本文主要的工作是改进SLIM算法,改进点的动机是: SLIM没有充分考虑用户数据的稀疏性; 说白了,就是没有考虑estimated Matrix的秩的大小.因此要在loss function中加入秩大小的约束项.
原文说法:However, SLIM can only capture relations between items that are co-purchased/co-rated by at least one user, while an intrinsic characteristic of recommender systems is sparsity due to the fact that users typically rate only a small portion of the available items.
另一个篇文章也考虑到了这一点LorSLIM(说明这还真是个问题), LorSLIM的做法很直接,在loss function加入矩阵秩值的估计约束: nuclear norm (矩阵的奇异值之和,注意区别于特征值http://blog.csdn.net/xiahouzuoxin/article/details/41118351)
本文从另一个角度对矩阵秩进行了约束:利用了logdet() function, 即矩阵行列式对数估计, 当然,作者在原始logdet的基础上作了一些改进; 最后通过augmented Lagrangian multiplier (ALM) method 进行矩阵更新求解,效果也不错.
本文可以借鉴和学习的地方:
这篇文章有个说明我不是很同意:
它不应该把ranking based methods 同 model based methods分开, 因为他们之间有很多重合的部分
| 文献题目 | 去谷歌学术搜索 | ||||||||||
| Top-N Recommender System via Matrix Completion | |||||||||||
| 文献作者 | Zhao Kang Chong Peng Qiang Cheng | ||||||||||
| 文献发表年限 | 2016 | ||||||||||
| 文献关键字 | |||||||||||
| SLIM; nuclear; LorSLIM; augmented Lagrangian multiplier (ALM) method; logdet; 秩约束; nonconvex relaxation; convex relaxation; 非凸松弛; | |||||||||||
| 摘要描述 | |||||||||||
| Top-N recommender systems have been investigated widely both in industry and academia. However, the recommenda- tion quality is far from satisfactory. In this paper, we propose a simple yet promising algorithm. We fill the user-item ma- trix based on a low-rank assumption and simultaneously keep the original information. To do that, a nonconvex rank relax- ation rather than the nuclear norm is adopted to provide a better rank approximation and an efficient optimization strat- egy is designed. A comprehensive set of experiments on real datasets demonstrates that our method pushes the accuracy of Top-N recommendation to a new level. | |||||||||||
