I got the following from a web site:

The feature vectors represent each image as a linear combination of the eigenfaces defined by the coefficients in the feature vector; if we multiply each eigenface by its corresponding coefficient and then sum these weighted eigenfaces together, we can roughly reconstruct the input image.

The link is: https://blog.cordiner.net/2010/12/02/eigenfaces-face-recognition-matlab/

Some body please guide me.


  • 2
    $\begingroup$ What more precisely is your question? $\endgroup$ – Juho Nov 15 '18 at 15:16
  • $\begingroup$ Was my answer helpful? $\endgroup$ – John L. Apr 12 '19 at 14:55

Have you followed my recommendation in my answer to another question of yours to "read a tutorial on Principal Components Analysis by Lindsay I Smith, which is self-contained and easy to read"? Trust me, that is the fast way for you to learn and understand PCA. I might appear arrogant or opinionated. However, I want to emphasize you should follow my suggestion. That is probably the best help/answer you can get from asking all your recent questions.

Let me explain the quoted sentence a little bit. (It seems you are not familiar with linear algebra.) A linear combination of some eigenfaces means the sum of each of them multiplied by its corresponding coefficient. If this sum is the original image vector, we say the original image is represented by that linear combination. In particular, if we multiply all possible eigenfaces by its corresponding coefficient and then sum these weighted eigenfaces together, we will get exactly the original image vector, that is, we can exactly reconstruct the input image.

Why was "roughly" used in that article then? It was used only because we only have "20 eigenfaces that my training set generated". However, those are the most significant eigenfaces in the sense that their corresponding eigenvalues are the biggest 20. With only 20 eigenfaces, we can still reconstruct the input image but only "roughly". Another connotation of "roughly" comes from the fact that almost all numerical computations are approximations since, for example, we cannot expressed $\sqrt 2$ or even $1/3$ exactly in standard floating binary numbers.

  • $\begingroup$ Go through that tutorial line by line, repeating the computations. All other questions and answers are secondary, even the most popular question and answers on CrossValidated Stack Exchange. Even my answers won't count once you have finished reading that tutorial, since you will get a better understanding by then. (I assume that you are reading that paper with ghostly images as an assignment or something similar.) Asking questions piece by piece here is the slower and shaky way to learn. $\endgroup$ – John L. Nov 15 '18 at 17:35
  • $\begingroup$ Indeed, I cannot help but emphasizing again. Please read that tutorial line by line, repeating its computations by yourself. That is the fastest way for you learn once and for all. It probably take you less time doing that then asking many questions on different sites. You might be afraid of starting reading that tutorial, since it appears so long. Or you might be afraid of the mathematical computations or formulae there of. However, since you have so much time and courage to post many questions, you are able to complete that task, too. It should be, in fact, not hard for you. $\endgroup$ – John L. Nov 16 '18 at 4:03

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