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Integrating Context Similarity with Sparse Linear Recommendation Model

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- 1. Integrating Context Similarity with Sparse Linear Recommendation Model Yong Zheng, Bamshad Mobasher, Robin Burke Center for Web Intelligence, DePaul University, Chicago, USA The 23rd Conference on User Modeling, Adaptation and Personalization, Dublin, Ireland, June 29 – July 3, 2015 (UMAP 2015)
- 2. Agenda • RecSys and Context-aware RecSys • Contextual Modeling • SLIM and Contextual SLIM • Modeling Context Similarity • Experimental Evaluations • Conclusions and Future Work
- 3. Agenda • RecSys and Context-aware RecSys • Contextual Modeling • SLIM and Contextual SLIM • Modeling Context Similarity • Experimental Evaluations • Conclusions and Future Work
- 4. RecSys and Context-aware RecSys • Recommender Systems (RS) The data is usually a 2D rating matrix: User × Item ―> Ratings Task-1: Rating Predictions for <user, item> pair Task-2: Top-N Recommendations for a specific user, i.e., provide a list of ranked items to the user
- 5. • Context-aware RecSys (CARS) Context dimension: the variable, e.g., time, location, companion Context condition: values in dimension, e.g., weekend and weekday Context situation: a set of conditions, e.g., <weekend, home, sister> The data is represented in a multi-dimensional rating space. Task-1: Rating Predictions for <user, item, contexts> Task-2: Top-N Recommendations for a user in specific contexts, RecSys and Context-aware RecSys
- 6. Agenda • RecSys and Context-aware RecSys • Contextual Modeling • SLIM and Contextual SLIM • Modeling Context Similarity • Experimental Evaluations • Conclusions and Future Work
- 7. Contextual Recommendations • How to build CARS algorithms?
- 8. Contextual Recommendations • Contextual Modeling There are usually two ways for contextual modeling: 1). Independent Contextual Modeling Tensor Factorization, ACM RecSys 2010 2). Dependent Contextual Modeling 2.1). Deviation-Based Modeling Context-aware Matrix Factorization, ACM RecSys 2011 Contextual Sparse Linear Method, ACM RecSys 2014 2.2). Similarity-Based Modeling The proposal in this paper, UMAP 2015
- 9. Contextual Modeling • Independent Contextual Modeling Tensor Factorization (TF), ACM RecSys 2010 Assumption: context is independent with user/item dimension. But usually, there are dependencies involved.
- 10. Contextual Modeling • Dependent Contextual Modeling Context-aware Matrix Factorization (CAMF), ACM RecSys 2011 Contextual Sparse Linear Method (CSLIM), ACM RecSys 2014 Global average rating User bias Item bias Matrix Factorization: CAMF: Item bias in contexts
- 11. Contextual Modeling • Dependent Contextual Modeling Context-aware Matrix Factorization (CAMF), ACM RecSys 2011 Contextual Sparse Linear Method (CSLIM), ACM RecSys 2014 Those approaches are named as deviation-based modeling, since they tried to incorporate contextual rating deviations into recommendation algorithms by modeling dependencies or correlations between contexts and user/item dimensions. Any other alternatives? How about the dependencies or correlations among contexts? We name this approach of context modeling as similarity-based modeling.
- 12. Agenda • RecSys and Context-aware RecSys • Contextual Modeling • SLIM and Contextual SLIM • Modeling Context Similarity • Experimental Evaluations • Conclusions and Future Work
- 13. SLIM and Contextual SLIM • Why SLIM SLIM = Sparse Linear Method, which is an effective top-N recommendation algorithm in traditional RS. In this paper, we choose SLIM as the base algorithm, and introduce how to build contextual SLIM algorithms by incorporating context similarity. SLIM was demonstrated as the most effective top-N recommendation algorithms in previous work. Here, we focus on top-N contextual recommendation. Other algorithms, such as matrix factorization, can also be chosen as base algorithm.
- 14. • SLIM in Traditional RecSys Matrix R = rating matrix; W = coefficient matrix SLIM aggregates users’ ratings by coefficients between items. It learns item coefficients by minimizing the ranking score. Sparse Linear Method (SLIM)
- 15. • CSLIM in Context-aware RecSys P is multidimensional contextual rating space; W is item coefficient matrix; Matrix D estimates the rating deviation from one context to another. 1). By Deviation-Based Contextual Modeling, RecSys 2014, CIKM 2014 Contextual SLIM (CSLIM)
- 16. • CSLIM in Context-aware RecSys Previous dependent contextual modeling approaches mainly focused on modeling the correlations between context and user/item dimensions, but ignore the correlation between contexts themselves; Context similarity = similarity between two contexts, measuring inner similarities or correlations between two contextual situations; We propose and believe that modeling context similarities is another important way to develop dependent contextual modeling approaches, rather than modeling contextual rating deviations!!! 2). By Similarity-Based Contextual Modeling, UMAP 2015 Contextual SLIM (CSLIM)
- 17. • CSLIM in Context-aware RecSys Original SLIM: Deviation-Based CSLIM: Similarity-Based CSLIM: 2). By Similarity-Based Contextual Modeling, UMAP 2015 Deviation term Similarity term Contextual SLIM (CSLIM)
- 18. Agenda • RecSys and Context-aware RecSys • Contextual Modeling • SLIM and Contextual SLIM • Modeling Context Similarity • Experimental Evaluations • Conclusions and Future Work
- 19. Modeling Context Similarity • Context Similarity Context similarity can be obtained in the following ways: 1). Semantics But, it is hard to for <holiday, cinema> & <weekday, home>; Semantics is more useful for hierarchical or tree-based categorical data; 2). Calculation based on co-ratings in different contexts However, contextual rating data is usually sparse, which results in unreliable calculations for context similarity. 3). Learning methods Instead, we can learn the similarity directly by minimizing ranking errors. error = ranking score – predicted ranking score Minimizing this ranking error by gradient descent in CSLIM
- 20. Modeling Context Similarity • Context Similarity Learning methods Instead, we can learn the similarity directly by minimizing ranking errors. error = ranking score – predicted ranking score Minimizing this ranking error by gradient descent in CSLIM However, the performance may directly depend on how we represent and model context similarity. In this paper, we discuss 4 modeling: 1). Independent Context Similarity (ICS) 2). Latent Context Similarity (LCS) 3). Weighted Jaccard Context Similarity (WJCS) 4). Multidimensional Context Similarity (MCS)
- 21. Modeling Context Similarity • 1).Independent Context Similarity (ICS) Similarity-Based CSLIM: Independent Context Similarity (ICS) can be represented as follows: For example: Ck = {Time = Weekend, Location = Home}; Cm = {Time = Weekday, Location = Office} is: Similarity(Weekend, Weekday) × Similarity (Home, Office) Assumption: contextual variables are assumed as independent. What to be learnt: each individual similarity between two conditions;
- 22. Modeling Context Similarity • 2).Latent Context Similarity (LCS) Similarity-Based CSLIM: Latent Context Similarity (LCS) is an improvement over ICS. For example: Ck = {Time = Weekend, Location = Home}; Cm = {Time = Weekday, Location = Office} is: Similarity(Weekend, Weekday) × Similarity (Home, Office) Each condition is represented by a vector; What to be learnt: the weights in vectors for each contextual condition. Training: <weekend, weekday> <weekday, holiday> Testing: <weekend, holiday> Context Sparsity
- 23. Modeling Context Similarity • 3).Weighted Jaccard Context Similarity (WJCS) Weighted Jaccard Context Similarity refers to similarity between two strs. Assume those three context dimensions are equally weighted, w1 = w2 = w3 = 1. = # of matched dimensions / # of all dimensions = 2/3 What to be learnt: the weight for each context dimension. Similarity is measured by Weighted Jaccard similarity User Movie Time Location Companion Rating U1 Titanic Weekend Home Girlfriend 4 U2 Titanic Weekday Home Girlfriend 5 U3 Titanic Weekday Cinema Sister 4 U1 Titanic Weekday Home Sister ?
- 24. Modeling Context Similarity • 4).Multidimensional Context Similarity (MCS) Similarity-Based CSLIM: Multidimensional context similarity utilizes the distance metric. (NA, Home, Weekday) (NA, Home, Weekday) (Kids, Home, NA) (Kids, Home, NA)
- 25. Modeling Context Similarity • 4).Multidimensional Context Similarity (MCS) Similarity-Based CSLIM: Key points in MCS: 1). Each contextual variable is represented as an axis; 2). Each contextual condition is one position in corresponding axis; 3). Thus a contextual situation is mapped as a point in the space; 4). The distance between two points is viewed as dissimilarity; Any distance metric can be applied; here we use Euclidean distance. What to be learnt: the positions of each condition in axises.
- 26. Modeling Context Similarity • Summary Similarity-Based CSLIM: What to be learnt in each context similarity model: ICS LCS The correlation (real value) for each individual pair of context conditions The vector representation (weights in factors) for each contextual condition WJCS MCS The weights for each context dimension. The positions (real values) for each contextual condition
- 27. Agenda • RecSys and Context-aware RecSys • Contextual Modeling • SLIM and Contextual SLIM • Modeling Context Similarity • Experimental Evaluations • Conclusions and Future Work
- 28. Experimental Evaluations • Data Sets Note: The number of context-aware data sets is really limited!! We use 5-folds cross validation for evaluation purposes. We use Precision and Mean Average Precision (MAP) as metrics: - Precision: measuring the hit ratio towards relevant items; - MAP: additional taking the rankings of items into account.
- 29. Experimental Evaluations • Algorithms for Comparison 1). Baseline Algorithms CASA = Context-aware Splitting Approaches (a pre-filtering approach) TF = Tensor Factorization (independent contextual modeling) CAMF = Context-aware MF (dependent contextual modeling) Deviation Model = CSLIM using deviation-based contextual modeling 2). New Algorithms Four algorithms using different context similarity representations: Similarity-ICS Model, Similarity-LCS Model Similarity-WJCS Model, Similarity-MCS Model Note: all those models were built on SLIM.
- 30. Experimental Evaluations
- 31. Experimental Evaluations • Summary of the results 1). Which algorithm is the best? Answer: Similarity-Based CSLIM using Multidimensional Context Similarity 2). Which one is better? Deviation or similarity-based modeling? Answer: we can always find a similarity-based contextual modeling outperforming the deviation-based modeling; but, the appropriate representation for context similarity should be selected. 3). Which representation is the best? Generally speaking, latent context similarity always outperforms independent context similarity; and multidimensional context similarity is the best choice. Weighted Jaccard context similarity shows non-stable recommendation performance in the experiments.
- 32. Agenda • RecSys and Context-aware RecSys • Contextual Modeling • SLIM and Contextual SLIM • Modeling Context Similarity • Experimental Evaluations • Conclusions and Future Work
- 33. Conclusions & Future Work • Conclusions We propose a new way to build dependent contextual modeling – similarity- based contextual modeling; We choose SLIM as the base algorithm and incorporate context similarity into SLIM to formulate new contextual SLIM algorithms; We discuss different representations to model context similarity; We demonstrated the advantages of similarity-based CSLIM by experimental evaluations over multiple context-aware data sets. • Future Work Multidimensional Context Similarity (MCS) is the best representation to model context similarity; but it increases computational costs at the same time. In our future work, we’d like to explore how to reduce the computational costs for MCS, e.g., reducing context dimensions, merging contextual conditions, etc.
- 34. Conclusions & Future Work • Stay Tuned Context similarity can also be incorporated into matrix factorization. Yong Zheng, Bamshad Mobasher, Robin Burke. "Incorporating Context Correlation Into Context-aware Matrix Factorization". Workshop on Intelligent Personalization @ IJCAI 2015 Yong Zheng, Bamshad Mobasher, Robin Burke. "Correlation-Based Context- aware Matrix Factorization". In DePaul CDM School of Computing Research Symposium, 2015 (Best Paper Award) • Survey: Context-aware Movie Ratings Welcome to fill out it: http://depaul.qualtrics.com/SE/?SID=SV_4TrIZbAnQtzaHsx Short URL: http://tinyurl.com/surveycars
- 35. Integrating Context Similarity with Sparse Linear Recommendation Model Yong Zheng, Bamshad Mobasher, Robin Burke Center for Web Intelligence, DePaul University, Chicago, USA The 23rd Conference on User Modeling, Adaptation and Personalization, Dublin, Ireland, June 29 – July 3, 2015 (UMAP 2015)

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