I am afraid I ask an easy question, but here are my questions:
What is weakly-labeled data and is there any strongly-labeled data? In what situation do we use them?
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Weakly-labeled data is data that has not explicitly been labeled by hand / manually. However, it is not unlabeled, because you know that certain assumptions do hold for an entire data set.
To give an example, let's say you want to design some recognition software that works with images of humans.
A labeled (infrequently also called fully-labeled or strongly-labeled) data set would not only contain the images of specific humans, but would also contain labels that were created manually, like gender, hair color, occupation, body height, weight, ...
A weakly-labeled data set would only contain unlabeled sets of images including meta information that holds for every image inside a set. For example, if you do not label the images, but record only male people, only firemen, ... then you basically have "unlabeled" data but you know at least some meta-information that you can use to categorize your data. Thus, the knowledge of this data is less strong / informative compared to labeled data, but it is not zero.
An unlabeled data set in comparison really contains zero information that could be used to distinguish single samples of the data set. For our example of humans this would be recording people of any gender, hair color, occupation, ..., resulting in one big data set without meta information about the single samples.