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Title: Rethinking Generalized Matrix Factorization for Recommendation: The Importance of Multi-hot Encoding

Paper content:
Learning good representations of users and items is crucially important to recommendation with implicit feedback.
Matrix factorization is the basic idea to derive the representations of users and items by decomposing the given interaction matrix.
However, existing matrix factorization based approaches share the limitation in that the interaction between user embedding and item embedding is only weakly enforced by fitting the given individual rating value, which may lose potentially useful information.
In this paper, we propose a novel Augmented Generalized Matrix Factorization (AGMF) approach that is able to incorporate the historical interaction information of users and items for learning effective representations of users and items.
Despite the simplicity of our proposed approach, extensive experiments on four public implicit feedback datasets demonstrate that our approach outperforms state-of-the-art counterparts.
Furthermore, the ablation study demonstrates that by using multi-hot encoding to enrich user embedding and item embedding for Generalized Matrix Factorization, better performance, faster convergence, and lower training loss can be achieved.
In the era of big data, we are seriously confronted with the problem of information overload.
Recommender systems play an important role in dealing with such issue, thereby having been widely deployed by social media, E-commerce platforms, and so on.
Among the techniques used in recommender systems, collaborative filtering (Sarwar et al., 2001; Hu et al., 2008; Su & Khoshgoftaar, 2009; Wang et al., 2019) is the dominant one that leverages user-item interaction data to predict user preference.
Among various collaborative filtering methods, Matrix Factorization (MF) is the most popular approach that has inspired a large number of variations (Koren, 2008; Rendle et al., 2009; Xue et al., 2017) .
MF aims to project users and items into a shared latent space, and each user or item could be represented by a vector composed by latent features.
In this way, the user-item interaction score could be recovered by the inner product of the two latent vectors.
Most of the existing extensions of MF normally focus on the modeling perspective (Wang et al., 2015; and the learning perspective (Xue et al., 2017; .
For example, BPR-MF (Rendle et al., 2009 ) learns user embedding and item embedding from implicit feedback by optimizing a Bayesian pairwise ranking objective function.
NeuMF learns compact embeddings by fusing the outputs from different models.
DeepMF (Xue et al., 2017) employs deep neural networks to learn nonlinear interactions of users and items.
Although these approaches have achieved great success, they still cannot resolve the inherent limitation of MF.
Specifically, apart from the interaction by inner product, there are no explicit relationships between user embedding and item embedding.
In other words, the connection between user embedding and item embedding is only weakly enforced by fitting the given individual rating value.
However, in real-world scenarios, user embedding and item embedding may be interpreted as some high-level descriptions or properties of user and item, which are supposed to have some explicit connections.
For example, a user likes some item, probably because the user and the item share some similar high-level descriptions or properties.
Which means, the latent features of a user could be potentially enriched by taking into account the latent features of the user's interacted items, since these interacted items could expose the latent features of the user to some degree.
Similarly, the latent features of an item may also be enriched by the latent features of the item's interacted users.
However, most of the existing approaches regrettably ignore such useful information.
An exception is the SVD++ model (Koren, 2008) , which provides each user embedding with additional latent features of items that the user has interacted with.
Despite the effectiveness of the SVD++ model, it suffers from two major problems.
First, it only enriches user embedding, and ignores the fact that item embedding could also be enriched by the latent features of users that the item has interacted with.
Second, the latent features of the interacted items are averagely integrated without discrimination, while each user normally has different preferences on different items.
Note that there are also other approaches that regularize or enrich user embedding and item embedding by exploiting supplementary information, such as social relations (Ma et al., 2011; Guo et al., 2017 ) and text reviews (Chen et al., 2018) .
However, in this paper, we do not assume there is any supplementary information, and only focus on the data with implicit feedback.
Motivated by the above observations, this paper proposes a novel Augmented Generalized Matrix Factorization (AGMF) approach for learning from implicit feedback.
Different from existing approaches, AGMF aims to enrich both user embedding and item embedding by applying multi-hot encoding with the attention mechanism on historical items and users.
In this way, user embedding and item embedding are explicitly related to each other, which could further improve the performance of the Generalized Matrix Factorization (GMF) model.
Extensive experimental results clearly demonstrate our contributions.
Learning good representations of users and items is crucially important to recommendation with implicit feedback.
In this paper, we propose a novel Augmented Generalized Matrix Factorization (AGMF) model for learning from implicit feedback data.
Extensive experimental results demonstrate that our proposed approach outperforms state-of-the-art counterparts.
Besides, our ablation study clearly demonstrates the importance of multi-hot encoding for Generalized Matrix Factorization.
As user-item interaction relationships are vitally important for learning effective user embedding and item embedding, hence in future work, we will investigate if there exist better user-item interaction relationships that can be exploited to improve the recommendation performance.

assistant: text: A simple extension of generalized matrix factorization can outperform state-of-the-art approaches for recommendation.