这也是一篇改进SLIM的文章, 主要区别在于在原来的item-space 的基础上, 引入latent factor vector, 使他成为一个更general的method
具体做法:
(1) 用常用的矩阵分解模式,求得用户隐因子向量
(2) 利用学出的U进一步学习P和W , P为prototype matrix, W为the sparse coding coefficients
(3) 学出P和W再反过来update U (无法理解这样做的好处, 信号的分解和重构?)
相比于SLIM,本文方法多学了一个P,这是表象,实质是更general, 值得借鉴.
Appendix
这种带有prototype matrix 有经典的算法求解,如下(注意该博文中, 信号量和原子的长度应该是k而不是n; n为原子的个数)
Orthogonal Matching Pursuit (OMP) algorithm
这里主要讲的是如何利用信号分解(正交分解), 将原信号分解到多个原子上(多个原子的线性组合); 最后利用原子和线性组合系数,还原信号量.
有个问题是: 如何初始化或者学习原子矩阵P, 在确定了P之后,W中的系数倒是可以逐步学出来.
| 文献题目 | 去谷歌学术搜索 | ||||||||||
| Towards Improving Top-N Recommendation by Generalization of SLIM | |||||||||||
| 文献作者 | Santiago Larraín, Denis Parra, Alvaro Soto | ||||||||||
| 文献发表年限 | 2015 | ||||||||||
| 文献关键字 | |||||||||||
| SLIM; GSLIM; latent factor vectors; encoding; prototype matrix; Orthogonal Matching Pursuit (OMP) algorithm; 原子; 信号分解 | |||||||||||
| 摘要描述 | |||||||||||
| Sparse Linear Methods (SLIM) are state-of-the-art recommendation approaches based on matrix factorization, which rely on a regularized l 1 -norm and l 2 -norm optimization –an alternative optimization problem to the traditional Frobenious norm. Although they have shown outstanding performance in Top-N recommendation, existent works have not yet analyzed some inherent assumptions that can have an important effect on the performance of these algorithms. In this paper, we attempt to improve the performance of SLIM by proposing a generalized formulation of the aforementioned assumptions. Instead of directly learning a sparse representation of the user-item matrix, we (i) learn the latent factors’ matrix of the users and the items via a traditional matrix factorization approach, and then (ii) reconstruct the latent user or item matrix via prototypes which are learned using sparse coding, an alternative SLIM commonly used in the image processing domain. The results show that by tuning the parameters of our generalized model we are able to outperform SLIM in several Top-N recommendation experiments conducted on two different datasets, using both nDCG and nDCG@10 as evaluation metrics. These preliminary results, although not conclusive, indicate a promising line of research to improve the performance of SLIM recommendation. | |||||||||||
