How MapReduce Helps Scale to Analyze Movie Recommendations
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Join For FreeThe content of this article was written by Edwin Chen and can be found at his blog, linked here.
This is going to be an inyourface introduction to Scalding, the (Scala + Cascading) MapReduce framework that Twitter recently opensourced.
In 140: instead of forcing you to write raw map and reduce functions, Scalding allows you to write natural code like
// Create a histogram of tweet lengths. tweets.map('tweet > 'length) { tweet : String => tweet.size }.groupBy('length) { _.size }
Not much different from the Ruby you’d write to compute tweet distributions over small data? Exactly.
Two notes before we begin:
 This Github repository contains all the code used.
 For a gentler introduction to Scalding, see this Getting Started guide on the Scalding wiki.
Movie Similarities
Imagine you run an online movie business, and you want to generate movie recommendations. You have a rating system (people can rate movies with 1 to 5 stars), and we’ll assume for simplicity that all of the ratings are stored in a TSV file somewhere.
Let’s start by reading the ratings into a Scalding job.
/** * The input is a TSV file with three columns: (user, movie, rating). */ val INPUT_FILENAME = "data/ratings.tsv" /** * Read in the input and give each field a type and name. */ val ratings = Tsv(INPUT_FILENAME).read .mapTo((0, 1, 2) > ('user, 'movie, 'rating)) { fields : (String, String, Double) => fields } /** * Let's also keep track of the total number of people who rated each movie. */ val numRaters = ratings // Put the number of people who rated each movie into a field called "numRaters". .groupBy('movie) { _.size }.rename('size > 'numRaters) // Rename, since Scalding requires both sides to have distinct fields when we join. .rename('movie > 'movieX) // Merge `ratings` with `numRaters`, by joining on their movie fields. val ratingsWithSize = ratings .joinWithSmaller('movie > 'movieX, numRaters) .discard('movieX) // Remove the extra field. // ratingsWithSize now contains the following fields: (user, movie, rating, numRaters).
You want to calculate how similar pairs of movies are, so that if someone watches The Lion King, you can recommend films like Toy Story. So how should you define the similarity between two movies?
One way is to use their correlation:
 For every pair of movies A and B, find all the people who rated both A and B.
 Use these ratings to form a Movie A vector and a Movie B vector.
 Calculate the correlation between these two vectors.
 Whenever someone watches a movie, you can then recommend the movies most correlated with it.
Let’s start with the first two steps.
/** * To get all pairs of corated movies, we'll join `ratings` against itself. * So first make a dummy copy of the ratings that we can join against. */ val ratings2 = ratingsWithSize .rename(('user, 'movie, 'rating, 'numRaters) > ('user2, 'movie2, 'rating2, 'numRaters2)) /** * Now find all pairs of corated movies (pairs of movies that a user has rated) by * joining the duplicate rating streams on their user fields, */ val ratingPairs = ratingsWithSize .joinWithSmaller('user > 'user2, ratings2) // Dedupe so that we don't calculate similarity of both (A, B) and (B, A). .filter('movie, 'movie2) { movies : (String, String) => movies._1 < movies._2 } .project('movie, 'rating, 'numRaters, 'movie2, 'rating2, 'numRaters2) // By grouping on ('movie, 'movie2), we can now get all the people who rated any pair of movies.
Before using these rating pairs to calculate correlation, let’s stop for a bit.
Since we’re explicitly thinking of movies as vectors of ratings, it’s natural to compute some very vectory things like norms and dot products, as well as the length of each vector and the sum over all elements in each vector. So let’s compute these:
/** * Compute dot products, norms, sums, and sizes of the rating vectors. */ val vectorCalcs = ratingPairs // Compute (x*y, x^2, y^2), which we need for dot products and norms. .map(('rating, 'rating2) > ('ratingProd, 'ratingSq, 'rating2Sq)) { ratings : (Double, Double) => (ratings._1 * ratings._2, math.pow(ratings._1, 2), math.pow(ratings._2, 2)) } .groupBy('movie, 'movie2) { group => group.size // length of each vector .sum('ratingProd > 'dotProduct) .sum('rating > 'ratingSum) .sum('rating2 > 'rating2Sum) .sum('ratingSq > 'ratingNormSq) .sum('rating2Sq > 'rating2NormSq) .max('numRaters) // Just an easy way to make sure the numRaters field stays. .max('numRaters2) // All of these operations chain together like in a builder object. }
To summarize, each row in vectorCalcs now contains the following fields:
 movie, movie2
 numRaters, numRaters2: the total number of people who rated each movie
 size: the number of people who rated both movie and movie2
 dotProduct: dot product between the movie vector (a vector of ratings) and the movie2 vector (also a vector of ratings)
 ratingSum, rating2sum: sum over all elements in each ratings vector
 ratingNormSq, rating2Normsq: squared norm of each vector
So let’s go back to calculating the correlation between movie and movie2. We could, of course, calculate correlation in the standard way: find the covariance between the movie and movie2 ratings, and divide by their standard deviations.
But recall that we can also write correlation in the following form:
Corr(X,Y)=n∑xy−∑x∑yn∑x2−(∑x)2√n∑y2−(∑y)2√
(See the Wikipedia page on correlation.)
Notice that every one of the elements in this formula is a field in vectorCalcs! So instead of using the standard calculation, we can use this form instead:
val correlations = vectorCalcs .map(('size, 'dotProduct, 'ratingSum, 'rating2Sum, 'ratingNormSq, 'rating2NormSq) > 'correlation) { val fields : (Double, Double, Double, Double, Double, Double) => correlation(fields._1, fields._2, fields._3, fields._4, fields._5, fields._6) } def correlation(size : Double, dotProduct : Double, ratingSum : Double, rating2Sum : Double, ratingNormSq : Double, rating2NormSq : Double) = { val numerator = size * dotProduct  ratingSum * rating2Sum val denominator = math.sqrt(size * ratingNormSq  ratingSum * ratingSum) * math.sqrt(size * rating2NormSq  rating2Sum * rating2Sum) numerator / denominator }
And that’s it! To see the full code, check out the Github repository here.
Book Similarities
Let’s run this code over some real data. Unfortunately, I didn’t have a clean source of movie ratings available, so instead I used this dataset of 1 million book ratings.
I ran a quick command, using the handy scald.rb script that Scalding provides…
# Send the job off to a Hadoop cluster scald.rb MovieSimilarities.scala input ratings.tsv output similarities.tsv
…and here’s a sample of the top output I got:
As we’d expect, we see that
 Harry Potter books are similar to other Harry Potter books
 Lord of the Rings books are similar to other Lord of the Rings books
 Tom Clancy is similar to John Grisham
 Chick lit (Summer Sisters, by Judy Blume) is similar to chick lit (Bridget Jones)
Just for fun, let’s also look at books similar to The Great Gatsby:
(Schoolboy memories, exactly.)
More Similarity Measures
Of course, there are lots of other similarity measures we could use besides correlation.
Cosine Similarity
Cosine similarity is a another common vectorbased similarity measure.
def cosineSimilarity(dotProduct : Double, ratingNorm : Double, rating2Norm : Double) = { dotProduct / (ratingNorm * rating2Norm) }
Correlation, Take II
We can also also add a regularized correlation, by (say) adding N virtual movie pairs that have zero correlation. This helps avoid noise if some movie pairs have very few raters in common (for example, The Great Gatsby had an unlikely raw correlation of 1 with many other books, due simply to the fact that those book pairs had very few ratings).
def regularizedCorrelation(size : Double, dotProduct : Double, ratingSum : Double, rating2Sum : Double, ratingNormSq : Double, rating2NormSq : Double, virtualCount : Double, priorCorrelation : Double) = { val unregularizedCorrelation = correlation(size, dotProduct, ratingSum, rating2Sum, ratingNormSq, rating2NormSq) val w = size / (size + virtualCount) w * unregularizedCorrelation + (1  w) * priorCorrelation }
Jaccard Similarity
Recall that one of the lessons of the Netflix prize was that implicit data can be quite useful – the mere fact that you rate a James Bond movie, even if you rate it quite horribly, suggests that you’d probably be interested in similar action films. So we can also ignore the value itself of each rating and use a setbased similarity measure like Jaccard similarity.
def jaccardSimilarity(usersInCommon : Double, totalUsers1 : Double, totalUsers2 : Double) = { val union = totalUsers1 + totalUsers2  usersInCommon usersInCommon / union }
Incorporation
Finally, let’s add all these similarity measures to our output.
val PRIOR_COUNT = 10 val PRIOR_CORRELATION = 0 val similarities = vectorCalcs .map(('size, 'dotProduct, 'ratingSum, 'rating2Sum, 'ratingNormSq, 'rating2NormSq, 'numRaters, 'numRaters2) > ('correlation, 'regularizedCorrelation, 'cosineSimilarity, 'jaccardSimilarity)) { fields : (Double, Double, Double, Double, Double, Double, Double, Double) => val (size, dotProduct, ratingSum, rating2Sum, ratingNormSq, rating2NormSq, numRaters, numRaters2) = fields val corr = correlation(size, dotProduct, ratingSum, rating2Sum, ratingNormSq, rating2NormSq) val regCorr = regularizedCorrelation(size, dotProduct, ratingSum, rating2Sum, ratingNormSq, rating2NormSq, PRIOR_COUNT, PRIOR_CORRELATION) val cosSim = cosineSimilarity(dotProduct, math.sqrt(ratingNormSq), math.sqrt(rating2NormSq)) val jaccard = jaccardSimilarity(size, numRaters, numRaters2) (corr, regCorr, cosSim, jaccard) }
Book Similarities Revisited
Let’s take another look at the book similarities above, now that we have these new fields.
Here are some of the top BookCrossing pairs, sorted by their shrunk correlation:
Notice how regularization affects things: the Dark Tower pair has a pretty high raw correlation, but relatively few ratings (reducing our confidence in the raw correlation), so it ends up below the others.
And here are books similar to The Great Gatsby, this time ordered by cosine similarity:
Input Abstraction
So our code right now is tied to our specific ratings.tsv input. But what if we change the way we store our ratings, or what if we want to generate similarities for something entirely different?
Let’s abstract away our input. We’ll create a VectorSimilarities class that represents input data in the following format:
// This is an abstract method that returns a Pipe (aka, a stream of rating tuples). // It takes in three symbols that name the user, item, and rating fields. def input(userField : Symbol, itemField : Symbol, ratingField : Symbol) : Pipe val ratings = input('user, 'item, 'rating) // ... // The rest of the code remains essentially the same.
Whenever we want to define a new input format, we simply subclass VectorSimilarities and provide a concrete implementation of the input method.
BookCrossings
For example, here’s a class I could have used to generate the book recommendations above:
class BookCrossing(args : Args) extends VectorSimilarities(args) { override def input(userField : Symbol, itemField : Symbol, ratingField : Symbol) : Pipe = { val bookCrossingRatings = Tsv("bookcrossingratings.tsv") .read .mapTo((0, 1, 2) > (userField, itemField, ratingField)) { fields : (String, String, Double) => fields } bookCrossingRatings } }
The input method simply reads from a TSV file and lets the VectorSimilarities superclass do all the work. Instant recommendations, BOOM.
Song Similarities with Twitter + iTunes
But why limit ourselves to books? We do, after all, have Twitter at our fingertips…
rated Born This Way by Lady GaGa 5 stars itun.es/iSg92N#iTunes
Since iTunes lets you send a tweet whenever you rate a song, we can use these to generate music recommendations!
Again, we create a new class that overrides the abstract input defined in VectorSimilarities…
class ITunes(args : Args) extends VectorSimilarities(args) { // Example tweet: // rated New Kids On the Block: Super Hits by New Kids On the Block 5 stars http://itun.es/iSg3Fc #iTunes val ITUNES_REGEX = """rated (.+?) by (.+?) (\d) stars .*? #iTunes""".r override def input(userField : Symbol, itemField : Symbol, ratingField : Symbol) : Pipe = { val itunesRatings = // This is a Twitterinternal tweet source, but you could just as easily scrape // Twitter yourself and provide your own source of tweets: https://dev.twitter.com/docs TweetSource() .mapTo('userId, 'text) { s => (s.getUserId, s.getText) } .filter('text) { text : String => text.contains("#iTunes") } .flatMap('text > ('song, 'artist, 'rating)) { text : String => ITUNES_REGEX.findFirstMatchIn(text).map { _.subgroups }.map { l => (l(0), l(1), l(2)) } } .rename(('userId, 'song, 'rating) > (userField, itemField, ratingField)) .project(userField, itemField, ratingField) itunesRatings } }
…and snap! Here are some songs you might like if you recently listened to Beyoncé:
And some recommended songs if you like Lady Gaga:
GG Pandora.
Location Similarities with Foursquare Checkins
But what if we don’t have explicit ratings? For example, we could be a news site that wants to generate article recommendations, and maybe we only have user visits on each story.
Or what if we want to generate restaurant or tourist recommendations, when all we know is who visits each location?
I'm at Empire State Building (350 5th Ave., btwn 33rd & 34th St., New York) 4sq.com/zZ5xGd
Let’s finally make Foursquare checkins useful. (I kid, I kid.)
Instead of using an explicit rating given to us, we can simply generate a dummy rating of 1 for each checkin. Correlation doesn’t make sense any more, but we can still pay attention to a measure like Jaccard simiilarity.
So we simply create a new class that scrapes tweets for Foursquare checkin information…
class Foursquare(args : Args) extends VectorSimilarities(args) { // Example tweet: I'm at The Ambassador (673 Geary St, btw Leavenworth & Jones, San Francisco) w/ 2 others http://4sq.com/xok3rI // Let's limit to New York for simplicity. val FOURSQUARE_REGEX = """I'm at (.+?) \(.*? New York""".r override def input(userField : Symbol, itemField : Symbol, ratingField : Symbol) : Pipe = { val foursquareCheckins = TweetSource() .mapTo('userId, 'text) { s => (s.getUserId.toLong, s.getText) } .flatMap('text > ('location, 'rating)) { text : String => FOURSQUARE_REGEX.findFirstMatchIn(text).map { _.subgroups }.map { l => (l(0), 1) } } .rename(('userId, 'location, 'rating) > (userField, itemField, ratingField)) .unique(userField, itemField, ratingField) foursquareCheckins } }
…and bam! Here are locations similar to the Empire State Building:
Here are places you might want to check out, if you checkin at Bergdorf Goodman:
And here’s where to go after the Statue of Liberty:
Power of Twitter, yo.
RottenTomatoes Similarities
UPDATE: I grabbed RottenTomatoes data from tweets…
My review for 'How to Train Your Dragon' on Rotten Tomatoes: 4 1/2 stars > bit.ly/xtw3d3
So here’s a sample of the most similar movies:
We see that
 Lord of the Rings, Harry Potter, and Star Wars movies are similar to other Lord of the Rings, Harry Potter, and Star Wars movies
 Big science fiction blockbusters (Avatar) are similar to big science fiction blockbusters (Inception)
 People who like one Justin Timberlake movie (Bad Teacher) also like other Justin Timberlake Movies (In Time). Similarly with Michael Fassbender (A Dangerous Method, Shame)
 Art house movies (The Tree of Life) stick together (Tinker Tailor Soldier Spy)
Let’s also look at the movies with the most negative correlation:
(The more you like loud and dirty popcorn movies (Thor) and vamp romance (Twilight), the less you like impressionistic trees of life? Well I never.)
Next Steps
Hopefully I gave you a taste of the awesomeness of Scalding. To learn even more:
 Check out Scalding on Github.
 Read this Getting Started Guide on the Scalding wiki.
 Run through this codebased introduction, complete with Scalding jobs that you can run in local mode.
 Browse this set of code snippets, which shows examples of different Scalding functions (e.g., map, filter, flatMap, groupBy, count, join).
 And all the code for this post is here.
Watch out for more documentation soon, and you should most definitely follow @Scalding on Twitter for updates or to ask any questions.
Mad Props
And finally, a huge shoutout to Argyris Zymnis, Avi Bryant, and Oscar Boykin, the mastermind hackers who have spent (and continue spending!) unimaginable hours making Scalding a joy to use.
@argyris, @avibryant, @posco: Thanks for it all. #awesomejobguys #loveit
Source: http://blog.echen.me/2012/02/09/movierecommendationsandmoreviamapreduceandscalding/
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