Enhance micro-blogging recommendations of posts with an homophily-based graph
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1 Enhance micro-blogging recommendations of posts with an homophily-based graph Quentin Grossetti 1,2 Supervised by Cédric du Mouza 2, Camelia Constantin 1 and Nicolas Travers 2 1 LIP6 - Université Pierre Marie Curie - Paris, France 2 CEDRIC Laboratory - CNAM - Paris, France BDA - Novembre 2017 Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
2 Introduction Context Growth of microblogging plateforms since millions of messages/day in millions of messages/day in millions of publications/day in millions of pictures/day in 2017 Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
3 Introduction Real life examples Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
4 Introduction Real life examples Finding Users of Interest in Micro-blogging Systems (EDBT 2016) Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
5 Problem How to connect users to relevant messages? Recommendation of messages 700M new messages every day 300M of users Real time Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
6 Table of contents 1 State of the art 2 Data Analysis Topology Retweets Homophily 3 Approach Similarity graph Propagation Model 4 Experiments Protocol Results Updating strategies 5 Conclusion 6 Annexes Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
![State of the art State of the art Content-based [Lops (2011)] Method Pros Cons Content-based No need of interactions tweets](/docs-images/79/79230656/images/7-0.jpg "are hard to describe Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre 2017 6 /")
7 State of the art State of the art Content-based [Lops (2011)] Method Pros Cons Content-based No need of interactions tweets are hard to describe Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
![State of the art State of the art Collaborative filtering [Schafer (2007)] Method Pros Cons Content-based No need of interactions tweets are hard to describe](/docs-images/79/79230656/images/8-0.jpg "Collaborative filtering simple model and good results too large matrix Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre")
8 State of the art State of the art Collaborative filtering [Schafer (2007)] Method Pros Cons Content-based No need of interactions tweets are hard to describe Collaborative filtering simple model and good results too large matrix Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
9 State of the art State of the art Matrix Factorization [Koren (2009)] Method Pros Cons Content-based No need of interactions tweets are hard to describe Collaborative filtering simple model and good results too large matrix Matrix Factorization efficient to fight sparsity matrix growing too fast Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
![State of the art State of the art Hybrid systems [Bostandjiev (2010)] Method Pros Cons Content-based No need of interactions tweets are hard to describe Collaborative filtering simple model and good](/docs-images/79/79230656/images/10-0.jpg "results too large matrix Matrix Factorization efficient to fight sparsity matrix growing too fast Hybrid systems increase user engagement hard to describe relationship Enhance micro-blogging")
10 State of the art State of the art Hybrid systems [Bostandjiev (2010)] Method Pros Cons Content-based No need of interactions tweets are hard to describe Collaborative filtering simple model and good results too large matrix Matrix Factorization efficient to fight sparsity matrix growing too fast Hybrid systems increase user engagement hard to describe relationship Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
11 State of the art State of the art Random walks models [Sharma (2016)] Method Pros Cons Content-based No need of interactions tweets are hard to describe Collaborative filtering simple model and good results too large matrix Matrix Factorization efficient to fight sparsity matrix growing too fast Hybrid systems increase user engagement hard to describe relationship Random walks models very cheap low memory Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
12 State of the art State of the art Not only recommendations User recommendation (topology,content-based, demographic etc...) Hashtag (Bayesian model, euclidien...) Timeline Filtering (Deep Learning) Few papers on tweets recommendation except Twitter in 2016 Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
13 Data Analysis Data Analysis Dataset Updated connected component from the graph found in [Kwak (2009)]. No of nodes 2,182,867 No of edges 325,451,980 No of tweets 2,571,173,369 Avg. out-degree 57.8 Avg. in-degree 69.4 max out-degree 348,595 max in-degree 185,401 Diameter 15 Average shortest path 3.7 Table Twitter dataset characteristics Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
14 Data Analysis Topology Data Analysis Topology Number of paths Small world with average distance of Smallest path Figure Twitter smallest paths distribution Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
15 Data Analysis Retweets Data Analysis Retweets Number of tweets retweet - 7% 2-5 retweets - 1% ,2% Number of retweets Figure Distribution of the number of retweets per tweet Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
16 Data Analysis Retweets Data Analysis Lifespan Nb of messages < 1hour : 40% < 3days : 90% ,000 Lifespan (in hours) Figure Lifespan of a message Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
17 Data Analysis Homophily Data Analysis Homophily Distance No of users % Mean similarity ,65 0, ,86 0, ,13 0, ,14 0, ,03 0, ,0008 Impossible 216 0,18 0,0017 Table Evolution of the similarity score through distance in the network sim(u, v) = i L u L v 1 log(1+pop(i)) L u L v (1) Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
18 Data Analysis Homophily Table Link beetween distance in the network and position in the Top-N ranking Enhance micro-blogging Top-N recommendations of posts with an homophily-based graph BDA - Novembre / 31 Data Analysis Homophily 10 2 Average score Position in the ranking Distances distribution (%) Rank Average Distance ,55 57,03 31,53 10,64 0,8 2 1,68 49,60 33,13 16,87 0,4 3 1,8 42,45 36,02 20,72 0,8 4 1,86 38,71 38,71 20,56 2,02 5 1,98 31,44 40,16 27,59 0,81
19 Data Analysis Homophily Data Analysis Conclusions Many conclusions from this analysis : Freshness is crucial (Messages dies very fast) real-time recommendation Few users have high similarity use transitivity Distance 2 successfully gather important users rely on this homophily Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
20 Approach Similarity graph Similarity Graph Building process V Y Z2 U W X Z3 Z Z1 Z4 Figure Twitter Graph Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
21 Approach Similarity graph Graphe de similarité Exemple de construction V Y Z2 U W X Z3 Z Z1 Z4 Figure Twitter Graph Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
22 Approach Similarity graph Similarity Graph Building process V Y Z2 U W X Z3 Z Z1 Z4 Figure Twitter Graph Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
23 Approach Similarity graph Graphe de similarité Exemple de construction V Y Z2 U W X Z3 Z Z1 Z4 Figure Twitter Graph Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
24 Approach Similarity graph Similarity Graph Building process V sim(u, v) U sim(u, y) Y sim(u, z1) Z1 Figure Similarity Graph Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
25 Approach Similarity graph Similarity Graph Characteristics Twitter Network Similarity Graph No of nodes No of edges 325,451, Avg. similarity score Mean out-degree Table Similarity Graph Characteristics Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
26 Approach Similarity graph Propagation Model In a nutshell p(u, t) = v Fu p(u v, t) Fu (2) With Fu the set of users influential to u and p(u v, t) a probability estimation that u likes t determined by the behavior of the user v. p(u v, t) = p(v, t) sim(u, v) (3) Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
27 Approach Similarity graph Propagation Model Example V 0.1 Y U 0.5 W 0.5 X Figure Propagation example Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
28 Approach Propagation Model Propagation Model Example V 0.1 Y U 0.5 W 0.5 X t1 Figure Propagation example - a tweet t1 is published Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
29 Approach Propagation Model Propagation Model Example V 0.1 Y U 0.5 W 0.5 X t1 Figure Propagation example - X shares/likes t1 p(x, t1) = 1 Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
30 Approach Propagation Model Propagation Model Example V 0.1 Y U 0.5 W 0.5 X t1 Figure Propagation example - Propagation p(w, t1) = p(w v,t) v Fw Fw = = 0.25 Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
31 Approach Propagation Model Propagation Model Example V 0.1 Y U 0.5 W 0.5 X t1 Figure Propagation example - Propagation p(u, t1) = = Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
32 Approach Propagation Model diagonally dominant. Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31 Propagation Model Convergence Let n be users (u 1, u 2,..., u n ) : a 11 p u1 + a 12 p u a 1n p un = b 1 a 21 p u1 + a 22 p u a 2n p un = b 2... =... a n1 p u1 + a n2 p u a nn p un = b n Could also be written as Ap = b with A = u 1 u 2 u n u 1 a 11 a a 1n u 2 a 21 a a 2n p = u n a n1 a n2... a nn p(u 1 ) p(u 2 ). b = p(u n ) b 1 b 2 b n. Because u, v sim(u, v) 1, a jj a ij for every i, the matrix A is j i
33 Approach Propagation Model Propagation Model Optimizations Speed up the convergence Let (u, t1) = p(u, t) k+1 p(u, t) k If (u, t1) < β we stop the propagation Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
34 Approach Propagation Model Propagation Model Optimizations Speed up the convergence Let (u, t1) = p(u, t) k+1 p(u, t) k If (u, t1) < β we stop the propagation Limitation of popular messages If p(u, t) < f (t) no need to propagate. f (t) = 1 k p k p +pop(t) p Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
35 Experiments Protocol Experiments Protocol 130 Millions of messages shared at least twice Split the ranked set 90% - 10% Compute recommendation during this 10% for 1500 random users (500 small, 500 medium, 500 big) Comparison with CF : naive collaborative filtering Bayes : probabilistic model GraphJet : Twitter used solution Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
36 Experiments Results Experiments Hits Number of hits ( 10 4 ) Bayes CF GraphJet SimGraph Number of daily recommendations per user Linear growth of CF Fast growth for SimGraph GraphJet stuck around 5000 hits Figure Hits pour 1500 utilisateurs Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
37 Experiments Results Experiments Hits according to user profiles Number of hits Bayes CF GraphJet SimGraph Number of daily recommendations per user 6,000 5,000 4,000 3,000 2,000 1,000 Bayes CF GraphJet SimGraph Number of daily recommendations per user Bayes CF GraphJet SimGraph Number of daily recommendations per user Figure 500 small Figure 500 medium Figure 500 big users small < 50 ; medium < 1000 ; big > 1000 Tendencies are very stables no matter the profile of users Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
38 Experiments Results Experiments Hits accuracy Avg. number of shares Bayes CF GraphJet SimGraph Number of daily recommendations per user Figure Hits popularity Bayes targets close messages GraphJet targets popular messages CF and SimGraph are mixing both popular and close messages Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
39 Experiments Results Experiments F1 scores F1 Score ( 10 2 ) Bayes CF GraphJet SimGraph Small values Peak around 20 recommendations Number of daily recommendations per user Figure F1 Scores Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
40 Experiments Results Experiments Running time init. (per user) init total time time (per message) total time (70 cores //) total time 1,149,374 users 13,238,941 Tweets (Trial period) init + recos Bayes 10ms 0.04h 975ms 51.22h 51.26h CF 8,583ms 39.40h 0.5ms 0.02h 41.01h SimGraph 311ms 1.41h 38ms 2.00h 3.41h init. (per user) init total time time (per user) total time (70 cores //) total time 1,149,374 users 1,149,374 users * 66 days (Trial period) init + recos GraphJet 0ms 0h 14ms 4.2h 4.2h Table Initialization and recommendation time (in ms) Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
41 Experiments Updating strategies Experiments Updating strategies How to update SimGraph? Split the last 10% in 2 Evaluate hits prediction impact for the remaining 5% : do nothing recompute everything update only weights crossfold Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
42 Experiments Updating strategies Experiments Updating strategies 6,000 Number of hits 5,000 4,000 3,000 2,000 recompute everything do nothing 1,000 crossfold update weights Number of daily recommendations per user Figure Hits / updating strategies doing nothing is the same as updating weights crossfold (very cheap) works very well Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
43 Experiments Updating strategies Experiments Convergence property of the SimGraph Iteration Number of edges Table Number of edges evolution through iterations Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
44 Conclusion Conclusion Contribution Construction and analysis of a large Twitter dataset Method relying on homophily to find nearest neighbors at low cost Construction and optimization of a convergent propagation model Comparison of the recommendations made by our model with state of the art solutions Possibility for the model to be updated at low cost Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
45 Conclusion Conclusion Future works Densify points of comparison between users Burst recommendation bubbles Work on the crossfold convergence of the model Add a popularity prediction optimization Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
46 Conclusion Thanks for you attention! Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
47 Annexes ANNEXES Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
48 Annexes Annexes Lifespan and popularity 10 4 Avg. number of retweets Avg. lifepan (hours) Strong correlation up to 10 3 hours After a month, the correlation fades Figure Correlation between lifespan and popularity Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
49 Annexes Annexes Topology Number of paths Shortest distance Diameter of 21 for an average path of 7.5 Figure Smallest path distribution for the similarity graph Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
50 Annexes Annexes Similarities 10 2 Score moyen 0.5 Really weak scores Breaks after the fifth most similar user Position dans le classement Figure Score similarity evolution Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
51 Annexes Figure Parts of hits included in SimGraph Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31 Annexes Intersections Ratio of hits in common with SimGraph Bayes CF GraphJet SimGraph Number of daily recommendations per user
52 Annexes Annexes Number of recommendations Number of actual recommendations Bayes CF GraphJet SimGraph Number of daily recommendations per user Figure Recall capacity CF is less limited Other methods are bunched together Threshold effect for SimGraph and Bayes Enhance micro-blogging recommendations of posts with an homophily-based graph BDA - Novembre / 31
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