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This might be a general question but I thought this might be the best place to brainstorm. If I had a video website that only wants to retain videos on-demand for a certain number of days before getting rid of them to maximize operating dollars, what sort of data measures/methods would I want to consider or use in general to decide the time period?

Just like a typical website, the video can be tracked for views, followers etc. and the trade off could be on views/operating cost

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Clustering can be an ideal choice here. From the question, seems the data will most probably be in continuous format. Essentially, clustering is a method of finding groups of similar objects. The similarity between the objects is determined by the type of distance measure being used. With this background, you can start by finding the videos that are most liked or disliked by people. Measurements like mutual information gain can be helpful.

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