Will uploading a half completed paper to Arxiv hurt my chances of getting admitted to a grad school? I worked on a independent research project during my free time in college. Nobody guided me and nobody assisted me. I developed a algorithm for a problem and I tried it out on few data-sets and compared it with some leading algorithms(Papers for which I could find implementation online) on the same data-sets and the results were great. I didn't get enough time to finish the paper and now I am working in a job.

I wish to apply to US colleges for spring for MS. As I don't have time currently, I am thinking of just uploading the unfinished paper that I prepared in college to Arxiv. The paper will just lists my results on 4 ~ 5 data-sets and nothing else as I don't have the comparison data with me anymore.

Will uploading a half completed paper to Arxiv and mentioning it in my SOP give me any advantage or will it hurt my chances of getting admitted?

Also what should my affiliation be in that paper?
I don't think the arxiv is the right place to upload unfinished work, no matter what you hope to gain from it.  It would be worth reading what the arxiv says about what should be submitted as well as talking to others and seeing what is done in practice in your field.  My own understanding is that the arxiv is an "e-print server", i.e., an electronic preprint server.  A preprint is a completed paper which has not yet been published.  (Though one can still upload published papers to the arxiv in many cases...)

It is only fair to mention that a small but non-negligible percentage of arxiv papers are not intended for submission to journals in their current forms.  For instance, I currently have 27 arxiv papers; a few of them have not been submitted yet, and one of them is not intended for journal submission in its current form.  I was asked to upload it to the arxiv because a colleague of mine wanted to cite it in his accepted journal article and the journal had asked for something a little more formal and stable than my own homepage.  In retrospect, I think this was a good idea on their part.  But all of my arxiv submissions are "complete". 

Concerning incomplete submissions, here is a sentence from the webpage linked to above:


  Please note that we do not accept submissions with omitted figures, tables or sections. We also do not accept "abstract only" submissions. Such submissions are unhelpful to readers and of very limited archival value.


Based on what you describe, I am concerned that your putative arxiv submission would violate either the letter or the spirit of this requirement.  You certainly do not want to submit to the arxiv in this case, because the arxiv is moderated, and low quality submissions can cause you to lose future privileges (as well as giving you a very poor reputation with at least the arxiv moderators, who presumably have some stature and influence in the academic community).

On the other hand, in many cases whether a paper is "unfinished" is known only to the author, and it would probably be possible for you to prepare a version of your paper which meets the above requirements.  In my opinion, as an undergraduate you should not upload (or widely distribute in any e-forum) work that you know to be seriously incomplete.  Work that you upload to the arxiv stays there forever.  (Truly: even if you withdraw a paper, the record of it remains and people can still access all the earlier versions.  I don't know about anyone else, but when I see a withdrawn paper it makes me curious and thus more likely to look at earlier versions.)  Outsiders are not going to judge your work by undergraduate standards; in many cases they will not know that the work was written by an undergraduate.  They'll look at a paper that has the level of an incomplete undergraduate project: that is not making a good name for yourself.

If you want to include your unfinished manuscript in your application, that's a different story: definitely do so if you spent a lot of time on the work and are proud of it.  (Even mature academics list unfinished manuscripts on their CV and sometimes even post them on their webpage.  I do this, although less often as time goes on.)  I may as well say the obvious thing though: it would be better if you finished it.  Couldn't a hard-nosed faculty evaluator say that if you were really passionate, serious and competent, then you would have finished your project?  As above, having the submitted version be formally complete as a document though you yourself know that you'd like to do more with it seems like a good idea.