k NN CF: A Temporal Social Network

1. kNN CF: A Temporal Social Network Neal Lathia, Stephen Hailes, Licia Capra University College London RecSys’08 Advisor: Hsin-Hsi Chen Reporter: Y.H Chang 2009/03/09 kNN CF: A Temporal Social Network

2. INTRODUCTION(1/4) • Recommender System: • It has been an important component, or even core technology, of online business. • EX: Amazon, Netflix (Netflix prize competition) • The process of computing recommendations is reduced to a problem of predicting the correct rating that users would apply to unrated items kNN CF: A Temporal Social Network

3. INTRODUCTION(2/4) • k-Nearest Neighborhood Collaborative Filtering(kNN CF/ kNN) has surfaced amongst the most popular underlying algorithms of recommender systems. • Collaborative Filtering: using a set of user rating profiles to predict ratings of unrated items kNN CF: A Temporal Social Network

4. INTRODUCTION(3/4) • In order to understand the effect of kNN, the algorithm can be viewed as a process that generates a social networkgraph, where nodes are users and edges connect k similar users. • In this work (1)we analyse user-user kNN graph from temporal perspective (2) we observe the emergent properties of the entire graph as algorithm parameters change. kNN CF: A Temporal Social Network

5. INTRODUCTION(4/4) The analysis is decomposed into four separate stages: • Individual Nodes • Node Pairs • Node Neighborhoods • Community Graphs kNN CF: A Temporal Social Network

6. I. USER PROFILES OVER TIME kNN CF: A Temporal Social Network

7. USER PROFILES OVER TIME (1/2) • In this work we focus on the two MovieLens datasets • 100t MovieLens • 100, 000 ratings of 1682 movies by 943 users. (1997.09.20 to 1998.04.22) • 1000t MovieLens • About 1 million ratings of 3900 movies by 6040 users. (2000.04.25 to 2003.02.28) kNN CF: A Temporal Social Network

8. USER PROFILES OVER TIME (2/2) kNN CF: A Temporal Social Network

9. II. USER PAIRS OVER TIME kNN CF: A Temporal Social Network

10. user a, item i b is a’s neighbor :item i’s rating of neighbor b :neighbor b’s mean rating USER PAIRS OVER TIME(1/6) • Predictions are often computed as a weighted average of deviation from neighbor means: Similarity between the User a and its’ neighbor b kNN CF: A Temporal Social Network

11. USER PAIRS OVER TIME(2/6) - four highly cited methods of the similarity between users Total n items kNN CF: A Temporal Social Network

12. USER PAIRS OVER TIME(3/6) -evolution of similarity kNN CF: A Temporal Social Network

13. USER PAIRS OVER TIME(4/6) • In this work we plot the similarity at time t, sim(t) against the similarity at the time of the next update, sim(t + 1). • The distance from points to the diagonal represents the changed from one update to the next. kNN CF: A Temporal Social Network

14. COR wPCC Range:-1~+1 PCC Range:-1~+1 VS USER PAIRS OVER TIME(5/6)- sim(t) against sim(t+1) sim(t + 1) sim(t) kNN CF: A Temporal Social Network

15. USER PAIRS OVER TIME(6/6) We classified those similarity methods according to their temporal behavior— • Incremental:COR and wPCC • The differnce between (t) and (t+1) is small. • Growing • Corrective: VS method • Jumps from 0 to near-perfect then degrade • Near-random: PCC • near-random behavior kNN CF: A Temporal Social Network

16. III. DYNAMIC NEIGHBOURHOODS kNN CF: A Temporal Social Network

17. DYNAMIC NEIGHBOURHOODS(1/2) • The often-cited assumption of collaborative filtering is that users who have been like-minded in the past will continue sharing opinions in the future. • When applying user-user kNN CF, we would expect each user’s neighborhood to converge to a fixed set of neighbors over time kNN CF: A Temporal Social Network

18. DYNAMIC NEIGHBOURHOODS(2/2) (This experiment updated daily.) The actual number of neighbors that a user will be connected to depends on: • similarity measure • neighborhood size k The stepper they are, the faster the user is meeting other recommenders. COR and wPCC outperform the VS and PCC (N.Lathia et al.,2008) New recommend-ers Left time kNN CF: A Temporal Social Network

19. IV. NEAREST-NEIGHBOUR GRAPHS kNN CF: A Temporal Social Network

20. NEAREST-NEIGHBOUR GRAPHS(1/5) • The last section, we focus on non-temporal characteristics of the dataset.(wPCC) • Path Length • Connectedness (using only positive sim) • Reciprocity: a characteristic of graphs explored in social network analysis; in this work, it is the proportion of users who are in other’s top-k kNN CF: A Temporal Social Network

21. NEAREST-NEIGHBOUR GRAPHS(2/5) kNN CF: A Temporal Social Network

22. NEAREST-NEIGHBOUR GRAPHS(3/5) (1)There may be some users who are not in any other’s top-k. Their ratings are therefore inaccesible and will not be used in any prediction. power law kNN CF: A Temporal Social Network

23. NEAREST-NEIGHBOUR GRAPHS(4/5) (2)Some users will have incredible high in-degree. We call this group “power users” kNN CF: A Temporal Social Network

24. NEAREST-NEIGHBOUR GRAPHS(5/5) • More experiments about “power users”: • 1. remove the power users’ ability to prediction • 2. only the top power users are allow to contribute to the prediction • Results: • The remaining users can still make significant contribution to each user’s predictions • The 10 topmost power users hold access to over 50% of the dataset. kNN CF: A Temporal Social Network

25. DISCUSSION • The evolution of similarity between any pair of users is dominated by the similarity method, and the four measures we explored can be classified into three categories (incremental, corrective, near-random) based on the temporal properties • Measures that are known to perform better display the same behavior: they are incremental, connect each user quicker, and offer broader access to the ratings in the training set. kNN CF: A Temporal Social Network