would be a great help if someone could help me out with the coding.

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for i = 1 : 22
  for a = 1 : 12
      if (i == req_idx(a))
          for j = 1 : 22
              Y_dr(i,j) = Y(i,j);
          end
      else
          for k = 1 : 22
              Y_dr(i,k) = 0;
          end
      end
  end
end

I have written the code as shown above and have used the sort function to get the principal components which gives an ascending or descending order but I need the 'req_idx' variable to be in appropriate order.

Kindly Help !

Related Solutions

MATLAB: Questions about dimensionality reduction in Matlab using PCA.

Trying to answer your questions roughly in the order you asked.

The total number of principal components (PC) is equal to the number of your variables. The PC variables are simply a linear combination of the original variables, projected onto a different set of mutually perpendicular axes.

MATLAB will always generate p principal components, where p is the number of variables (columns) in your data. The transformed data will have the same number of dimensions as the original data. There is no dimensional reduction until you choose to select only a subset of the PCs (thereby accepting some loss of the ability to explain all of the variation).

The explained vector will be length p. It does list how much of your data’s variance is included in the resulting principal components. If you sum up the entire vector, it will sum to 100, as you say. Suppose p = 5 and

   explained = [60; 20; 10; 7; 3]

It sums to 100. But if you decide to only use the first two PCs, then you will have explained 80% of the total variation. Not 100% (as you seem to imply in your question).

For the answer to your last questions about the score variable, take a look at my answer here, which has a detailed example (using more informative variable names). I think I explain it there.

If you search "cyclist" and "PCA" in this forum, you will find some other stuff from me that might be helpful.

MATLAB: Won’t this run? (dimension mismatch)

 A = [1:62]
 B = [1:62]

okay so far -- though you can just use

 A = 1:62;
 B = 1:62;

Then

   n = size(A,2)

okay, A is 1 x 62 so its second dimension is 62, so n will be assigned 62.

Then

C + size(62, n+1)

62 is a scalar, something that is size 1 by 1.

n is 62 so n+1 is 63. Then size(62, 63) is asking what the length is of the 63rd dimension of the 1 x 1 scalar that has value 62. In MATLAB, all trailing dimensions automatically have length 1 -- for example [5 6 7] is 1 x 3 x 1 x 1 x 1 x 1 x 1 x 1 x 1 ... indefinitely x 1. So size(62, 63) is 1. So C will become 1.

C(:,1:n+1) = [A,B]

the ":" part is asking to write values into all rows of the scalar value 1 that is in C, which is a bit oddly phrased for this kind of task but is valid. The ,1:n+1 is going to be ,1:62+1 and with C only being 1 x 1, your left hand side is going to be C(1,1:63)

[A,B] meanwhile is the result of putting the 1 x 62 array in A together with the 1 x 62 array in B, which is a total of 124 elements.

So your left hand side is saying that you should store in the 63 locations from C(1,1) to C(1,63), but your right hand side of the assignment says that there are 124 values to write into those 63 locations.

Unfortunately your code has no comments about what your desired outcome was, so we do not know what to suggest to you as replacement.

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Related Solutions

MATLAB: Questions about dimensionality reduction in Matlab using PCA.

MATLAB: Won’t this run? (dimension mismatch)

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