update README

Author: mLuby

README.md

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-# TODO
+# Recommendation Engine
+***A recommendation engine is a tool that predicts what a user will like among a list of items.***
 
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+![](https://colleenvoiceover.files.wordpress.com/2009/12/theroom_netflixrecom.png)
+
+## How it works
+A simple recommendation engine has four parts:
+- a set of users
+- a set of items (e.g. videos)
+- ratings that join users and items (e.g. thumbs on YouTube)
+- a program that maps this information to predictions (AKA recommendations) of what items a user will like.
+
+Our program is based on the **assumption** that users have similar preferences, i.e. one user liking an item means similar users will probably like that item too.
+
+## Concepts
+To determine which users are similar, it's helpful to think about the union and intersection of preference sets.
+
+### Sets
+**union**: *the set comprised of items that appear in both input sets.*
+E.g. `[1,2,3] u [1,3,4] -> [1,3]`
+
+**intersection**: *the set comprised of items that appear in only one of the input sets.*
+E.g. `[1,2,3] n [1,3,5] -> [2,5]`
+
+### Similarity
+**Similarity**: *A user is similar if they have more in common than not.*
+We can represent this by looking at the number of elements in the union of two users' preferences over the total items those users have rated, or `A u B / A + B`
+
+A more advanced concept is that users who disagree about an item (e.g. a likes 1, b *dis*likes 1) are more dissimilar than those who do not (e.g. a likes 1, b likes 2).
+
+### Predicting Preferences
+Once you determine a users' similarity, you can look for items your target user has not yet rated, and see if similar users liked that item.
+
+### Recommendations
+**Recommendations**: *An list of items, ordered such that the item with the greatest probability of being liked is first.*
+
+Generating a list of recommendations is straightfoward:
+1. getting a list of items the target user has not yet rated
+2. predicting the probability the target user will like each item
+3. sorting the resulting items by greatest probability of being liked first.
+
+![](http://www.ecommercejuice.com/wp-content/uploads/2010/06/Email-Personalization.jpg)
+
+Sources: http://www.toptal.com/algorithms/predicting-likes-inside-a-simple-recommendation-engine