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November 1st, 2017, 06:39 PM  #1 
Newbie Joined: Nov 2017 From: Sydney, Australia Posts: 3 Thanks: 0  log2(3/2)=0.584
Hi All, I'm learning a basic course on Big Data and one of the lectures touches on Vector Model, and in that it has this equation. Term Doc Frequency IDF "new" 2 log2(3/2)=0.584 I understand why 3/2 as it's 2 occurrences of the term "new" in 3 documents. But 3/2=1.5, so how does log2(1.5)=0.584? Could someone break it down for me? Thanks. MGS 
November 1st, 2017, 06:45 PM  #2 
Senior Member Joined: Aug 2012 Posts: 1,702 Thanks: 448  
November 1st, 2017, 06:53 PM  #3 
Newbie Joined: Nov 2017 From: Sydney, Australia Posts: 3 Thanks: 0 
Ok, thanks but I probably should have said, explain it to me, not break it down EDIT Ah, wait, so 2 to the power of 0.584963 = 1.5 or there abouts? Last edited by MarkGsargent; November 1st, 2017 at 06:57 PM. 
November 1st, 2017, 07:04 PM  #4 
Senior Member Joined: Aug 2012 Posts: 1,702 Thanks: 448 
That's the base 2 logarithm of 1.5. In other words, what power do I have to raise 2 to, in order to get 1.5? For example, what is the base 2 log of 32? It's 5, because 5 is the power that we have to raise 2 to in order to get 32. Now $2^0 = 1$ and $2^1 = 2$ so we'd expect the base 2 log of 1.5 to be somewhere between 0 and 1. So .5something is about right. Yes. 
November 1st, 2017, 07:56 PM  #5 
Newbie Joined: Nov 2017 From: Sydney, Australia Posts: 3 Thanks: 0 
Ok, cool thanks. Now I just need to understand more why we even use log2 for this scenario.

November 1st, 2017, 09:58 PM  #6  
Senior Member Joined: Aug 2012 Posts: 1,702 Thanks: 448  Quote:
This seems vaguely related to your question. Perhaps you can explain more about the context of your problem. I don't know what the base 2 log is for. ps  I found this ... https://en.wikipedia.org/wiki/Tf%E2%80%93idf It's interesting but it doesn't say anything about base 2 logs. Is any of this relevant to your question? Last edited by Maschke; November 1st, 2017 at 10:04 PM.  
November 2nd, 2017, 08:04 AM  #7 
Senior Member Joined: May 2016 From: USA Posts: 889 Thanks: 357 
This is a pure guess, but the durations of binary searches would be conveniently measured in powers of 2, and that might lead to using log base 2.


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