Regularized Matrix Factorization Algorithm
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A Regularized Matrix Factorization Algorithm is a matrix factorization algorithm that is implemented by a regularized matrix factorization system (to solve a regularized matrix factorization task.
- Context:
- It can range from being an Unweighted Regularized Matrix Factorization Algorithm to being a Weighted Regularized Matrix Factorization Algorithm.
- See: Non-Regularized Matrix Factorization.
References
2013
- http://www.quuxlabs.com/blog/2010/09/matrix-factorization-a-simple-tutorial-and-implementation-in-python/#regularization
- QUOTE: The above algorithm is a very basic algorithm for factorizing a matrix. There are a lot of methods to make things look more complicated. A common extension to this basic algorithm is to introduce regularization to avoid overfitting. This is done by adding a parameter [math]\displaystyle{ \beta }[/math] and modify the squared error as follows: : [math]\displaystyle{ e_{ij}^2 = (r_{ij} - \sum_{k=1}^K{p_{ik}q_{kj}})^2 + \frac{\beta}{2} \sum_{k=1}^K{(||P||^2 + ||Q||^2)} }[/math] In other words, the new parameter [math]\displaystyle{ \beta }[/math] is used to control the magnitudes of the user-feature and item-feature vectors such that P and Q would give a good approximation of R without having to contain large numbers. In practice, [math]\displaystyle{ \beta }[/math] is set to some values in the range of 0.02. The new update rules for this squared error can be obtained by a procedure similar to the one described above. The new update rules are as follows. : [math]\displaystyle{ p'_{ik} = p_{ik} + \alpha \frac{\partial}{\partial p_{ik}}e_{ij}^2 = p_{ik} + \alpha(2 e_{ij} q_{kj} - \beta p_{ik} ) }[/math] : [math]\displaystyle{ q'_{kj} = q_{kj} + \alpha \frac{\partial}{\partial q_{kj}}e_{ij}^2 = q_{kj} + \alpha(2 e_{ij} p_{ik} - \beta q_{kj} ) }[/math]
2008
- (Rendle & Schmidt-Thieme, 2008) ⇒ Steffen Rendle, and Lars Schmidt-Thieme. (2008). “Online-updating Regularized Kernel Matrix Factorization Models for Large-scale Recommender Systems.” In: Proceedings of the 2008 ACM conference on Recommender systems. ISBN:978-1-60558-093-7 doi:10.1145/1454008.1454047
- QUOTE: Regularized matrix factorization models are known to generate high quality rating predictions for recommender systems. One of the major drawbacks of matrix factorization is that once computed, the model is static. For real-world applications dynamic updating a model is one of the most important tasks. Especially when ratings on new users or new items come in, updating the feature matrices is crucial.