This document presents a recommender system based on a bipartite graph, focusing on clustering users and items using the modularity metric for the Recsys Challenge 2014. The study involves using the Louvain algorithm for clustering and estimating engagement based on interactions with tweets. Experimental results demonstrate the effectiveness of the proposed approach, with higher engagement estimates leading to improved recommendation strategies.

1. Recommender System Based on
Modularity
Maria A. A. Sibaldo1;2, Tiago B. A. de Carvalho1;2,
Tsang Ing Ren1, George D. C. Cavalcanti1
1Centro de Informática, UFPE, Recife, Brasil
2Unidade Acadêmica de Garanhuns, UFRPE, Garanhuns, Brasil
www.cin.ufpe.br/viisar
{maas2, tbac, tir, gdcc}@cin.ufpe.br
1. Introduction
This work presents a solution for the RecSys Challenge 2014 by performing a clustering
in a bipartite graph whose vertices are of two types: user and item, having the edges
as the engagement given to a tweet. The Modularity metric was used to form the
groups that contain users and movies.
2. The Proposed Approach
2.1 Bipartite Graph
The generated bipartite graph is modeled on an adjacency matrix composed by all
nodes of both classes: user and item, this results in a sparse graph shown in Figure 1.
0 0.5 1 1.5 2 2.5 3 3.5
x 104
0
0.5
1
1.5
2
2.5
3
3.5
x 104
non zeros = 15964
Figure 1: Adjacency matrix formed by users (1-22079) and items (22080-35697).
Figure 2 shows the power-law degree distribution of the one-mode item graph, then
our bipartite graph can be considered a scale-free network (Birmele [2009]).
0 1 2 3 4 5 6 7 8 9
6
4
2
0
One−mode User Graph
log(degree)
log(frequency)
0 1 2 3 4 5 6 7 8
6
4
2
0
One−mode Item Graph
log(degree)
log(frequency)
Figure 2: Degree distribution of the user and item one-mode graphs.
2.2 Louvain Algorithm and Modularity
The Louvain algorithm (Blondel et al. [2008]) is used for clustering the bipartite graph
(see Figure 3) based on the Modularity metric (Newman and Girvan [2004]):
Q =
1
2m
X
ij
Aij
kikj
2m
(ci; cj); (1)
where Aij represents the weight in the edge that links i and j,
P
ij Aij is the sum of
the weights of every edge in the graph, ki =
P
j Aij is the sum of the weigths that
has endpoint in i, ci is the community to which the vertex i is assigned. The function
(ci; cj) is 1 if ci = cj and 0 otherwise, and m = 1
2
P
ij Aij.
Figure 3: Clusters formed by the Louvain algorithm: G1 = U1; U2; I1; I2; I3 e G2 =
U3; U4; I4; I5.
2.3 Engagement estimation
Let k be the vertex that represents the item and gk is the group label to which the
item k belongs:
Vk is the set that contains every vertex that is in the same group as the k vertex:
Vk = fvjgv = gkg; (2)
Wk contains every weight bigger than zero of every edge linking a vertex that is
part of the same group of k, V is the set of all vertices in the graph:
Wk = fwabjwab 0; a 2 Vk; b 2 V g; (3)
^ wku is the estimated weight for the edge linking the item k to any user u:
^ wku =
1
jWkj
X
a2Vk;b2V
wab; (4)
wku 2 Wk, jWkj is the number of elements of Wk.
Motivated by the NDCG@10 evaluation (Loiacono et al. [2014]), we redefined the
recommendation to a rank function. Therefore, the number of engagement for each
tweet is calculated according to Equation 5:
engiu = ^ wiu + rateiu + 10 tweet_retweetediu; (5)
where engiu is the estimated engagement for a tweet, rateiu is the rating given by the
user u to the item i and tweet_retweetediu is a boolean value. The engiu value that are
bigger than user_followers_count, are set to this attribute value.
3. Experiments and Results
All zero Set all the engagements of the test dataset to 0.
Clusters For each tweet in the test dataset, we obtain the item k posted in the tweet
and obtain the average ^ wiu, that was set as the engagement value of that tweet.
Improved clusters Adding to ^ wiu the user rate value to that item and multiplying by
10 the attribute tweet_retweeted. If the estimated engagement is bigger than the
user_followers_count attribute, it is set to the value of the this attribute.
Table 1: NDCG@10 evaluation value for the strategies
Strategy Evaluation
All zero 0.7494269049198918
Clusters 0.7901253952498258
Improved clusters 0.8279531044818939
4. Conclusions
It is not necessary to transform the bipartite graph into one-mode graph;
Engagement estimation obtained using the Modularity metric;
This tecnique can be also used with the data in a time window.
References
Etienne Birmele. A scale-free graph model based on bipartite graphs. Discrete Ap-plied
Mathematics, 157(10):2267–2284, 2009.
Vincent D. Blondel, Jean-Loup Guillaume, Renaud Lambiotte, and Etienne Lefebvre.
Fast unfolding of community hierarchies in large networks. CoRR, abs/0803.0476,
2008.
Daniele Loiacono, Andreas Lommatzsch, and Roberto Turrin. Recsys challenge 2014:
Learning to rank. 2014.
M. E. J. Newman and M. Girvan. Finding and evaluating community structure in net-works.
Physical Review E, 69(2):026113, February 2004.
This work was partially supported by CIn/UFPE and Brazilian agencies: CNPq, CAPES and FACEPE.