问题
I use Matlab to read the MNIST database. Those images are, originally, 28x28 (=784) pixels. So, I have a 2D 784x1000 array (meaning, I have read 1000 images).
Supposing my 2D array's name is IMGS, the Matlab expression: IMGS(:, 1), would give me the first image.
In order to perform PCA, so to extract some of the features of the image (from the 784 of them):
- I transpose the array IMGS, putting the images to rows and features (dimensions) to columns, in an array called IMGS_T (IMGS_T(1, :) corresponds to first image).
I use the princomp function like this: [COEFF, SCORES] = princomp(IMGS_T];
My question is this (and it may be a little trivial but, I want to be sure for this): Supposing I want to extract 100 features from the overall of the 784 of them, all I need is the first 100 columns of SCORES?
So, in Matlab terms, all I need is to write: IMGS_PCA = IMGS(:, 100)' and I will have created an 100x1000 array, called IMGS_PCA which will hold my 1000 MNIST images in its columns and the first 100 most important features of them in its rows?
回答1:
Basically it's correct. Note that in princomp rows of input correspond to observations, and columns to variables.
To illustrate your procedure,
IMGS = rand(1000,784);
[COEFF, SCORE] = princomp(IMGS);
To prove the use of function is correct, you can try to recover the original image,
recovered_IMGS = SCORE / COEFF + repmat(mean(IMGS,1), 1000, 1);
then IMGS - recovered_IMGS will give you the zero matrix (within numerical error).
To use only the first 100 features, you can just
for i=101:784
SCORE(:,i) = zeros(1000,1);
end
Then use the same code to recover the images:
recovered_IMGS_100 = SCORE / COEFF + repmat(mean(IMGS,1), 1000, 1);
Or you can, as you mentioned , created another 100 x 1000 array to achieve the same result.
来源：https://stackoverflow.com/questions/21640801/feature-extraction-for-mnist-images-using-pca