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Matrix Factorization Technique for Recommender Systems

Recommender systems analyze patterns of user interest in
products to provide personalized recommendations. They seek to predict the rating or preference that user would
give to an item. Some of the most successful realizations of latent factor models are based on matrix factorization...

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Matrix Factorization Technique for Recommender Systems

  1. 1. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion MATRIX FACTORIZATION TECHNIQUE FOR RECOMMENDER SYSTEMS Oluwashina Aladejubelo Universite Joseph Fourier, Grenoble, France June 6, 2015 Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  2. 2. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion About Me Bachelor of Science, Ambrose Alli University, Nigeria (2004-2008) IT Business Analyst, Virgin Nigeria Airlines (2009-2011) Team Lead/Software Architect, Speckless Innovations Limited (2011-2014) Master of Informatics (M2 MOSIG), Universit Joseph Fourier, Grenoble (2014-2015) Master Thesis on ”Distributed Large-Scale Learning” with Pr. Massih-Reza Amini. Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  3. 3. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Overview 1 Introduction 2 Matrix Factorization Methods 3 Netflix Prize Competition 4 Conclusion Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  4. 4. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion 1 Introduction Recommender Systems Content Filtering Approach Collaborative Filtering Approach Content vs Collaborative Filtering 2 Matrix Factorization Methods Matrix Factorization Model (MFM) Stochastic Gradient Descent Alternating Least Squares Adding Biases Additional Input Source Temporal Dynamics Varying confidence levels 3 Netflix Prize Competition 4 Conclusion Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  5. 5. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Recommender Systems Recommender systems analyze patterns of user interest in products to provide personalized recommendations They seek to predict the rating or preference that user would give to an item Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  6. 6. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Recommender Systems Such systems are very useful for entertainment products such as movies, music, and TV shows. Many customers will view the same movie and each customer is likely to view numerous different movies. Huge volume of data arise from customer feedbacks which can be analyzed to provide recommendations Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  7. 7. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Content Filtering Approach creating profile for each user or product to characterize its nature. programs associate users with matching products. it requires gathering external information that may not be available Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  8. 8. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Collaborative Filtering Approach depends on past user behaviour, e.g. previous transactions or product rating does not rely on creation of explicit profiles Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  9. 9. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Collaborative Filtering Approach the primary areas of collaborative filtering are neighborhood methods and latent factor models neighborhood is based on computing the relationships between items or users latent factor models tries to explain by characterizing both items and users on say, 20 to 100 factors inferred from the ratings patterns Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  10. 10. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Content vs Collaborative Filtering Collaborative filtering address data aspects that are difficult to profile. it is generally more accurate suffers from cold startup problem (new product / new user) in which case content filtering is better Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  11. 11. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion 1 Introduction Recommender Systems Content Filtering Approach Collaborative Filtering Approach Content vs Collaborative Filtering 2 Matrix Factorization Methods Matrix Factorization Model (MFM) Stochastic Gradient Descent Alternating Least Squares Adding Biases Additional Input Source Temporal Dynamics Varying confidence levels 3 Netflix Prize Competition 4 Conclusion Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  12. 12. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Matrix Factorization Model (MFM) some of the most successful realizations of latent factor models are based on matrix factorization it characterizes both items and users by vectors of factors inferred from item rating patterns high correspondence between item and user factors leads to a recommendation Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  13. 13. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Matrix Factorization Model (MFM) MFM maps both users & items to a joint latent factor space of dimensionality f the user-item interactions are modeled as inner products in space f each item i is associated with a vector qi ∈ Rf each user u is associated with a vector pu ∈ Rf Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  14. 14. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Matrix Factorization Model (MFM) the approximate user rating is given by ˆrui = qT i Pu (1) carelessly addressing only the relatively few known entries is highly prone to overfitting observed ratings can be modeled directly with regularization as follows minq∗,p∗ (u,i)∈κ (rui − qT i pu)2 + λ(||qi ||2 + ||pu||2 ) (2) κ is a set of (u, i) pairs for which rui is known Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  15. 15. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Stochastic Gradient Descent (SGD) - Simon Funk; 2006 SGD approach can be used for solving the equation (2) For each given training case, the system predicts rui and computes the prediction error eui = rui − qT i pu it modifies the parameters by a magnitude proportional to γ in the opposite direction of the gradient, yielding∈ Rf qi ← qi + γ.(eui .pu − γ.qi ) pu ← pu + γ.(eui .qi − γ.pu) combines ease with a relatively fast runtime Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  16. 16. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Alternating least squares Because both qi and pu are unknown, equation (2) is not convex if we fix one of the unknowns the quadratic optimization can be solved optimally when all pu are fixed the system recomputes the qi by solving a least-squares problem and vice versa each step decreases the minimization problem until convergence massively parallelizable Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  17. 17. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Adding Biases rating values are also affected by biases independent of any interaction a first-order approximation of the bias involved in rating rui is bui = µ + bi + bu (3) µ denotes the average rating, bu and bi are the observed deviations of user u on item i therefore, ˆr = µ + bi + bu + qT i pu (4) equation(2) also becomes, minq∗,p∗,b∗ (u,i)∈κ (rui −µ−bu−bi −qT i pu)2 +λ(||qi ||2 +||pu||2 +b2 u+b2 i ) (5) Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  18. 18. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Additional Input Sources cold start problem could be as a result of user supplying very few ratings-difficulty to conclude on their taste behavioural information such as purchase and browsing history can be used for implicit feedback let’s say N(u) denotes the set of itels for which user u expressed an implicit preference a new set of item factors is given by xi ∈ Rf Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  19. 19. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Additional Input Sources a user who showed a preference for items in N(u) is characterized by the vector i∈N(u) xi normalizing the sum we have, |N(u)|−0.5 i∈N(u) xi another information source is known as user attribute, e.g. demographics, gender, age, income level and so on let A(u) denote set of attributes of a user u Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  20. 20. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Additional Input Sources a distinct factor vector ya ∈ Rf corresponds to each attribute to describe a user through the set of user-associated attributes: a∈A(u) ya the matrix factorization model should intergrate all signal sources, with ehanced representation: ˆrui = µ + bi + bu + qT i [pu + |N(u)−0.5 i∈N(u) xi + a∈A(u) ya] (6) items can get a similar treatment Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  21. 21. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Temporal Dynamics in reality customers’ inclinations evolve, leading them to redefine their taste it is therefore important to accommodate this temporal effects reflecting the dynamic, time-drifting nature of user-item interactions the following terms vary over time: item biases, bi (t); user biases, bu(t); and user preferences, pu(t) equation (4) therefore becomes, ˆr(t) = µ + bi (t) + bu(t) + qT i pu(t) (7) Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  22. 22. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Varying Confidence Level other factors like massive advertisement can influence observed ratings, which do not reflect long-term characteristics hence the need for a weighting scheme or confidence confidence can stem from available numerical values that describe the frequency of actions, e.g. how much time the user watched a show in matrix factorization less weight is given to less meaningful action Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  23. 23. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Varying Confidence Level if confidence in observing rui is denoted as cui, then the model enhances equation (5) to account for confidence as follows minq∗,p∗,b∗ (u,i)∈κ cui (rui −µ−bu−bi −qT i pu)2 +λ(||qi ||2 +||pu||2 +b2 u+b2 i ) (8 Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  24. 24. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion 1 Introduction Recommender Systems Content Filtering Approach Collaborative Filtering Approach Content vs Collaborative Filtering 2 Matrix Factorization Methods Matrix Factorization Model (MFM) Stochastic Gradient Descent Alternating Least Squares Adding Biases Additional Input Source Temporal Dynamics Varying confidence levels 3 Netflix Prize Competition 4 Conclusion Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  25. 25. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Netflix Prize Competition in 2006, Netflix announced a contest to improve the state of its recommender system training data comprised of 100 million ratings sapnning 500,000 annonymous customers’ rating of 17,000 movies each movie was rated on a scale of 1 to 5 stars test data was 3million ratings the metrics was 10 percent or more root-mean-square error (RMSE) performance better than Netflix algorithm Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  26. 26. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Netflix Prize Competition Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  27. 27. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion 1 Introduction Recommender Systems Content Filtering Approach Collaborative Filtering Approach Content vs Collaborative Filtering 2 Matrix Factorization Methods Matrix Factorization Model (MFM) Stochastic Gradient Descent Alternating Least Squares Adding Biases Additional Input Source Temporal Dynamics Varying confidence levels 3 Netflix Prize Competition 4 Conclusion Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  28. 28. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Conclusion matrix factorization techniques have become a dominant methodology within collaborative filtering recommenders experience with the Netflix competion has shown that they deliver accuracy superior to classical nearest-neighbor techniques they integrate many crucial aspects of the data, such as multiple forms of feedback, temporal dynamics and confidence levels. Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  29. 29. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion Reference Y. Koren, R. Bell and C. Volinsky: Matrix Factorization Techniques for Recommender Systems, AT&T Labs-Research, 2009 Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems
  30. 30. Introduction Matrix Factorization Methods Netflix Prize Competition Conclusion THANK YOU! Oluwashina Aladejubelo Matrix Factorization Techniques for Recommender Systems

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