Fun with Vectors

Recently the high school age daughter of one of my parents college friends asked my Dad for some help with a math class project on the application of vectors. The following is part of my contribution.

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Consider a database that recommends movies. First users enter ratings, 1 to 5 stars, for movies they have seen. The database represents each rating as the component in dimension of a particular movie of the user's preference vector. Then when a user wants a recommendation, it searches for other user's preference vectors that point in similar directions and include movies that the user hasn't seen.



Given the ratings above, the database would expect Bill to give the new Keanu Reeves movie, "Constantine", a rating of just over 4 because Bill's preference vector most closely matches Bob's but tends to be a little higher on average. The example above uses 8 & 9 dimensional vectors, but a web site like NetFlix probably uses vectors with hundreds and hundreds of dimensions.