I just downloaded your data set and here is one particular observation - Are you retrieving the all the tweets of every user? Twitter allows you retrieve upto 3200 tweets of a user(if public) via pagination. You can download them to understand how "active" they are for a much better analysis.
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That would require several million API calls. This sample was taken with only 12500 calls.
Ah No - it should be quite easy to achieve. There are two types of API calls for the Twitter API (IP based and OAuth). Oauth provides you 350 requests per hour. It's quite easy and off the shelf packages are available. So, in summary you could use 10 Twitter accounts and make OAuth requests from each of these accounts by polling.
1 hour = 3600 seconds Assuming you use 3500 seconds to make API calls (the rest 100 seconds is used for performing disk operations) 10 accounts should be more than sufficient.
:-)
Your math is off. You could do 3500 requests per hour with 10 accounts. You'd still need thousands of hours (i.e. a few months) because we are talking about millions of API calls.