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CS246: Mining Massive Datasets Jure Leskovec, Stanford University http://cs246.stanford.edu High dim. data Graph data Infinite data Machine learning Apps Locality sensitive hashing PageRank, SimRank Filtering data streams SVM Recommen der systems Clustering Community Detection Web advertising Decision Trees Association Rules Dimensional ity reduction Spam Detection Queries on streams Perceptron, kNN Duplicate document detection 1/29/2013 Jure Leskovec, Stanford CS246: Mining Massive Datasets, http://cs246.stanford.edu 2 Customer X Buys Metallica CD Buys Megadeth CD 1/29/2013 Customer Y Does search on Metallica Recommender system suggests Megadeth from data collected about customer X Jure Leskovec, Stanford C246: Mining Massive Datasets 3 Examples: Search Recommendations Items 1/29/2013 Products, web sites, blogs, news items, … Jure Leskovec, Stanford C246: Mining Massive Datasets 4 Shelf space is a scarce commodity for traditional retailers Also: TV networks, movie theaters,… Web enables near-zero-cost dissemination of information about products From scarcity to abundance More choice necessitates better filters Recommendation engines How Into Thin Air made Touching the Void a bestseller: http://www.wired.com/wired/archive/12.10/tail.html 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 5 Source: Chris Anderson (2004) 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 6 Read http://www.wired.com/wired/archive/12.10/tail.html to learn more! 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 7 Editorial and hand curated List of favorites Lists of “essential” items Simple aggregates Top 10, Most Popular, Recent Uploads Tailored to individual users Amazon, Netflix, … 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 8 X = set of Customers S = set of Items Utility function u: X × S R R = set of ratings R is a totally ordered set e.g., 0-5 stars, real number in [0,1] 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 9 Avatar Alice 1 Bob Carol LOTR Matrix 0.2 0.5 0.2 0.3 1 0.4 David 1/29/2013 Pirates Jure Leskovec, Stanford C246: Mining Massive Datasets 10 (1) Gathering “known” ratings for matrix How to collect the data in the utility matrix (2) Extrapolate unknown ratings from the known ones Mainly interested in high unknown ratings We are not interested in knowing what you don’t like but what you like (3) Evaluating extrapolation methods How to measure success/performance of recommendation methods 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 11 Explicit Ask people to rate items Doesn’t work well in practice – people can’t be bothered Implicit Learn ratings from user actions E.g., purchase implies high rating What about low ratings? 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 12 Key problem: matrix U is sparse Most people have not rated most items Cold start: New items have no ratings New users have no history Three approaches to recommender systems: 1) Content-based Today! 2) Collaborative 3) Latent factor based 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 13 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 14 Main idea: Recommend items to customer x similar to previous items rated highly by x Example: Movie recommendations Recommend movies with same actor(s), director, genre, … Websites, blogs, news Recommend other sites with “similar” content 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 15 Item profiles likes build recommend match Red Circles Triangles User profile 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 16 For each item, create an item profile Profile is a set (vector) of features Movies: author, title, actor, director,… Text: Set of “important” words in document How to pick important features? Usual heuristic from text mining is TF-IDF (Term frequency * Inverse Doc Frequency) Term … Feature Document … Item 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 17 fij = frequency of term (feature) i in doc (item) j Note: we normalize TF to discount for “longer” documents ni = number of docs that mention term i N = total number of docs TF-IDF score: wij = TFij × IDFi Doc profile = set of words with highest TF-IDF scores, together with their scores 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 18 User profile possibilities: Weighted average of rated item profiles Variation: weight by difference from average rating for item … Prediction heuristic: Given user profile x and item profile i, estimate 𝒙·𝒊 𝑢(𝒙, 𝒊) = cos(𝒙, 𝒊) = | 𝒙 |⋅| 𝒊 | 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 19 +: No need for data on other users No cold-start or sparsity problems +: Able to recommend to users with unique tastes +: Able to recommend new & unpopular items No first-rater problem +: Able to provide explanations Can provide explanations of recommended items by listing content-features that caused an item to be recommended 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 20 –: Finding the appropriate features is hard E.g., images, movies, music –: Overspecialization Never recommends items outside user’s content profile People might have multiple interests Unable to exploit quality judgments of other users –: Recommendations for new users How to build a user profile? 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 21 Consider user x Find set N of other users whose ratings are “similar” to x’s ratings x N Estimate x’s ratings based on ratings of users in N 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 23 rx = [*, _, _, *, ***] ry = [*, _, **, **, _] Let rx be the vector of user x’s ratings Jaccard similarity measure Problem: Ignores the value of the rating rx, ry as sets: rx = {1, 4, 5} ry = {1, 3, 4} Cosine similarity measure sim(x, y) = cos(rx, ry) = 𝑟𝑥 ⋅𝑟𝑦 rx, ry as points: rx = {1, 0, 0, 1, 3} ry = {1, 0, 2, 2, 0} ||𝑟𝑥 ||⋅||𝑟𝑦 || Problem: Treats missing ratings as “negative” Pearson correlation coefficient Sxy = items rated by both users x and y 𝒔𝒊𝒎 𝒙, 𝒚 = 𝒔∈𝑺𝒙𝒚 𝒔∈𝑺𝒙𝒚 1/29/2013 rx, ry … avg. rating of x, y 𝒓𝒙𝒔 − 𝒓𝒙 𝒓𝒚𝒔 − 𝒓𝒚 𝒓𝒙𝒔 − 𝒓𝒙 𝟐 Jure Leskovec, Stanford C246: Mining Massive Datasets 𝒔∈𝑺𝒙𝒚 𝒓𝒚𝒔 − 𝒓𝒚 𝟐 24 Cosine sim: 𝒔𝒊𝒎(𝒙, 𝒚) = 𝒊 𝒓𝒙𝒊 𝟐 𝒊 𝒓𝒙𝒊 ⋅ 𝒓𝒚𝒊 ⋅ 𝟐 𝒊 𝒓𝒚𝒊 Intuitively we want: sim(A, B) > sim(A, C) Jaccard similarity: 1/5 < 2/4 Cosine similarity: 0.386 > 0.322 Considers missing ratings as “negative” Solution: subtract the (row) mean sim A,B vs. A,C: 0.092 > -0.559 Notice cosine sim. is correlation when data is centered at 0 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 25 Let rx be the vector of user x’s ratings Let N be the set of k users most similar to x who have rated item i Prediction for item s of user x: 𝑟𝑥𝑖 = 𝑟𝑥𝑖 = 1 𝑘 𝑦∈𝑁 𝑟𝑦𝑖 𝑦∈𝑁 𝑠𝑥𝑦 ⋅𝑟𝑦𝑖 𝑦∈𝑁 𝑠𝑥𝑦 Shorthand: 𝒔𝒙𝒚 = 𝒔𝒊𝒎 𝒙, 𝒚 Other options? Many other tricks possible… 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 26 So far: User-user collaborative filtering Another view: Item-item For item i, find other similar items Estimate rating for item i based on ratings for similar items Can use same similarity metrics and prediction functions as in user-user model rxi 1/29/2013 s rxj jN ( i ; x ) ij s jN ( i ; x ) ij sij… similarity of items i and j rxj…rating of user u on item j N(i;x)… set items rated by x similar to i Jure Leskovec, Stanford C246: Mining Massive Datasets 27 users 1 1 2 1 movies 5 2 4 6 4 2 5 5 4 4 3 7 8 2 3 10 11 12 5 4 4 5 3 9 4 4 4 2 2 1 3 5 2 3 2 2 3 - unknown rating 1/29/2013 6 5 1 4 1 4 3 2 3 3 5 4 - rating between 1 to 5 Jure Leskovec, Stanford C246: Mining Massive Datasets 28 users 1 1 2 1 movies 5 2 4 6 4 2 5 4 3 5 6 ? 5 4 1 4 1 4 3 2 3 3 7 9 10 11 12 5 4 4 2 3 5 3 8 4 4 2 1 3 5 4 2 3 2 2 2 3 5 4 - estimate rating of movie 1 by user 5 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 29 users 1 1 2 1 movies 5 2 4 6 4 2 5 4 3 5 6 ? 5 4 1 4 1 4 3 2 3 3 7 2 3 10 11 12 5 4 4 4 4 2 3 Neighbor selection: Identify movies similar to movie 1, rated by user 5 1/29/2013 9 4 5 3 8 Jure Leskovec, Stanford C246: Mining Massive Datasets 1.00 2 1 3 5 0.41 2 -0.10 2 2 sim(1,m) 4 3 5 -0.18 -0.31 0.59 Here we use Pearson correlation as similarity: 1) Subtract mean rating mi from each movie i m1 = (1+3+5+5+4)/5 = 3.6 row 1: [-2.6, 0, -0.6, 0, 0, 1.4, 0, 0, 1.4, 0, 0.4, 0] 2) Compute cosine similarities between rows 30 users 1 1 2 1 movies 5 2 4 6 4 2 5 5 6 ? 5 4 1 4 4 1 4 3 2 3 3 3 7 9 10 11 12 5 4 4 2 3 5 3 8 4 4 4 2 3 1.00 2 1 3 5 0.41 2 -0.10 2 2 sim(1,m) 4 3 5 -0.18 -0.31 0.59 Compute similarity weights: s13=0.41, s16=0.59 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 31 users 1 1 2 1 movies 5 2 4 6 4 2 5 6 4 4 3 5 7 8 2.6 5 1 4 1 4 3 2 3 3 10 11 12 5 4 4 2 3 5 3 9 4 4 4 2 3 2 r15 = (0.41*2 + 0.59*3) / (0.41+0.59) = 2.6 Jure Leskovec, Stanford C246: Mining Massive Datasets 1 3 5 3 2 2 Predict by taking weighted average: 1/29/2013 2 5 4 𝒓𝒊𝒙 = 𝒋∈𝑵(𝒊;𝒙) 𝒔𝒊𝒋 ⋅ 𝒓𝒋𝒙 𝒔𝒊𝒋 32 Before: rxi sr jN ( i ; x ) ij xj s jN ( i ; x ) ij Define similarity sij of items i and j Select k nearest neighbors N(i; x) Items most similar to i, that were rated by x Estimate rating rxi as the weighted average: rxi bxi s ( r b ) ij xj xj jN ( i ; x ) s jN ( i ; x ) ij baseline estimate for rxi 𝒃𝒙𝒊 = 𝝁 + 𝒃𝒙 + 𝒃𝒊 1/29/2013 μ = overall mean movie rating bx = rating deviation of user x = (avg. rating of user x) – μ bi = rating deviation of movie i Jure Leskovec, Stanford C246: Mining Massive Datasets 33 Avatar Alice LOTR 1 David Pirates 0.8 0.5 Bob Carol Matrix 0.9 1 1 0.3 0.8 0.4 In practice, it has been observed that item-item often works better than user-user Why? Items are simpler, users have multiple tastes 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 34 + Works for any kind of item No feature selection needed - Cold Start: Need enough users in the system to find a match - Sparsity: The user/ratings matrix is sparse Hard to find users that have rated the same items - First rater: Cannot recommend an item that has not been previously rated New items, Esoteric items - Popularity bias: Cannot recommend items to someone with unique taste Tends to recommend popular items 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 35 Implement two or more different recommenders and combine predictions Perhaps using a linear model Add content-based methods to collaborative filtering Item profiles for new item problem Demographics to deal with new user problem 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 36 - Evaluation - Error metrics - Complexity / Speed 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 37 movies 1 3 4 3 5 4 5 5 5 2 2 3 users 3 2 5 2 3 1 1 3 1 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 38 movies 1 3 4 3 5 4 5 5 5 ? ? 3 users 3 2 ? 2 3 1 Test Data Set ? ? 1 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 39 Compare predictions with known ratings Root-mean-square error (RMSE) 𝑥𝑖 𝑟𝑥𝑖 − ∗ 2 𝑟𝑥𝑖 where 𝒓𝒙𝒊 is predicted, 𝒓∗𝒙𝒊 is the true rating of x on i Precision at top 10: % of those in top 10 Rank Correlation: Spearman’s correlation between system’s and user’s complete rankings Another approach: 0/1 model Coverage: Number of items/users for which system can make predictions Precision: Accuracy of predictions Receiver operating characteristic (ROC) Tradeoff curve between false positives and false negatives 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 40 Narrow focus on accuracy sometimes misses the point Prediction Diversity Prediction Context Order of predictions In practice, we care only to predict high ratings: RMSE might penalize a method that does well for high ratings and badly for others 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 42 Training data 100 million ratings, 480,000 users, 17,770 movies 6 years of data: 2000-2005 Test data Last few ratings of each user (2.8 million) Evaluation criterion: root mean squared error (RMSE) Netflix Cinematch RMSE: 0.9514 Competition 2700+ teams $1 million prize for 10% improvement on Cinematch 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 43 Expensive step is finding k most similar customers: O(|X|) Too expensive to do at runtime Could pre-compute Naïve pre-computation takes time O(N ·|C|) We already know how to do this! Near-neighbor search in high dimensions (LSH) Clustering Dimensionality reduction 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 44 Leverage all the data Don’t try to reduce data size in an effort to make fancy algorithms work Simple methods on large data do best Add more data e.g., add IMDB data on genres More data beats better algorithms http://anand.typepad.com/datawocky/2008/03/more-data-usual.html 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 45 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 46 Next topic: Recommendations via Latent Factor models Exoticness / Price Overview of Coffee Varieties B2 B1 I2 I1C6 L5 Exotic S5 C1 S2S1 S7 S6 C7 R4 S3 R6 R3 R2 C2 C4 a1 L4C3 FR S4 TE F9 R5 R8 Popular Roasts and Blends Flavored F8 F3 F2 F1 F0 F6 F5 F4 Com plexity of Flavor The bubbles above represent products sized by sales volume. Products close to each other are recommended to each other. 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 47 [Bellkor Team] serious The Color Purple Geared towards females Braveheart Amadeus Sense and Sensibility Ocean’s 11 Lethal Weapon Geared towards males Dave The Lion King The Princess Diaries Independence Day Dumb and Dumber Gus escapist 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 48 Koren, Bell, Volinksy, IEEE Computer, 2009 1/29/2013 Jure Leskovec, Stanford C246: Mining Massive Datasets 49