矩阵分解技术应用到推荐系统

Tuesday, October 20, 2020
15
6.1、Stochastic Gradient Descent
Loop through all ratings in the training set For each given traing case,the system predicts and computes the associated prediction error
Matrix Factorization techniques for recommender systems
Catalogue
1. Paper Background 2. Introduction 3. Recommender Systems Strategies 4. Matrix Factorization Methods 5. A Basic Matrix Factorization Model 6. Learning Algorithm 7. Adding Biases 8. Adding Input Sources 9. Temporal Dynamics 10. Input With Varying Confidence Levels 11. Netflix Prize Competition 12. Conclusion
Dot product captures the user’s estimated interest in the item:
q p T
rui
iu
(1)
Here，the elements of q measure the extent to i
which the item possesses those factors,the
Approaches:
Singular Value Decompositionn(SVD)
Tuesday, October 20, 2020
12
5.1、Singular Value Decomposition
Require factoring the user-item rating matrix Conventional SVD is undefined for incomplete Imputation to fill in missing values
3、Recommender System Strategies
Content Filtering Collaborative Filtering
1.Neighborhood methods user-oriented item-oriented
tent Fator Model
Tuesday, October 20, 2020
Tuesday, October 20, 2020
6
3.2、Collaborative Filtering
Analyze relationships between users and interdepencies among products to identify new user-item asSocitions. Disadvantages: cold start Two primary areas:
b u ，b i indicate the observed deviations of user
and item i.
Including bias parameters in the prediction:
ቤተ መጻሕፍቲ ባይዱ
Optimize:
r bb qp
T
ui
i u iu
（4)
m p .q . ,b . ,( u ,i) ( r i u n i b u b i q T ip u ) 2 (q i2 p u 2 b u 2 b i 2 )(5)
7、Adding Biases
A first-order approximation of the bias involved
in rating rui is as follows:
bu i bubi （3）
Here, is the overall average;the parameters
Assumption : Ratings can be inferred from a model put together from a smaller number of parameters.
Tuesday, October 20, 2020
10
4、Matrix Factorization Methods
e r q p def
T
ui
ui
iu
By magnitude proportional to in the opposite
direction of the gradient
q q e ( .
i
i
ui
p.q)
u
i
p u
pu(eui.qi .
p) u
6.2、Alternating Least Squares
neighborhood methods user-oriented item-oriented
Latent factor models
Tuesday, October 20, 2020
7
3.2.1、Neighborhood methods
Centered on computing the relationships between items or users.
5
3.1、Contents Filtering
Create a profile for each user or product to characterize its nature.
Need to gather external information.
A known successful realization of content filtering is the Music Genome Project,which is used for the Internet radio service .
the extent of regularization,determined by cross-
validation.
6、Learning Algorithms
Two methods to minizing Equation (2)
Stochastic Gradient Descent Altering Least Squares
Measures:a regularized model
m p .q ,. (u ,i)i (n ru iq T ip u )2 (q i2p u2 )
(2)
Here, is the set of the (u,i)pairs for which r ui
is known(the training set);the constant controls
elements
of
p u
measure
the
extent
of
interest
the
user has in items that are high on the
corresponding factors.
Challenge:How to compute a mapping of items and users factor vectors?
Increases the amount of data Modeling directly the observed ratings
We need to approach that can simply ignore missing value
5.1、Singular Value Decomposition
, implicit feedback . Implicit feedback :purchase history , browsing
history ,search patterns , mouse movement and so on.
Tuesday, October 20, 2020
11
5、A Basic Matrix Factorization Model
Tuesday, October 20, 2020
2
1、Paper Background
1.Yehuda Koren,Yahoo Research 2.Robert Bell and Chris Volinsky,AT&T LabsResearch 3.Paper published by the IEEE Computer Society in August 2009 4.Author won the grand Netflix Prize Competition in September 2009
Tuesday, October 20, 2020
3
2、Introduction
Modern consumers are inundated with choices. More retailor have become interested in RS,which
analyze patterns of user interest in products to pride personalized recommendations that suit a user's taste. Netflix and have made RS a salient part of their websites. Particularly userful for entainment products such as movies,music,and TV shows.
Characterize both items and users by vectors of factors inferred from item rating patterns.
RS rely on different types of input data. Strength: incorporation of additional information
ALS teachniques rotate between fixing the q ' S and i
fixing the p ' S u
ALS is favorable in at least two cases: Allows massive parallelization Centered on implicit data
Item
The item-oriented approach evaluates a user’s preference for an item based on ratings of “neighboring” items by the same user.
The user-oriented approach identifies like-minded users who can complement each other’s ratings.
Tuesday, October 20, 2020
18
8、Adding Input Sources
Problem:cold start
Solution:incorporate additional sources of information about the users.
Two information:item attributes,user attributes
Tuesday, October 20, 2020
8
Example:
3.2.2、Latent Factor Models
Find features that describe the characteristics of rated objects.
Item characteristics and user preferences are described with numerical factor values.