Designing Specific Weighted Similarity Measures to Improve Collaborative Filtering Systems
Presentation CF approaches Similarities
Experiments
L. Candillier, F. Meyer, F. Fessant France Telecom R&D Lannion ICDM 2008
Global Focus
Conclusions
1 Presentation
Collaborative Filtering Approaches Similarity Measures 2 Experiments
Global Experiments Focus on Weigthed Pearson 3 Conclusions
Collaborative Filtering on an example
Presentation CF approaches Similarities
I like the movie matrix but not titanic Will I like cube ? Propose me a movie ?
Experiments Global Focus
Conclusions
me dave john frank maria janis brad
matrix 4 4 2
cube ? 4 5 2
aladdin
toystory
titanic 1 1
2 5 4
5 5
4 4
dave and you rate the movies in the same way cube and matrix are rated in the same way
3 5
User-based approaches Recommend items appreciated by users whose tastes are similar to the ones of the active user a [Resnick et al., 1994] Presentation CF approaches Similarities
Experiments Global Focus
Conclusions
1
define a similarity measure between users sim(a, u)
2
select the K nearest neighbours of user a (Ta ) choose a prediction scheme
3
Su = {rui } : set of items i rated by user u prediction using weighted sum P {u∈T |i ∈Su } sim(a, u) × rui pai = P a {u∈Ta |i ∈Su } |sim(a, u)| ru : mean rating of user u prediction using weighted sum of deviations from the mean P {u∈Ta |i ∈Su } sim(a, u) × (rui − ru ) P pai = ra + {u∈Ta |i ∈Su } |sim(a, u)|
Item-based approaches
Presentation
Recommend items similar to those appreciated by the active user a [Karypis, 2001]
CF approaches Similarities
Experiments Global Focus
Conclusions
⇒ dual of user-based approach P pai = ri +
{j∈Sa ∩Ti } sim(i , j)
× (raj − rj )
P
{j∈Sa ∩Ti } |sim(i , j)|
sim(i , j) : similarity measure between items i and j Sa : set of items rated by user a Ti : set of nearest neighbours of item i ri : mean rating on item i
Traditional similarity measures Pearson : cosine of deviations from the mean Presentation CF approaches Similarities
Experiments Global Focus
Conclusions
P
{i ∈Sa ∩Su } (rai
− ra ) × (rui − ru ) P 2 2 {i ∈Sa ∩Su } (rui − ru ) {i ∈Sa ∩Su } (rai − ra )
sim(a, u) = qP Cosine
cosine(a, u) = qP
P
{i ∈Sa ∩Su } rai
2 {i ∈Sa ∩Su } rai
× rui
2 {i ∈Sa ∩Su } rui
P
Manhattan (ratings ∈ [minr , Maxr ]) 1 manhattan(a, u) = 1− × Maxr − minr
P
{i ∈Sa ∩Su } |rai
− rui |
|{i ∈ Sa ∩ Su }|
Weighting similarity measures Current problem : only the set of attributes in common between 2 vectors are considered Presentation CF approaches Similarities
Experiments Global Focus
Conclusions
⇒ 2 vectors may be completely similar even if they only share 1 appreciation on 1 attribute Jaccard similarity measures the overlap that 2 vectors share with their attributes jaccard(a, u) =
|{Sa ∩ Su }| |{Sa ∪ Su }|
But jaccard doesn’t take into account the difference of ratings between the vectors ⇒ combine jaccard with the others : with simple product (wpearson, wcosine, wmanhattan)
Experiments
Presentation CF approaches Similarities
Experiments
Testing parameters similarity measure neighbourhood size K prediction scheme ⇒ deviations from the mean
Global Focus
Conclusions
Evaluation protocol [Herlocker et al., 2004] movie rating datasets MovieLens (6,040 × 3,706 → 1 million) Netflix (480,189 × 17,770 → 100 millions)
cross-validation (9/10th learn, 1/10th test) Mean Absolute Error Rate on test set T = {(u, i , r )} MAE =
1 |T |
X
(u,i ,r )∈T
|pui − r |
Item-based approaches, MovieLens
MAE Presentation CF approaches Similarities
Experiments Global Focus
Conclusions
jaccard manhattan cosine pearson wmanhattan wcosine wpearson
0.78 0.76 0.74 0.72 0.7 0.68 0.66 0.64 0.62
0
500
1000
1500
2000
2500
3000
K
User-based approaches, MovieLens
MAE
jaccard manhattan cosine pearson wmanhattan wcosine wpearson
Presentation CF approaches Similarities
Experiments Global Focus
0.8
Conclusions
0.75
0.7
0.65 0
1000
2000
3000
4000
5000
K
Item-based approaches, Netflix
MAE Presentation CF approaches Similarities
Experiments Global Focus
Conclusions
jaccard manhattan cosine pearson wmanhattan wcosine wpearson
0.76 0.74 0.72 0.7 0.68 0.66 0.64 0.62 0.6 0
2000
4000
6000
8000 10000 12000 14000 16000 K
Summary of the best results / type of approach MovieLens neighbour number
learning time
prediction time
MAE
precision4
default
/
1 sec.
1 sec.
0.6855
0.7676
user-based
300
4 min.
3 sec.
0.6533
0.7810
item-based
100
2 min.
1 sec.
0.6213
0.7915
neighbour number
learning time
prediction time
MAE
precision4
default
/
6 sec.
15 sec.
0.6903
0.7392
user-based
1,000
9h
28 min.
0.6440
0.7655
item-based
70
2 h 30
1 min.
0.5990
0.7827
Presentation CF approaches Similarities
Experiments Global Focus
Conclusions
Netflix
Interest of the weighting scheme Compare the mean number of common attributes (C) between nearest item neighbours on MovieLens when considering different neighbourhood sizes (K) Presentation
C
jaccard pearson wpearson
CF approaches Similarities
Experiments Global Focus
Conclusions
100 80 60 40 20 0
0
500
1000
1500
2000
2500
3000
K
Item-based approaches with power, MovieLens
MAE
pearson pearson2 pearson3
Presentation CF approaches Similarities
Experiments
wpearson wpearson2 wpearson3
0.75
Global Focus
Conclusions
0.7
0.65
0.6
0
500
1000
1500
2000
2500
3000
K
Item-based approaches with power, Netflix
MAE Presentation CF approaches Similarities
pearson pearson2 pearson3
0.75
Experiments Global Focus
wpearson wpearson2 wpearson3
0.7
Conclusions
0.65
0.6
0
2000
4000
6000
8000 10000 12000 14000 16000 K
Summary of the best results of item-based approaches / use of the weighting scheme MovieLens Presentation
neighbour number
learning time
prediction time
MAE
precision4
non-weighted
1,500
3 min.
7 sec.
0.6500
0.7808
weighted
500
2 min.
3 sec.
0.6075
0.7958
neighbour number
learning time
prediction time
MAE
precision4
non-weighted
10,000
7h
38 min.
0.6291
0.7712
weighted
200
2 h 30
1 min.
0.5836
0.7881
CF approaches Similarities
Experiments Global Focus
Conclusions
Netflix
Our contribution
Presentation CF approaches Similarities
Experiments Global Focus
Conclusions
Interest of the weighting scheme nearest neighbours share much more attributes fewer neighbours need to be considered improves the predictive performance and scalability of both user- and item-based approaches the best : weighted pearson
Our observation
Presentation CF approaches Similarities
Experiments Global Focus
Conclusions
The item-based approach better predictive performance than user-based approach better scalability than user-based approach (needs fewer neighbours, and there are generally more users than items) relevant predictions as soon as a user has rated 1 item is also appropriate to navigate in item catalogues even with no user information user privacy is preserved
Next
Presentation CF approaches Similarities
Experiments Global Focus
Conclusions
Optimise the similarity matrix using other combinations than simple product using item content information [Vozalis and Margaritis, 2004] optimisation led by cross-validation [Bell and Koren, 2007] Combine approaches ensemble methods [Polikar, 2006] specific for collaborative filtering [Bell et al., 2007]
Presentation CF approaches Similarities
Experiments Global Focus
Conclusions
Bell, R. and Koren, Y. (2007). Improved neighborhood-based collaborative filtering. In ICDM’07: IEEE International Conference on Data Mining, pages 7–14, San Jose, California, USA. ACM. Bell, R., Koren, Y., and Volinsky, C. (2007). Modeling relationships at multiple scales to improve accuracy of large recommender systems. In KDD’07: Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 95–104, New York, NY, USA. ACM. Herlocker, J., Konstan, J., Terveen, L., and Riedl, J. (2004). Evaluating collaborative filtering recommender systems. ACM Transactions on Information Systems, 22(1):5–53.
Presentation CF approaches Similarities
Experiments Global Focus
Conclusions
Karypis, G. (2001). Evaluation of item-based top-N recommendation algorithms. In 10th International Conference on Information and Knowledge Management, pages 247–254. Polikar, R. (2006). Ensemble systems in decision making. IEEE Circuits & Systems Magazine, 6(3):21–45. Resnick, P., Iacovou, N., Suchak, M., Bergstrom, P., and Riedl, J. (1994). Grouplens: An open architecture for collaborative filtering of netnews. In Conference on Computer Supported Cooperative Work, pages 175–186. ACM.
Presentation CF approaches Similarities
Experiments Global Focus
Conclusions
Vozalis, M. and Margaritis, K. G. (2004). Enhancing collaborative filtering with demographic data: The case of item-based filtering. In 4th International Conference on Intelligent Systems Design and Applications, pages 361–366.
