Matrix factorization (recommender systems): Difference between revisions

Revision as of 21:13, 7 October 2020

Revision as of 20:55, 14 October 2020

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<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>{{cite journal|last1=Zhu|first1=Yunzhang|last2=Shen|first2=Xiaotong|last3=Ye|first3=Changqing|year=2016|title=Personalized prediction and sparsity pursuit in latent factor models.|url=https://amstat.tandfonline.com/doi/abs/10.1080/01621459.2016.1219261|journal=Journal of the American Statistical Association|publisher=|volume=111|issue=513|pages=241-252|doi=}}</ref><ref name="bi2017">{{cite journal|last1=Bi|first1=Xuan|last2=Qu|first2=Annie|last3=Wang|first3=Junhui|last4=Shen|first4=Xiaotong|year=2017|title=A group-specific recommender system.|url=https://amstat.tandfonline.com/doi/abs/10.1080/01621459.2016.1219261|journal=Journal of the American Statistical Association|publisher=|volume=112|issue=519|pages=1344-1353|doi=}}</ref>.

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

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=== Group-specific SVD ===

A group-specific SVD can be an effective approach for the [[Cold start (recommender systems)|cold-start]] problem in many scenarios<ref>{{cite journal|last1name=Bi|first1=Xuan|last2=Qu|first2=Annie|last3=Wang|first3=Junhui|last4=Shen|first4=Xiaotong|year=2017|title=A group-specific recommender system.|url=https://amstat.tandfonline.com/doi/abs/10.1080/01621459.2016.1219261|journal=Journal of the American Statistical Association|publisher=|volume=112|issue=519|pages=1344-1353|doi=}}<"bi2017"/ref>. It clusters users and items based on dependency information and similarities in characteristics. Then once a new user or item arrives, we can assign a group label to it, and approximates its latent factor by the group effects (of the corresponding group). Therefore, although ratings associated with the new user or item are not necessarily available, the group effects provide immediate and effective predictions.

The predicted rating user ''u'' will give to item ''i'' is computed as: