Matrix factorization (recommender systems): Difference between revisions

Revision as of 13:46, 12 December 2020

Revision as of 23:39, 20 December 2020

Line 16:

<math>\tilde{r}_{ui} = \sum_{f=0}^{n factors} H_{u,f}W_{f,i}</math>

It is possible to tune the expressive power of the model by changing the number of latent factors. It has been demonstrated <ref name="Jannach13">{{cite book |last1=Jannach |first1=Dietmar |last2=Lerche |first2=Lukas |last3=Gedikli |first3=Fatih |last4=Bonnin |first4=Geoffray |title=What Recommenders Recommend – An Analysis of Accuracy, Popularity, and Sales Diversity Effects |journal=User Modeling, Adaptation, and Personalization |volume=7899 |date=2013 |pages=25–37 |doi=10.1007/978-3-642-38844-6_3 |publisher=Springer Berlin Heidelberg |language=en|series=Lecture Notes in Computer Science |isbn=978-3-642-38843-9 |citeseerx=10.1.1.465.96 }}</ref> that a matrix factorization with one latent factor is equivalent to a ''most popular'' or ''top popular'' recommender (e.g. recommends the items with the most interactions without any personalization). Increasing the number of latent factor will improve personalization, therefore recommendation quality, until the number of factors becomes too high, at which point the model starts to [[overfitting|overfit]] and the recommendation quality will decrease. A common strategy to avoid overfitting is to add [[regularization (mathematics)|regularization]] terms to the objective function.<ref name="bi2017">{{citeFunk journal|last1=Bi|first1=Xuan|last2=Qu|first2=Annie|last3=Wang|first3=Junhui|last4=Shen|first4=Xiaotong|year=2017|title=AMF group-specificwas recommenderdeveloped system.|url=https://amstat.tandfonline.com/doi/abs/10.1080/01621459.2016.1219261|journal=Journalas ofa the American Statistical Association|volume=112|issue=519|pages=1344–1353|doi=10.1080/01621459.2016.1219261|s2cid=125187672}}</ref><ref>{{cite journal|last1=Zhu|first1=Yunzhang|last2=Shen|first2=Xiaotong|last3=Ye|first3=Changqing|year=2016|title=Personalized''rating prediction'' andproblem, sparsitytherefore pursuitit inuses latentexplicit factornumerical models.|url=https://amstat.tandfonline.com/doi/abs/10.1080/01621459.2016.1219261|journal=Journalratings ofas theuser-item American Statistical Association|volume=111|issue=513|pages=241–252|doi=10.1080/01621459.2016interactions.1219261|s2cid=125187672}}</ref>

Funk MF was developed as a ''rating prediction'' problem, therefore it uses explicit numerical ratings as user-item interactions.

All things considered, Funk MF minimizes the following objective function: