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 )
 
  
 
== 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.

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