Difference between revisions of "Feature-based matrix factorization"
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* User temporal factor( user feature ) | * User temporal factor( user feature ) | ||
* User implicit/explicit feedback( user feature ) | * User implicit/explicit feedback( user feature ) | ||
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== Related Models == | == Related Models == |
Revision as of 22:39, 30 September 2011
Feature-based matrix factorization is an abstract matrix factorization model that uses features to describe the global bias and user/item factors. The the model allows development of new model simply by feature defining. We can incorporate information such as temporal information, neighborhood information, taxonomy information into feature-based matrix factorization to make the model informative. If we have a solver for feature-based matrix factorization, we only need to design context-aware or informative collaborative filtering(or ranking) models by feature-defining, without engineering efforts for writing codes for each new model.
Contents
Model Formalization
The feature-based matrix factorization model can be formalized as follows:
<math>y = \mu+\left(\sum_j \gamma_j b^g_j +\sum_j \alpha_j b^u_j + \sum_j \beta_j b^i_j\right) +\left(\sum_j \alpha_j p_j\right)^T\left( \sum_j \beta_j q_j\right)</math>
We call <math>\gamma </math> global feature, <math>\alpha </math> user feature and <math>\beta </math> item feature. Defining different kinds of features will result in different variants of models.
Example Information that can be Incorporated into the Model
- Neighborhood information( global feature )
- Global item temporal bias( global feature )
- Item taxonomy information( item feature )
- User temporal factor( user feature )
- User implicit/explicit feedback( user feature )
Related Models
- Factorization Machine: feature-based matrix factorization can be viewed as a restricted case of factorization machine to distinguish different types of features, allowing us to overcome some shortcomings of FM(e.g: including neighborhood information, exact implementation of rank,svd++ ). We call the model feature-based matrix factorization instead of restricted FM because the idea descends more naturally from matrix factorization using features.
Implementation
- SVDFeature is an efficient and scalable implementation of feature-based matrix factorization.
References
- Tianqi Chen, Zhao Zheng, Qiuxia Lu and Yong Yu: Feature-based Matrix Factorization, http://arxiv.org/abs/1109.2271