矩阵分解技术应用到推荐系统

b
ui
bu bi
（3）
bi indicate the observed deviations of user b ，
u
and item i. Including bias parameters in the prediction:
rui bi bu q
Optimize:
T i ui u
i
u
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5.1、Singular Value Decomposition

Require factoring the user-item rating matrix Conventional SVD is undefined for incomplete
5.1、Singular Value Decomposition
Measures:a
Here, is
regularized model
min
p .,q.
the set of the (u,i)pairs for which
T ( q r ui i ( u ,i )
pu)
2
(
qi
2

pu
2
)
(2)
r
ui
is known(the training set);the constant controls the extent of regularization,determined by crossvalidation.
6、Learning Algorithms

ቤተ መጻሕፍቲ ባይዱ
Two methods to minizing Equation (2)

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4、Matrix Factorization Methods

Characterize both items and users by vectors of factors inferred from item rating patterns.
Matrix Factorization techniques for recommender systems
Catalogue
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
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3.2、Collaborative Filtering

Analyze relationships between users and interdep-
encies among products to identify new user-item as-
Socitions.

Disadvantages: cold start Two primary areas:

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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. Assumption : Ratings can be inferred from a model put together from a smaller number of parameters.
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5、A Basic Matrix Factorization Model


Dot product captures the user’s estimated interest in the item: (1) r q p Here，the elements of q measure the extent to which the item possesses those factors,the elements of p 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? Approaches: Singular Value Decompositionn(SVD)
7、Adding Biases

A first-order approximation of the bias involved in rating rui is as follows: Here, is the overall average;the parameters

T i
p
（4)
u
min
p.,q.,b.
T ( q rui bu bi i ( u ,i )
pu)
2
(
qi
2

pu bu bi )
2
2
2
(5)
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8、Adding Input Sources

Problem:cold start Solution:incorporate additional sources of information about the users. Two information:item attributes,user attributes Item attribute： x Normalizing the sum

3、Recommender System Strategies

Content Filtering Collaborative Filtering
1.Neighborhood methods
user-oriented item-oriented
tent Fator Model
Stochastic Gradient Descent
Altering Least Squares
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6.1、Stochastic Gradient Descent

Loop through all ratings in the training set For each given traing case,the system predicts
def T i
and computes the associated prediction error
e

ui
rui q
p
u
By magnitude proportional to
i i ui u

i
in the opposite
direction of the gradient
u u
q q (e . p . q ) p p (e . q . p )
neighborhood methods
user-oriented item-oriented
Latent factor models
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3.2.1、Neighborhood methods

Centered on computing the relationships between items or users.
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3.1、Contents Filtering

Create a profile for each user or product to characterize its nature. Need to gather external information.
ui i u
6.2、Alternating Least Squares
ALS teachniques rotate between fixing the qi ' S and fixing the p ' S

u

ALS is favorable in at least two cases: Allows massive parallelization Centered on implicit data

Imputation to fill in missing values
Increases the amount of data Modeling directly the observed ratings

We need to approach that can simply ignore missing value