=Paper=
{{Paper
|id=Vol-1441/recsys2015_poster14
|storemode=property
|title=Network-Based Extension of Multi-Relational Factorization Models
|pdfUrl=https://ceur-ws.org/Vol-1441/recsys2015_poster14.pdf
|volume=Vol-1441
|dblpUrl=https://dblp.org/rec/conf/recsys/VahedianBM15
}}
==Network-Based Extension of Multi-Relational Factorization Models==
https://ceur-ws.org/Vol-1441/recsys2015_poster14.pdf
Network-Based Extension of
Multi-Relational Factorization Models
Fatemeh Vahedian, Robin Burke & Bamshad Mobasher
Center for Web Intelligence, Depaul University, Chicago, IL 60604
{fvahedia, rburke, mobasher}@cs.depaul.edu
ABSTRACT
Complex heterogeneous networks contain many types of re-
lations, both local to a particular entity and distant in the
network. Multi-relational factorization schemes that incor-
porate multiple local relations have shown improved recom-
mendation accuracy. This paper extends this prior work on
multi-relational factorization to include extended relations
derived from network data and demonstrates improved ac-
curacy for these extended hybrids.
1. INTRODUCTION
Multi-relational factorization models have emerged as a state-
of-the-art approach to recommendation in areas such as so-
cial networks, where both items and users are character- Figure 1: Heterogeneous network example
ized by relations of multiple types [4, 3]. In such formula-
tions, there is a main “target” relation for which predictions
will be generated and multiple “auxiliary” relations that con- composition of relations created by the edges that exist be-
tribute information. For example, in a movie recommenda- tween two object types. Since there may be multiple edges
tion setting, the relation “user-movie” is the target relation that correspond to a given edge type, traversing a meta-
and other relations, such as “movie-genre”, would be consid- path yields not a single node, but rather a set of destination
ered auxiliary. In this paper, we extend the multi-relational nodes. For example, consider in the Movie schema, a meta-
approach in [3] to include multi-step relations. path consisting of just the movie-genre edge. If we start
Figure 1 shows an example of a network containing movie with “Whiplash” from Figure 1 and follow this meta-path, we
preference data. We can view each relation as a typed edge would arrive at a set of destination nodes: {“Drama”, “Mu-
in such a heterogeneous network. For example, there is a sic”}. In our examples, we will typically denote an edge type
“genre” edge connecting each movie with the genre by which with the initials of the beginning and ending node types.
it is labeled, and we can create a movie-genre relation by col- Prior work has demonstrated that meta-paths of various
lecting all such edges. More distant relations can be created lengths could contribute to a multi-component weighted hy-
by considering multi-step typed paths, called meta-paths [7]. brid in a variety of network settings [1, 2, 6, 5]. In this work
For example, the user-actor relation, which does not appear we use meta-paths to build multiple relations for a multi-
directly in the data, can be composed by following all user- relational factorized model.
movie/movie-actor meta-paths.
2. HETEROGENEOUS NETWORKS 3. MULTI-RELATIONAL FACTORIZATION
Multi-relational factorization models have improved predic-
A heterogeneous network is a directed graph in which both
tion performance and are currently considered a state-of-
nodes and edges have types. Two edges of the same type, by
the-art models in recommender systems and relational pre-
definition, share the same object types at their originating
diction research [3]. To date, this work has used direct re-
and end points. A meta-path is a sequence of edge types, a
lations, such as user-movie or movie-actor in our example.
Our contribution here is to extend this work with relations
generated using extended meta-paths.
In multi-relational matrix factorization models, one tar-
get relation is predicted and the remaining auxiliary rela-
tions are used as side information. For example, if the task
is to recommend movies to users, the user-movie relation is
the target relation and the other links between nodes such
Copyright is held by the author(s). RecSys 2015 Poster Proceedings,
September 16-20, 2015, Austria, Vienna. as movie-genre and movie-actor are auxiliary. In the multi-
Copyright 2015 ACM X-XXXXX-XX-X/XX/XX ...$15.00. relational matrix factorization model DMF described in [3],
different latent feature models are defined for each relation. The user rating data was randomly partitioned into 80%
Parameters are learned from the factorization process in training and 20% test data. Relations were generated from
such a way that they are optimized for the best performance the training data and factorized. Figure 3 shows the results
on each relation, associating one latent feature vector model for recall and precision on recommendation lists of length
with each relation. 1-10 for the five algorithm variants shown in Figure 2.
The CATSMF model is proposed in [3] to improve the ef- The key finding is that the versions of the DMF algorithm
ficiency of the DMF model when applied to multiple predic- that incorporate longer meta-paths demonstrate improve-
tion targets. Since the DMF model must learn parameters ments in both precision and recall. The best performing
for each relation individually, the number of parameters to variant is DMF3, which does not include the two-step rela-
be learned grows by a factor of number of relations in the tions UMA, UMD, UMG. This finding makes sense in that
network. In order to deal with this problem, CATSMF limits the movie-actor, movie-director, and movie-genre relations
the parameters needed for the auxiliary relations by coupling are already incorporated in the DMF model.
them together. It also enables the learning of interactions Unlike the results in [3] using different data, we did not
between the different auxiliary relations. find that CATSMF with its coupled approach offered bet-
ter results than DMF algorithm. Part of the reason may be
the increased level of personalization required by this rec-
4. EXPERIMENTS AND RESULTS ommendation task, as opposed to the relational completion
We build on the DMF and CATSMF models by incorpo- tasks used in the CATSMF work. We are still exploring the
rating additional relations built from extended meta-paths. reasons for these differences in performance.
For this paper, we used a 33% subset of the MovieLens 1M
dataset 1 . There are four relations directly available in this 5. CONCLUSION
data, as indicated in our prior examples: user-movie, movie-
We have shown that recommendation using multi-relational
actor, movie-director, and movie-genre. In addition to these
matrix factorization in networked data can be enhanced
four direct relations, we generated six meta-path relations
through in the inclusion of relations derived from meta-path
starting from the user. Figure 2 shows the meta-paths gen-
expansions. Although the results here are only for a single
erated and the different experimental conditions. We ran
data set, we have found benefits of such extended paths in
the DMF and CATSMF algorithms using only the direct re-
other data sets in our work with linear weighted hybrids and
lations, and then built augmented versions of each using ad-
are exploring the application of multi-relational factorization
ditional relations derived from the meta-paths shown. The
in these areas as well.
models were optimized using BPR as the optimization cri-
Previous work [2] has shown that the utility of relations
terion (BPR-opt), as described in [3].
based on extended meta-paths is not necessarily a decreas-
ing function of path length – a finding confirmed here. Since
the set of meta-path relations is by its nature unbounded, it
is essential to find some means for limiting the set of com-
ponents considered. We are exploring heuristics to enable
the selection of the most useful relations.
Acknowledgments
This work was supported in part by the National Science
Figure 2: Relations in each recommendation model Foundation under Grant No. IIS-1423368 (Multi-dimensional
Recommendation in Complex Heterogeneous Networks).
6. REFERENCES
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