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I have a dataset of Tweets along with their Retweet Counts and Favorite Counts. After extracting features from the Tweets, I am training a model to predict the Retweet Counts and Favorite Counts. I want to calculate a value called "Popularity" by taking the weighted average of Retweet Count and Favorite Count for each Tweet. For this, I need score values (or weights) for Retweet Count and Favorite Count. How do I determine these weights? I am writing a research paper and need to justify why I assigned those weights for Retweet Count and Favorite Count.

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Retweet and Favourite are totally different features and although they are correlated with the popularity of the tweet, the exact correlation will be subjective to the training dataset you are using.

One way to come up with the weights is: Information Gain

This paper tries to come up with a weighted average using the user and tweet features for the prediction of retweet counts for a given tweet: http://www.nlpr.ia.ac.cn/2012papers/gjhy/gh154.pdf

Steps by step procedure:
1) Give every tweet a popularity score between 0 to 5 (You have to label your training data)
2) Calculate information gain for different weights of Retweet and Favourite count (refer: https://homes.cs.washington.edu/~shapiro/EE596/notes/InfoGain.pdf)

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