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Collaborative filtering using orthogonal nonnegative matrix

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    Collaborative filtering using orthogonal nonnegative matrix Collaborative filtering using orthogonal nonnegative matrix Presentation Transcript

    • COLLABORATIVE FILTERING USING ORTHOGONAL NONNEGATIVE MATRIX Presenter: Meng-Lun Wu Authors: Gang Chen, Fei Wang and Changshui Zhang Source: Information Processing and Management (2009), pp. 368-379
    • OUTLINE
      • Introduction
      • Related Work
      • Orthogonal nonnegative matrix tri-factorization
      • Framework
      • Experiments
      • Conclusion
    • INTRODUCTION
      • Collaborative filtering can predict a test user’s rating for new items based on similar users.
      • Collaborative filtering can be categorized into…
        • Memory-based (similarity)
          • user-based and item-based
        • Model-based
          • Establish a model using training examples.
    • INTRODUCTION (CONT.)
      • This paper apply orthogonal nonnegative matrix tri-factorization(ONMTF) to circumvent the two kinds of collaborative filtering.
      • ONMTF is applied to simultaneously co-cluster the rows and columns, and attain individual predictions for an unknown test rating.
      • This paper possesses the following superiorities:
        • Sparsity problem
        • Scalability problem
        • Fusing prediction results
    • RELATED WORK
      • Researchers have proposed some hybrid approaches in order to combine the memory based and model based approaches.
        • Xue et. al. (2005) resolve the sparsity and scalability by using clusters to smooth ratings and clustering.
      • However, Xue only consider user-based approach, this paper extend the idea to integrate model based, user-based and item-based approaches.
    • RELATED WORK (CONT.)
      • Matrix decomposition can used to solve the co-clustering problem.
        • Ding et al. (2005) proposed co-clustering based on nonnegative matrix factorization. (NMF)
          • In 2006, they proposed ONMTF.
        • Long et al. (2005) provided co-clustering by block value decomposition.
    • ORTHOGONAL NONNEGATIVE MATRIX TRI-FACTORIZATION
      • The NMF is first brought into machine learning and data mining fields by Lee et al. (2001).
      • Ding et al. (2006) proved the equivalence between NMF and K-means, and extended NMF to ONMTF.
      • The idea is to approximate the original matrix X to the combination matrix, and the optimization problem is
    • ORTHOGONAL NONNEGATIVE MATRIX TRI-FACTORIZATION (CONT.)
      • The optimization problem can be solved using the following update rules.
      • After co-clustering, we could get the user centroid SV T and item centroid US .
    • FRAMEWORK
      • Notations
        • X = [u 1 ,…,u p ] T , u j =(x j1 ,…,x jn ) T , j  {1,…,p}
        • X = [i 1 ,…,i n ], i m =(x 1m ,…,x pm ) T , m  {1,…,n}
    • MEMORY-BASED APPROACHES
      • User’s neighbor selection
        • Compute the similarities between a user and all the user-cluster centroids SV T .
        • Select the top K user cluster as the user set u h .
        • The item’s neighbor selection is similar.
      • The cosine similarity between the j 1 th user and the j 2 th user.
        • Given an user-item pair <u j , i m >, where u h  {the most similar K-user of u j }.
    • MEMORY-BASED APPROACHES
      • The adjusted-cosine similarity between the m 1 th and m 2 th items. (T is the set of users who both rated m 1 and m 2 )
        • Given an user-item pair <u j , i m >, where i h  {the most similar K-items of i m }
      • The final prediction result could be linearly combined the three different types of predictions.
    • ALGORITHM
      • The user-item matrix X is factorized as USV T by using ONMTF .
      • Calculate the similarities between the test user/item and user/item-cluster centroids.
      • Sort the similarities and select the most similar C user/item clusters as the test user/item neighbor candidate set.
      • Identify the most K neighbors of the test user/item by searching for the user/item candidate set.
      • Predict the unknown ratings by using user based and item based approaches.
      • Linearly combine three different predictions.
    • EXPERIMENTS
      • Dataset
        • MovieLens: 500 users and 1000 items (1-5 scales)
          • Training set: the first 100, 200 and 300 users, called ML_100, ML_200 and ML_300.
          • Testing set: the last 200 users
        • We randomly selected 5, 10 and 20 items rated by test users, called Given5, Given10 and Given20.
      • Evaluation metric
        • Mean absolute error (MAE) as evaluation metric.
        • Where N is the number of tested ratings.
    • DIFFERENT CLUSTER
      • The ML_300 dataset is used for training, and try 10 different values of k or l (2,5,10,20,…,80)
    • PERCENTAGE OF NEIGHBORS
      • The percentage of pre-selected neighbors reaches around 30%.
    • SIZE OF NEIGHBORS
    • COMBINATION COEFFICIENTS
      • Fix  =0, the optimal value of  is approximately between 0.5 and 0.7.
    • COMBINATION COEFFICIENTS (CONT.)
      • Fix  =0.6, the optimal value of  is approximately between 0.2 and 0.4.
    • PERFORMANCE COMPARISON
      • Wang et al., 2006, similarity fusion (SF2)
      • Xue et al., 2005, cluster-based Pearson correlation coefficient (SCBPCC)
      • Rennie and Srebro, 2005, maximum margin matrix factorization (MMMF)
      • Ungar and Foster, 1999, cluster-based collaborative filtering (CBCF)
      • Hofmann and Puzicha, 1999, aspect model (AM)
      • Pennock et al., 2000, personality diagnosis (PD)
      • Breese et al., 1998, user-based Pearson correlation coefficient (PCC)
    • CONCLUSIONS
      • This paper presented a novel fusion framework for collaborative filtering.
      • The model-based and memory-based and naturally assembled via ONMTF.
      • Empirical studies verified our framework effectively improves the prediction accuracy.
      • Future work is investigate new co-clustering techniques and develop better fusion models.