This paper proposes a similarity-based approach for contextual modeling in context-aware recommender systems. It introduces three methods for representing context similarity - independent, latent, and multidimensional - and applies them to context-aware matrix factorization and sparse linear models. Experimental results on four datasets show the multidimensional context similarity approach outperforms deviation-based contextual modeling and independent context modeling. The paper concludes similarity-based contextual modeling provides a general way to incorporate contexts and recommends exploring solutions to reduce costs in multidimensional modeling and applying other base recommender algorithms.

1. Similarity-Based Context-aware Recommendation
Yong Zheng, Bamshad Mobasher, Robin Burke
Center for Web Intelligence, DePaul University, USA
International Conference on Web Information Systems Engineering,
Miami, Florida, USA, Nov, 2015

2. Intro: RecommenderSystems

3. Recommender Systems (RS)
 Recommender Systems (RS)

4. Recommender Systems (RS)
 Sample of Data in RS
Usually, it is a 2D rating matrix: User × Item ―> Ratings

5. Intro: Context-awareRecommender Systems

6. Context-aware Recommender Systems (CARS)
 Context-aware Recommender Systems
Pattern: User preferences change from contexts to contexts;
It is necessary to adapt users’ preferences to dynamic situations;

7. Context-aware Recommender Systems (CARS)
 Sample of Data Set in CARS
Multidimensional space: User × Item × Contexts ―> Ratings
Context: time, location, companion, weather, mood, etc
Context dimension = variable, Context condition = values in each dimension

8. Context-aware Recommender Systems (CARS)
 Context-aware Recommendation Algorithms

9. Contextual Modeling

10. Contextual Modeling
 There are potentially two ways for contextual modeling
1). Independent Contextual Modeling
Tensor Factorization
ACM RecSys 2010

11. Contextual Modeling
 There are potentially two ways for contextual modeling
2). Dependent Contextual Modeling
2.1). Deviation-Based Contextual Modeling
Context-awareMatrix Factorization, ACM RecSys 2011
Contextual Sparse Linear Method, ACM RecSys 2014
2.2). Similarity-Based Contextual Modeling
Similarity-BasedContextual Sparse Linear Method, UMAP 2015
Similarity-BasedContextual Recommendation, WISE 2015

12. Contextual Modeling
2). Dependent Contextual Modeling
Deviation-Based (adjust context in β) Similarity-Based (adjust context in ∂)
y = Ground truth (real rating or ranking);
ŷ = ∂X + β is the predictive model, where X is any traditional recommender
dotted line ŷ = contextual model by adapting to contextual situations

13. Base Algorithm:
Matrix Factorization & Sparse Linear Method

14. Matrix Factorization (MF)
In rating prediction task:
: user-factor vector,
How a user likes latent factors
: item-factor vector,
How an item obtains those factors
Predicted rating can also be used
as ranking score in top-N recsys

15. Sparse Linear Method (SLIM)
For example: i =2, j =1
Estimate ranking score for user
u2 on item t1.
Step1:
Extractu2’s rating on th (h!=1);
i.e. Yellow row in matrix R
Step2:
Extractcoefficient Wh,1
i.e. Yellow column in matrix W
Step3:
Aggregation

16. Deviation-BasedContextual Modeling
ŷ = ∂X + β, incorporatecontexts into β

17. Deviation-Based Context-aware MF
ŷ = ∂X + β; For example, X = matrix factorization =
Deviation-Based Context-aware Matrix Factorization: CAMF-Dev
The biases can be viewed as rating deviations
In CAMF-Dev, rating deviation is modeled as the dependency between item and contexts
Similarly, it could also be represented by dependency between user and contexts
Global average rating User bias Item bias in contexts
X: standard MF
Deviation term

18. Deviation-Based Contextual SLIM
ŷ = ∂X + β; For example, X = SLIM =
Deviation-Based Contextual SLIM: CSLIM-Dev
L = # of context dimension, cm and ck are two contexts, l indicates the lth condition
Due to the fact that SLIM is an aggregation of ratings for top-N recommendation algorithm,
the deviation term is directly incorporated into the prediction function in SLIM
deviation term (from one context to another)

19. Similarity-BasedContextual Modeling
ŷ = ∂X + β, incorporatecontexts into ∂

20. Similarity-Based Contextual Modeling
ŷ = ∂X + β; For example, X = matrix factorization =
In Matrix Factorization:
In Sparse Linear Method:
In other words, the similarity between two contexts is incorporated into prediction;
In SLIM, it is able to use the similarity between any two contexts;
In MF, latent factor model does Not use known ratings, so cE is used to represent
empty contexts, i.e., condition in each dimension is Empty or Unkown.
Similarity term

21. How to Represent Context Similarity?
We propose three representations of context similarity:
Ck = {time = weekend, location = home, companion = kid}
Cm = {time = weekday, location = cinema, companion = family}
1). Independent Context Similarity (ICS)
Sim (Ck, Cm) = sim(weekend, weekday) x sim(home, cinema) x sim(kid, family)
2). Latent Context Similarity (LCS)
Each individual similarity is represented by a dot product of two latent vectors
e.g. sim(kid, family) = Vkid ∙ Vfamily
3).Multidimensional Context
Similarity (MCS)
Each condition is represented
by a position in each context
dimension. Thus each context
is a point in the space.
Context similarity ss the reversed
distance between two points.

22. ExperimentalEvaluations

23. Data sets and Evaluation metrics
Context-aware Data sets
Evaluations
For each data set, we use 5-fold cross validation for evaluating top-N recommendation
We choose Precision and Mean Average Precision (MAP) as evaluation metrics

24. Results based on CAMF
Summary:
1). Best performing one is
CAMF-MCS
2). LCS is better than ICS model
3). We can always find a
similarity-based model working
better than deviation-based
CAMF model

25. Results based on CSLIM
Summary:
1). Best performing one is
CSLIM-MCS
2). LCS is better than ICS model
3). We can always find a
similarity-based model working
better than deviation-based
CSLIM model

26. CAMF or CSLIM?
1). CAMF-MCS is better than CAMF-Dev
2). CSLIM-MCS is better than CSLIM-Dev
3). CSLIM-Dev is better than CAMF-Dev
4). CSLIM-MCS is better than CAMF-MCS
It is not surprising, since SLIM is specifically
designed for top-N recommendation

27. Conclusions and Future Work

28. Conclusions and Future Work
Conclusions
Future Work
1). Try other recommender as base algorithm,such as slope one recommender
2). Try to explore solutions to reduce costs in multidimensional context similarity modeling
We propose similarity-based contextual modeling which is a general way to incorporate
contexts into recommender systems, and it is demonstrated to work better than the
deviation-based contextual modeling, as well as independent context modeling.
CARSKit (https://github.com/irecsys/CARSKit)
An open-source Java-based context-aware recommendation library.

29. Similarity-Based Context-aware Recommendation
Yong Zheng, Bamshad Mobasher, Robin Burke
Center for Web Intelligence, DePaul University, USA
International Conference on Web Information Systems Engineering,
Miami, Florida, USA, Nov, 2015