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I have got a confusion in PCA:

Is the concept of weight same as Eigenvalues as discussed in the research paper Eigenfaces for Recognition by Matthew Turk and Alex Pentland:

efficient way to learn and recognize faces would be to build up the characteristic features by experience over time and recognize particular faces by comparing the feature weights needed to (approximately) reconstruct them with the weights associated with known individuals. Each individual, therefore, would be characterized by the small set of feature or eigenpicture weights needed to describe and reconstruct them—an extremely compact representation when compared with the images themselves.

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  • $\begingroup$ The usual rule is one question per post. Please split your question into two posts. $\endgroup$ – Yuval Filmus Nov 6 '18 at 17:05
  • $\begingroup$ A weight just means the quantity of a certain feature present in an image. In the context of PCA, you project a vector down to the space spanned by the top eigenvectors. Then you can represent this projection as a linear combination of top eigenvectors. The weigths are the coefficients of the eigenvectors in this linear combination. The idea presented in the paragraph is a small number of features are sufficient to fairly accurately describe images, and so you only need a small number of weights to closely approximate an image. $\endgroup$ – Solomonoff's Secret Nov 6 '18 at 19:33
  • $\begingroup$ To continue @Solomonoff'sSecret's comment, the concept of weight is NOT sigenvalues. Each eigenvalue is associated to an eigenvector. If you want to ignore some less significant principle components, you can choose those eigenvectors that have smaller eigenvalues. $\endgroup$ – Apass.Jack Nov 7 '18 at 5:35
  • $\begingroup$ edit :you can choose those eigenvectors that have larger eigenvalues $\endgroup$ – user2994783 Nov 9 '18 at 23:13
  • $\begingroup$ Choose those with smaller eigenvalue if you want to ignore some of them. $\endgroup$ – Apass.Jack Nov 14 '18 at 22:44

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