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Why this algorithm can not recover completely the images that are out of training samples ??? I mean ,if this method can only recover the images in the training examples perfectly,but those new test samples for which there will be a great loss on information even if you've selected all of the eigenvectors??

Why this algorithm can not I've trained an eigenvector matrix from 100 pictures through PCA algorithm.Then I tried to recover completely one of these 100 images using the matrix I gained,and succeed. It,however,was failure when I tried to recover those images other than in that are out of 100 training samples ??? I mean ,if this method can only recover the images samples.That is,information loss greatly.BTW,recovering in the training examples perfectly,but those new test samples for which there will be means projecting a great loss on information even if you've selected all of the eigenvectors??picture and then back project it.