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A novel temporal and topic-aware recommender model

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Abstract

Individuals’ interests and concerning topics are generally changing over time, with strong impact on their behaviors in social media. Accordingly, designing an intelligent recommender system which can adapt with the temporal characters of both factors becomes a significant research task. Namely both of temporal user interests and topics are important factors for improving the performance of recommender systems. In this paper, we suppose that users’ current interests and topics are transferred from the previous time step with a Markov property. Based on this idea, we focus on designing a novel dynamic recommender model based on collective factorization, named Temporal and Topic-Aware Recommender Model (TTARM), which can express the transition process of both user interests and relevant topics in fine granularity. It is a hybrid recommender model which joint Collaborative Filtering (CF) and Content-based recommender method, thus can produce promising recommendations about both existing and newly published items. Experimental results on two real life data sets from CiteULike and MovieLens, demonstrate the effectiveness of our proposed model.

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Notes

  1. http://www.citeulike.org/faq/data.adp

  2. http://www.grouplens.org/node/12

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Acknowledgments

This work was supported by National Key Research and Development Program of China (Grant No. 2016YFB1000902), National Program on Key Basic Research Project (973 Program, Grant No.2013CB329600), and National Natural Science Foundation of China (Grant No. 61472040).

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Correspondence to Dandan Song.

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Appendix: Derivation of Gradient Equation

Appendix: Derivation of Gradient Equation

Suppose R = [Rij]m×n,P = [Pij]m×k,Q = [Qij]k×n,C = [Cij]m×n.

$$\begin{array}{@{}rcl@{}} \lefteqn{\|R^{(t)} - [(1-\eta)P^{(t)}Q^{(t)} + \eta C^{(t)}]\|_{F}^{2}} \\ & = & tR\{\{R^{(t)}-[(1-\eta)P^{(t)}Q^{(t)} + \eta C^{(t)}]\}^{T} \\ & &\{R^{(t)}-[(1-\eta)P^{(t)}Q^{(t)} + \eta C^{(t)}]\}\} \\ & = & tR\{\{{R^{(t)}}^{T}-[(1-\eta){Q^{(t)}}^{T}{P^{(t)}}^{T} + \eta {C^{(t)}}^{T}]\} \\ & &\{R^{(t)}-[(1-\eta)P^{(t)}Q^{(t)} + \eta C^{(t)}]\}\} \\ & = & tR({R^{(t)}}^{T}R^{(t)})-2tR\{[(1-\eta){Q^{(t)}}^{T}{P^{(t)}}^{T}+\eta {C^{(t)}}^{T}]R^{(t)}\} \\ & & + \> tR\{[(1-\eta){Q^{(t)}}^{T}{P^{(t)}}^{T} + \eta {C^{(t)}}^{T}][(1-\eta)P^{(t)}Q^{(t)} + \eta C^{(t)}]\} \\ \end{array} $$
$$\begin{array}{@{}rcl@{}} & = & tR({R^{(t)}}^{T}R^{(t)}) - 2[(1-\eta)tR({Q^{(t)}}^{T}{P^{(t)}}^{T}R^{(t)})+\eta tR({C^{(t)}}^{T}R^{(t)})] \\ & & + \> (1-\eta)^{2}tR({Q^{(t)}}^{T}{P^{(t)}}^{T}P^{(t)}Q^{(t)}) \\ & & + \> 2\eta(1-\eta) tR({Q^{(t)}}^{T}{P^{(t)}}^{T}C^{(t)}) \\ & & + \> \eta^{2}tR({C^{(t)}}^{T}C^{(t)}) \end{array} $$
(18)

Then we derive:

$$\begin{array}{@{}rcl@{}} \nabla_{P^{(t)}}L & = & \nabla_{P^{(t)}}\|R^{(t)} - [(1-\eta)P^{(t)}Q^{(t)} + \eta C^{(t)}]\|_{F}^{2} + \nabla_{P^{(t)}}\alpha\|P^{(t)}\|_{F}^{2} \\ & = & -2(1-\eta)R^{(t)}{Q^{(t)}}^{T} + 2(1-\eta)^{2}P^{(t)}Q^{(t)}{Q^{(t)}}^{T} \\ & & + \> 2\eta(1-\eta)C^{(t)}{Q^{(t)}}^{T} + 2\alpha P^{(t)} \\ & = & 2P^{(t)}[(1-\eta)^{2}Q^{(t)}{Q^{(t)}}^{T} + \alpha I] \\ & & - \> 2[(1-\eta)R^{(t)} - \eta(1-\eta)C^{(t)}]{Q^{(t)}}^{T} \end{array} $$
(19)

Similarly we can derive the other two gradient equation as follows:

$$\begin{array}{@{}rcl@{}} \nabla_{Q^{(t)}}L & = & \nabla_{Q^{(t)}}\|R^{(t)} - [(1-\eta)P^{(t)}Q^{(t)} + \eta C^{(t)}]\|_{F}^{2} \\ & & + \> \nabla_{Q^{(t)}}\|R^{(t)} - [(1-\eta)s^{(t)}P^{(t-1)}Q^{(t)} + \eta C^{(t)}]\|_{F}^{2} \\ & & + \> \nabla_{Q^{(t)}}\beta\|Q^{(t)}\|_{F}^{2} \\ & = & 2(1-\eta)[-{P^{(t)}}^{T}R^{(t)}+\eta{P^{(t)}}^{T}C^{(t)}+(1-\eta){P^{(t)}}^{T}P^{(t)}Q^{(t)}] \\ & & + \> 2(1-\eta)[-{P^{(t-1)}}^{T}{s^{(t)}}^{T}R^{(t)}+\eta{P^{(t-1)}}^{T}{s^{(t)}}^{T}C^{(t)} \\ & & + \> (1-\eta){P^{(t-1)}}^{T}{s^{(t)}}^{T}s^{(t)}P^{(t-1)}Q^{(t)}]+ 2\beta Q^{(t)} \\ & = & 2(1-\eta){P^{(t)}}^{T}[\eta C^{(t)}+(1-\eta)P^{(t)}Q^{(t)}] \\ & & + \> 2(1-\eta){P^{(t-1)}}^{T}{s^{(t)}}^{T}[\eta C^{(t)}+(1-\eta)s^{(t)}P^{(t-1)}Q^{(t)}] \\ & & - \> 2(1-\eta)({P^{(t)}}^{T} + {P^{(t-1)}}^{T}{s^{(t)}}^{T})R^{(t)} + 2\beta Q^{(t)} \end{array} $$
(20)
$$\begin{array}{@{}rcl@{}} \nabla_{s^{(t)}}L & = & \nabla_{s^{(t)}}\|R^{(t)} - [(1-\eta)s^{(t)}P^{(t-1)}Q^{(t)} + \eta C^{(t)}]\|_{F}^{2} \\ & & + \> \nabla_{s^{(t)}}\gamma\|s^{(t)}\|_{F}^{2} + \nabla_{s^{(t)}}\lambda\|s^{(t)} - I\|_{F}^{2} \\ & = & 2(1-\eta)[-R^{(t)}{Q^{(t)}}^{T}{P^{(t-1)}}^{T} \\ & & + \> (1-\eta)s^{(t)}P^{(t-1)}Q^{(t)}{Q^{(t)}}^{T}{P^{(t-1)}}^{T} \\ & & + \> \eta C^{(t)}{Q^{(t)}}^{T}{P^{(t-1)}}^{T}]+ 2\gamma s^{(t)} + 2\lambda(s^{(t)}-I) \\ & = & 2(1-\eta)[(1-\eta)s^{(t)}P^{(t-1)}Q^{(t)}+ \eta C^{(t)}]{Q^{(t)}}^{T}{P^{(t-1)}}^{T} \\ & & + \> 2(\lambda+\gamma)s^{(t)} \\ & & - \> 2[(1-\eta)R^{(t)}{Q^{(t)}}^{T}{P^{(t-1)}}^{T} + \lambda I] \end{array} $$
(21)

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Song, D., Li, Z., Jiang, M. et al. A novel temporal and topic-aware recommender model. World Wide Web 22, 2105–2127 (2019). https://doi.org/10.1007/s11280-018-0595-9

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