闫岩【15-24期VALSE Webinar活动】 报告嘉宾3：（悉尼科技大学）主持人：张利军（南京大学）报告题目：Scalable Maximum Margin Matrix Factorization by Active Riemannian Subspace Search [Slides]报告时间：2015年8月5日晚21:20（北京时间）文章信息：[1] Yan, Y., Tan, M., Tsang, I., Yang, Y., Zhang, C., and Shi, Q. Scalable Maximum Margin Matrix Factorization by Active Riemannian Subspace Search. International Joint Conference on Artificial Intelligence (IJCAI), 2015. 报告摘要：The rapid increase of Web services has witnessed an increasing demand for predicting the preferences of users on products of interest, such as movies and music tracks. This task is known as the collaborative filtering (CF) problem, which is a heated topic in recommendation systems. There are many ways to deal with the CF task. Based on the fact that users tend to share the same or similar preference over the products, low-rank property is then introduced to the problem and becomes very popular. Traditional nuclear-norm-minimization is effective, but not rather efficient due to the computationally expensive large-scale singular value decomposition (SVD). Hence, matrix factorization (MF) is proposed to recover the rating matrix by factorizing the original matrix into two small factor matrices, which is often scalable.As for the user rating data, in general, they are given in the form of discrete values, including binary ratings and ordinal ratings The binary ratings can be either “+1” (like) or “-1” (dislike); while the ordinal ratings are in discrete values such as 1-5 “stars”, which are more popular in real world applications. To give more accurate prediction of such rating data, maximum margin matrix factorization (M3F) was proposed. This approach aims to find a margin between every two ordinal rating values, such as 3 and 4. Because of the ratings are in discrete values, M3F often achieve promising results. Existing M3F algorithms, however, either have massive computational cost or require expensive model selection procedures to determine the number of latent factors (i.e. the rank of the matrix to be recovered), making them less practical for large scale data sets. To address these two challenges, in this paper, we formulate M3F with a known number of latent factors as the Riemannian optimization problem on a fixed-rank matrix manifold and present a block-wise nonlinear Riemannian conjugate gradient method to solve it efficiently. As for the problem of detecting the number of latent factors, we then apply a simple and efficient active subspace search scheme to automatically estimate the rank of the matrix to be recovered. Empirical studies on both synthetic data sets and large real-world data sets demonstrate the superior efficiency and effectiveness of the proposed method. 报告人简介：Yan Yan received the B.E. degree in Computer Science and Technology from Tianjin University, Tianjin, China, in 2013. He is currently pursuing the Master degree with University of Technology, Sydney, Australia under the supervision of Dr. Yi Yang. His current research interest include computer vision and machine learning. |

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