隨著網路技術的興盛，人們經常面臨到網路上資訊高度負載的問題。推薦系統能夠幫助使用者過濾出可能感興趣的資訊，成為在各種應用上重要的工具。舉例來說，應用於大型的線上購物網站上，推薦系統幫助使用者從琳瑯滿目的商品中篩選出他們可能喜歡的商品，進而增加購買機會。推薦系統除了藉由分析使用者對商品的評分資料外，參考使用者社群朋友的品味也可增進推薦的品質和更貼近個人化的推薦。在眾多的推薦方法中，矩陣分解法被廣為運用於推薦預測，因其能夠有效率地降低資料維度，並且找出資料潛在關係進而提供較佳精準度的推薦；然而，推薦系統應用於不斷變化的線上環境，資料是大量且快速變動，若是使用傳統矩陣分解法，會面臨重新對整個評分矩陣進行分解而產生計算複雜度相當高的問題。因此，我們設計一個漸進式奇異分解法機制，當系統有新的評分資料能夠即時的更新評分矩陣，而無需分解整個評分矩陣。實驗結果顯示我們的漸進式機制在實際應用環境中對於整體效能有顯著改善，並且發現結合社群資訊的推薦能夠提高對於冷啟動用戶的推薦精準度。

With the advances in Internet technologies, users are often faced with the information overload problem. Recommender systems then become a necessity in various applications, especially in a large-scale online shop. In addition to the rating information provided by the users, social relationships of a user begin to be incorporated to further improve the performance of current recommender systems. Among several alternatives, matrix factorization is recognized as an effective technique to reduce the data dimensionality and to capture significant latent relationships between users and items. Furthermore, recommender systems are used in an ever-changing commercial environment and usually operate on the large-scale data. Note that there are always new users, items and ratings as time advances, resulting in a rating matrix of increasing size. This poses a very challenging problem because decomposing entire matrix is costly. In this work, we thus propose an incremental scheme to directly update the rating matrix without the need to decompose the entire rating matrix. This helps to achieve better efficiency at the cost of some approximation errors. Experimental results show that our scheme has high efficiency as expected and significantly enhances the prediction quality for cold-start users.

[1] G. Adomavicius and A. Tuzhilin, "Toward the Next Generation of Recommender Systems: A Survey of the State-of-the-art and Possible Extensions," IEEE Transactions on Knowledge and Data Engineering, 17(6):734-749, June 2005.
[2] M. Brand, "Incremental Singular Value Decomposition of Uncertain Data with Missing Values," Proceedings of the 7th European Conference on Computer Vision, pages 707-720, May 2002.
[3] M. W. Berry, S. T. Dumais and G. W. O'Brien, "Using Linear Algebra for Intelligent Information Retrieval," Journal of SIAM review, 37(4):573-595, December 1995.
[4] J. Bobadilla, F. Ortega, A. Hernando and A. Gutierrez, "Recommender Systems Survey," Journal of Knowledge-Based Systems, 46:109-132, July 2013.
[5] S. C. Deerwester, S. T. Dumais, T. K. Landauer, G. W. Furnas and R. A. Harshman, "Indexing by Latent Semantic Analysis," Journal of the American Society for Information Science, 41(6):391-407, September 1990.
[6] M. Deshpande and G. Karypis, "Item-based Top-N Recommendation Algorithms," ACM Transactions on Information Systems, 22(1):143-177, January 2004.
[7] C. Desrosiers and G. Karypis, "A Comprehensive Survey of Neighborhood-based Recommendation Methods," Recommender Systems Handbook, pages 107-144, 2011.
[8] J. A. Golbeck, "Computing and Applying Trust in Web-based Social Networks," PhD thesis, University of Maryland College Park, April 2005.
[9] G. Golub and C. F. Van Loan. "Matrix Computations (Vol. 3)," Johns Hopkins University Press, 1996.
[10] M. Hao, I. King and M.R. Lyu, "Learning to Recommend with Social Trust Ensemble," Proceedings of the 32nd International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 203-210, July 2009.
[11] M. Jamali and M. Ester, "A Matrix Factorization Technique with Trust Propagation for Recommendation in Social Networks," Proceedings of the Fourth ACM Conference on Recommender Systems, pages 135-142, September 2010.
[12] M. Jamali and M. Ester, "TrustWalker: A Random Walk Model for Combining Trust-based and Item-based Recommendation," Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, June 2009.
[13] W.A. Kamakura, "Cross-selling: Offering the Right Product to the Right Customer at the Right time," Journal of Relationship Marketing, 6(3-4):41-58, September 2008.
[14] Y. Koren, "Collaborative Filtering with Temporal Dynamics," Communications of the ACM, 53(4): 89-97, April 2010.
[15] Y. Koren, "Factor in the Neighbors: Scalable and Accurate Collaborative Filtering," Journal of ACM Transactions on Knowledge Discovery from Data, 4(1): 1, January 2010.
[16] Y. Koren, R. Bell, and C. Volinsky, "Matrix Factorization Techniques for Recommender Systems," IEEE Computer, 42(8): 30-37, August 2009.
[17] K. F. Lin and W. G. Teng, "An Incremental SVD-based Scheme for Large-scale Recommendation Systems," Proceedings of the Second International Joint Conference on Artificial Intelligence, pages 61-64, December 2010.
[18] L. Lü, M. Medo, C. H. Yeung, C. Zhang, Z. K. Zhang and Z. Tao, "Recommender Systems," Journal of Physics Reports, 519(1):1-49, February 2012.
[19] B. Liu, "Web Data Mining," Springer Berlin Heidelberg, page 565, 2011.
[20] P. Massa and B. Bhattacharjee, "Using Trust in Recommender Systems: An Experimental Analysis," Trust Management, Springer Berlin Heidelberg, pages 221-235, 2004.
[21] MovieLens Data Sets, http://www.grouplens.org/node/73.
[22] M. C. Pham, Y. Cao, R. Klamma and M. Jarke, "A Clustering Approach for Collaborative Filtering Recommendation Using Social Network Analysis," Journal of Universal Computer Science, 17(4):583-604, February 2011.
[23] P. Resnick and H. R. Varian, "Recommender Systems," Communications of the ACM, 40(3):56-58, March 1997.
[24] B. Sarwar, G. Karypis, J. Konstan and J. Riedl, "Item-based Collaborative Filtering Recommendation Algorithms," Proceedings of the 10th International Conference on World Wide Web, pages 285-295, May 2001.
[25] B. Sarwar, G. Karypis, J. Konstan and J. Riedl, "Application of Dimensionality Reduction in Recommender System - A Case Study," ACM WebKDD Workshop, July 2000.
[26] B. Sarwar, G. Karypis, J. Konstan and J. Riedl, "Incremental Singular Value Decomposition Algorithms for Highly Scalable Recommender Systems," Proceedings of Fifth International Conference on Computer and Information Science, pages 27-28, 2002.
[27] J.B. Schafer, J. Konstan and J. Riedi, "Recommender Systems in E-commerce," Proceedings of the 1st ACM Conference on Electronic Commerce, pages 158-166, November 1999.
[28] M. Smith, V. Barash, L.Getoor and H. W. Lauw, "Leveraging Social Context for Searching Social Media," Proceedings of the 2008 ACM Workshop on Search in Social Media, pages 91-94, October 2008.
[29] P. Stange, "On the Efficient Update of the Singular Value Decomposition," International Association of Applied Mathematics and Mechanics, 8(1):10827-10828, May 2008.
[30] X. Su and T. M. Khoshgoftaar, "A Survey of Collaborative Filtering Techniques," Journal of Advances in Artificial Intelligence, 2009:4, August 2009.
[31] J. Tang, H. Gao, H. Liu and A. Das Sarma, "eTrust: Understanding Trust Evolution in an Online World," Proceedings of the 18th International Conference on Knowledge Discovery and Data Mining, ACM, pages 253-261, August 2012.
[32] X. Yang, H. Steck, and Y. Liu, "Circle-based Recommendation in Online Social Networks," Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 1267-1275, August 2012.
[33] S. H. Yang, B. Long, A. Smola, N. Sadagopan, Z. Zheng and H. Zha, "Like Like Alike: Joint Friendship and Interest Propagation in Social Networks," Proceedings of the 20th International Conference on World Wide Web, pages 537-546, March 2011.
[34] H. Zha and H. D. Simon, "On Updating Problems in Latent Semantic Indexing," Journal on Scientific Computing, 21(2):782-791, 1999.