svd++
SVD++ refers to a matrix factorization model which makes use of implicit feedback information. In general, implicit feedback can refer to any kinds of users' history information that can help indicate users' preference.
CONTENTS[hide]
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MODEL FORMALIZATION
The SVD++ model is formally described as following equation:
where 
is the set of implicit information( the set of items user u rated ).
GENERAL FORMALIZATION FOR USER FEEDBACK INFORMATION
A more general form of utilizing implicit/explicit information as user factor can be described in following equation
Here 
is the set of user feedback information( e.g: the web pages the user clicked, the music on users' favorite list, the movies user watched, any kinds of information that can be used to describe the user). 
is a feature weightassociates with the user feedback information. With the most two common choices: (1) 
for implicit feedback, (2) 
for explicit feedback.
（一直搞不清楚上面公式当中yi到底是什么，现在清楚了，yi就是上面所写出来的隐式反馈！）
LEARNING
SVD++ can be trained using ALS.
It is slow to train a SVD++-style model using stochastic gradient descent due to the size of user feedback information, however, an efficient SGD training algorithm can be used. [1] describes efficient training with user feedback information in section 4
LITERATURE
- Yehuda Koren: Factorization meets the neighborhood: a multifaceted collaborative filtering model, KDD 2008, http://portal.acm.org/citation.cfm?id=1401890.1401944
IMPLEMENTATIONS
- The GraphLab Collaborative Filtering Library has implemented SVD++ for multicore: http://graphlab.org/pmf.html
- SVDFeature is a toolkit designed for feature-based matrix factorization, can be used to implement SVD++ and its extensions.
- LibFM can also be used to implement SVD++
- wooflix is a (not very fast) Python implementation of SVD++
- MyMediaLite: SVD++ source code on GitHub; see also [2]