kNN CF: A Temporal Social Network 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 Network2/25 INTRODUCTION(1/4)  Recommender System: It has been an important component, or even core technology, of online business. EX: Amazon, Netflix (Netflix prize competition)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

2009/03/09 kNN CF: A Temporal Social Network3/25 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

2009/03/09 kNN CF: A Temporal Social Network4/25 INTRODUCTION(3/4)  In order to understand the effect of kNN, the algorithm can be viewed as a process that generates a social network graph, 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.

2009/03/09 kNN CF: A Temporal Social Network5/25 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 I. USER PROFILES OVER TIME

2009/03/09 kNN CF: A Temporal Social Network7/25 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. ( to )  1000t MovieLens About 1 million ratings of 3900 movies by 6040 users. ( to )

2009/03/09 kNN CF: A Temporal Social Network8/25 USER PROFILES OVER TIME (2/2)

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

2009/03/09 kNN CF: A Temporal Social Network10/25 USER PAIRS OVER TIME(1/6)  Predictions are often computed as a weighted average of deviation from neighbor means: user a, item i b is a ’ s neighbor :item i ’ s rating of neighbor b :neighbor b ’ s mean rating Similarity between the User a and its ’ neighbor b

2009/03/09 kNN CF: A Temporal Social Network11/25 USER PAIRS OVER TIME(2/6) - four highly cited methods of the similarity between users Total n items

2009/03/09 kNN CF: A Temporal Social Network12/25 USER PAIRS OVER TIME(3/6) -evolution of similarity

2009/03/09 kNN CF: A Temporal Social Network13/25 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.

2009/03/09 kNN CF: A Temporal Social Network14/25 COR wPCC Range:-1~+1 VS PCC Range:-1~+1 USER PAIRS OVER TIME(5/6) - sim(t) against sim(t+1) sim(t) sim(t + 1)

2009/03/09 kNN CF: A Temporal Social Network15/25 USER PAIRS OVER TIME(6/6) We classified those similarity methods according to their temporal behavior — 1. Incremental:COR and wPCC The differnce between (t) and (t+1) is small. Growing 2. Corrective: VS method Jumps from 0 to near-perfect then degrade 3. Near-random: PCC near-random behavior

kNN CF: A Temporal Social Network III. DYNAMIC NEIGHBOURHOODS

2009/03/09 kNN CF: A Temporal Social Network17/25 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

2009/03/09 kNN CF: A Temporal Social Network18/25 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 IV. NEAREST-NEIGHBOUR GRAPHS

2009/03/09 kNN CF: A Temporal Social Network20/25 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

2009/03/09 kNN CF: A Temporal Social Network21/25 NEAREST-NEIGHBOUR GRAPHS(2/5)

2009/03/09 kNN CF: A Temporal Social Network22/25 NEAREST-NEIGHBOUR GRAPHS(3/5) power law (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.

2009/03/09 kNN CF: A Temporal Social Network23/25 NEAREST-NEIGHBOUR GRAPHS(4/5) (2)Some users will have incredible high in-degree. We call this group “ power users ”

2009/03/09 kNN CF: A Temporal Social Network24/25 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.

2009/03/09 kNN CF: A Temporal Social Network25/25 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.