核心思想：
1）离散化user向量b和item向量d，即向量元素属于{-1,1}
2）直接最优化排序指标AP（而不是转换成最优化pairwise间接指标）
解决方法：
针对1）将向量中的元素范围从{-1,1}改成[-1,1]，这样原来针对{-1,1}的海明相似度1/2+1/(2f)(b^T·d)就变的连续了，f为向量维度。此时AP目标只是连续，但不可导（因此存在排序操作）
针对2）主要是平滑排序操作，以往一般将list的排序转化成pairwise排序，这样可以用sigmoid函数进行平滑。
本文的做法：将score list：s先转换A方阵（A中元素=s_i - s_j），然后再利用s的排序以及A方阵，构造Z方阵，在计算Z中的元素时，有argmax函数，可进一步用softmax代替进行平滑，最后可以将Z替换AP中有关排序的部分，使得AP最优化目标可导。这就相当于score list作为整体输入到目标函数中，不用再计算某一个位置上的precision了。
最后求导依据落到b和d上。
| 文献题目 | 去谷歌学术搜索 | ||||||||||
| Discrete Listwise Personalized Ranking for Fast Top-N Recommendation with Implicit Feedback | |||||||||||
| 文献作者 | Fangyuan Luo , Jun Wu∗ , Tao Wang | ||||||||||
| 文献发表年限 | 2022 | ||||||||||
| 文献关键字 | |||||||||||
| 离散化向量；海明相似度（向量计算法）；最优化排序指标 | |||||||||||
| 摘要描述 | |||||||||||
| We address the efficiency problem of personalized ranking from implicit feedback by hashing users and items with binary codes, so that top-N rec- ommendation can be fast executed in a Hamming space by bit operations. However, current hashing methods for top-N recommendation fail to align their learning objectives (such as pointwise or pair- wise loss) with the benchmark metrics for rank- ing quality (e.g. Average Precision, AP), resulting in sub-optimal accuracy. To this end, we propose a Discrete Listwise Personalized Ranking (DLPR) model that optimizes AP under discrete constraints for fast and accurate top-N recommendation. To resolve the challenging DLPR problem, we devise an efficient algorithm that can directly learn bi- nary codes in a relaxed continuous solution space. Specifically, theoretical analysis shows that the optimal solution to the relaxed continuous optimization problem is exactly the same as that of the original discrete DLPR problem. Through extensive experiments on two real-world datasets, we show that DLPR consistently surpasses state-of-the-art hashing methods for top-N recommendation. | |||||||||||
