Semi-Disentangled Representation Learning in Recommendation System

Definition 1: internal block. It contains features about individual itself, which are extracted from content information.

Definition 2: external block. It expresses features based on interactions, i.e., user-item ratings, implicit feedback, etc.

Definition 3: other block. $other\ block$ denotes characteristics excluding those contained by the former blocks.

In this work, we utilize category information to supervise $internal\ block$. User-item ratings are employed as the supervision of $external\ block$. $other\ block$ generalizes some features belonged to individuals and interactions but beyond supervision (e.g., the color of a product or the director of a movie), as well as some random factors.

We identify the problem of semi-disentangled representation in recommendation system, to preserve complicated information while strengthening the representation explainability and generality with proper disentanglement. It requires to embed all features into three blocks using limited labels as supervision. It could be formally defined as follows.

Input: The normalized user-item ratings $R$ and item categories $C^{I}$ are taken as the input, in which $R_{i,j}=r$ denotes that the $i$-th user rates $j$-th item as $r$ points and $C^{I}_{p,q}=1$ means that the $p$-th item belongs to $q$-th category.

Output: Each user and item needs to be represented as a $k$-dimension vector consisting of three blocks, $internal\ block$, $external\ block$ and $other\ block$.

Objective: The goal is to (1) make representation $Z$ preserve more original information of users and items and (2) encourage $internal\ block$ and $external\ block$ to express more features related to categories and interactions respectively. The objective function is defined as follows.

where $U$ and $I$ represent initial embeddings of users and items, $Z$ denotes their representation in semi-disentangled space, $Z_{int}$ and $Z_{ext}$ are the corresponding $internal\ block$ and $external\ block$, and $C=C^{I}\cup C^{U}$ contains category labels of items and users. $P(A|B)$ means the possibility of generating $A$ given $B$.

We exploit autoencoders to transform representation in initial space into semi-disentangled space.

Autoencoder is an unsupervised deep neural network (hinton_autoencoders_1993, ; vincent_stacked_2010, ), which has been extensively applied for network representation learning (wu_collaborative_2016, ; tallapally_user_2018, ). It has two modules of encoder and decoder as follows,

Encoder denotes the mapping $f$ that transforms the input vector $x\in R^{d}$ into the latent representation $y\in R^{d^{\prime}}$, where $W\in R^{d^{\prime}\times d}$ is a weight matrix and $b\in R^{d^{\prime}}$ is an offset vector. The mapping $g$ is called the decoder, reconstructing $y$ in the latent space into $x^{\prime}$ in the initial space, in which $W^{\prime}\in R^{d\times d^{\prime}}$ and $b^{\prime}\in R^{d}$ denote the weight matrix and the offset vector respectively. $\sigma(.)$ is an activation function.

The objective of autoencoder is to minimize the reconstruction error. Stacked autoencoders (vincent_stacked_2010, ) is a widely used variant, which has been experimentally verified the improvement of representation quality. Therefore, we employ it to generate representations of users and items.

Different from typical autoencoders, we use three encoders $Encoder_{int}$, $Encoder_{ext}$ and $Encoder_{oth}$ to produce the corresponding $internal\ block$, $external\ block$ and $other\ block$, respectively. The generation process of users is as follows,

$Z^{U}_{int}$, $Z^{U}_{ext}$ and $Z^{U}_{oth}$ represent the above three blocks respectively, $Z^{U}$ denotes the embeddings of users $U$ in semi-disentangled space, and $\hat{U}$ is the generated representations of users in the initial space. The representation of items also utilizes a similar process. The goal of the process is to reconstruct the representation of users and items in the initial space as well as user-item ratings with autoencoders. Considering that the number of unobserved interactions (i.e., there is no rating) far exceeds that of the observed, we employ Binary Cross Entropy (BCE) as the basic metric. We define the loss function of reconstruction as follows,

where $\hat{U}$, $\hat{I}$ denote the reconstructed users and items, $\hat{R}$ represent predicted ratings by matching $Z^{U}$ and $Z^{I}$. Details of BCE are as follow, where $y$ denote labels, $\hat{y}$ represent the predicted values and $N$ is the number of $y$,

Disentangled representation with weakly supervision has demonstrated its effectiveness in computer vision (locatello_disentangling_2020, ; chen_weakly_2020, ). The successful application and the complexity of interactions inspires us to improve the representation disentanglement using limited labels in recommendation system.

We aim at improving the expression ability and proper disentanglement of representation at the same time, so we combine the loss function of node representation and semi-disentanglement as follows,

We perform experiments on three real-world datasets: MovieLens-latest-small (ml-ls), MovieLens-10m (ml-10m) (harper_movielens_2016, ) and Amazon-Book (mcauley_image-based_2015, ; he_ups_2016, ), whose statistics are shown in Table 1. We filter out users and items with less than 20 ratings and employ 80% ratings as the training data and the others as test data. We compare our method with four baselines, NetMF (qiu_network_2018, ; rozemberczki_karate_2020, ), ProNE (zhang_prone_2019, ), VAECF (liang_variational_2018, ) and MacridVAE (ma_learning_2019, ), based on four metrics, $recall$, $precision$, $F1$ and $ndcg$ (shani_evaluating_2011, ).

We verify the effectiveness of SDRL in two common downstream tasks in recommendation system, Top-K recommendation and item classification. We run the experiments 20 times and report the average values and the standard deviation. We highlight the best values of baselines in bold and calculate the corresponding improvements.

Top-K Recommendation. We generate Top-5, 10 and 15 items according to predicted ratings as recommendations. The comparison results on three datasets are shown in Tables 2, 3 and 4, respectively. Based on the observations of comparison results, we find that our method SDRL achieves steady improvements compared with baselines. It at least improves F1 (ndcg) by 20.41% on MovieLens-latest-small, 35.24% on MovieLens-10m and 0.29% on Amazon-Book. It demonstrates that the proposed representation method SDRL significantly improves the Top-K recommendation performance especially on MovieLens datasets ml-ls and ml-10m. The possible reason is that more dense interactions (as shown in Table 1) reflect richer features and it could promote (semi-)disentangled representation more accurate overall.

Item Classification. Item classification also plays an important role in recommendation system such as cold-start task (zhao_categorical-attributes-based_2018, ). Since VAECF and MacridVAE do not generate item representations, we only utilize NetMF and ProNE as baselines and item categories as labels in item classification. We employ item embedding as the input and a MLPClassifier ²²2https://scikit-learn.org/ as the classification algorithm for all methods. The comparison results are shown in Tables 5, 6 and 7, respectively. We observe that our method SDRL outperforms baselines on three datasets with the help of category supervision.

To study the impacts of various blocks in SDRL, we develop the ablation study based on the same setting as comparison experiment. Not only highlighting the best values in bold, we also underline the second and third best values in the results.

Top-K Recommendation. Based on the observations of comparison results in Tables 8, 9 and 10, we have three major findings. (1) Overall, SDRL consisting of three blocks and SDRL’(int+ext) achieve a relatively better performance. We infer that both category- and rating-based features play an important role in Top-K recommendation. (2) Another find is that variants with separated blocks usually outperforms that with the only one block i.e., SDRL’(whole). It demonstrates that semi-disentanglement significantly improves the performance in Top-K recommendation.

(3) We also find a difference between the results on MovieLens datasets (i.e., ml-ls and ml-10m) and Amazon-Book. On MovieLens datasets, SDRL’(int+oth) outperforms SDRL’(ext+oth), while on Amazon-Book SDRL’(ext+oth) shows a better performance. That’s to say, the $internal\ block$ has a bigger impact on MovieLens datasets and the $external\ block$ takes more effects on Amazon-Book. We conduct further analysis and find that the difference may have a close relation with the statistical characteristics of datasets. As is shown in Fig. 3, on MovieLens datasets, over 80% users relate with at least 14 categories (77.78%); and on Amazon-Book, over 80% users only relate with at least 12 categories (54.55%). The statistical characteristics of datasets could affect the role of different features in downstream tasks, and (semi-)disentanglement increases the flexibility to emphasize certain features.

We also conduct a deeper analysis in terms of model optimization, to explore what causes the difference. As introduced in Section 3, we employ $loss_{int}$ (in Equation 12) to encourage the $internal\ block$ to express relatively more category-based features. Meanwhile, the $external\ block$ (in Equation 13) is expected to contain more interactive features with the optimization of $loss_{ext}$. In addition, $loss_{recon}$ (in Equation 9) optimizes the whole reconstruction of users, items and ratings, which would make the $internal\ block$ also contain some interactive features.

We draw the trends of each parts of loss functions for three methods (i.e., SDRL, SDRL’(int+oth) and SDRL’(ext+oth)) respectively in Fig. 4. We observe that there is a similar trend among $loss_{recon}$, $loss_{int}$ and $loss_{ext}$ on MovieLens datasets in Fig.s 4(a), 4(d) and 4(g) (or in Fig.s 4(b), 4(e) and 4(h)). That is, the training process fairly optimizes the $internal\ block$, $external\ block$ and the whole reconstruction. However, on Amazon-Book in Fig.s 4(c), 4(f) and 4(i), $loss_{int}$ obviously decreases faster than the other two losses.

It demonstrates that in the model training on Amazon-Book, the optimization for $internal\ block$ plays a more important role. The bias on Amazon-Book pushes the embeddings to contain more category-based features and relatively fewer rating-based features. The effect appears especially significant in SDRL’(int+oth), in which $loss_{ext}$ is removed from loss function. However, in Top-K recommendation, interactive features based on ratings may play a major part. It probably explain why SDRL’(int+oth) performs poorer than SDRL’(ext+oth) on Amazon-Book. Similarly, on MovieLens datasets, SDRL’(ext+oth) generates representations without the supervision of category-based information. Meanwhile, for SDRL’(int+oth), the fair optimization would encourage embeddings contain both category information and interactive features. Therefore, SDRL’(int+oth) outperforms SDRL’(ext+oth) on MovieLens datasets.

Last but not least, the difference also validates the importance of employing multiple features as supervision for different blocks in the representation learning, i.e., supervised (semi-)disentangled representation.

It is flexible to adjust the proportion of $internal\ block$, $external\ block$ and $other\ block$ in the embeddings. We set the proportion as 2:1:1, 1:2:1 and 1:1:2 to test their performance on Top-15 recommendation. The results in Fig. 5 show the variant with proportion 2:1:1 (i.e., a bigger proportion for $internal\ block$) outperforms the others on MovieLens datasets. On Amazon-Book, the variant with a bigger proportion for $external\ block$ performs better. Therefore, we set the proportion in SDRL as 2:1:1 on the Movielens datasets and 1:2:1 on Amazon-Book.

In SDRL, $internal\ block$ and $external\ block$ are expected to respectively express features from individual itself and user-item interactions. We visualize node representation to qualitatively analyze the semi-disentanglement of two parts.

In summary, we have the following findings in the experiments. (1) Overall, SDRL gains stable and general improvements, demonstrating its effectiveness in representation learning. (2) In consistent with expectation, $internal\ block$ and $external\ block$ respectively express more category-based and interactive features. (3) Semi-disentanglement enhances the explainability and generality in terms of representation in recommendation system.

Representation learning transforms the sparse data in recommendation system into structured embeddings, providing great convenience for complex network process (cui_survey_2019, ). Based on the type of source data, existing representation methods could be divided into three categories: structure-based (perozzi_deepwalk_2014, ; grover_node2vec_2016, ), content-based (zhang_prone_2019, ; zhao_deep_2020, ) and both-based (wang_reinforced_2020, ; he_lightgcn_2020, ; fu_magnn_2020, ). Among them, both-based approaches receive lots of attentions in recent years, e.g., graph neural network (GNN). It initializes representation with content features and then update it with structure information.

Our method SDRL also employs content and structure features as the input. The major difference between SDRL and GNN-based approaches is that SDRL embeds content- and structure-based information into different blocks (i.e., $internal\ block$ and $external\ block$ respectively) while they represent it as a whole.

Disentangled representation learning aims to separate embedding into distinct and explainable factors in an unsupervised way (bengio_representation_2013, ; do_theory_2020, ). It has been successfully applied into computer vision (nemeth_adversarial_2020, ). Recently, Locatello et al. (locatello_challenging_2019, ; locatello_commentary_2020, ) demonstrate that unsupervised disentangled representation learning without inductive biases is theoretically impossible. To deal with this problem, some works with (semi-)supervision are proposed (locatello_disentangling_2020, ; chen_weakly_2020, ). However, the assumption of factor independence makes typical disentangled representation not applicable for recommendation.

Our method differs from existing disentangled representation works in that we do not separate the whole embedding (i.e., we preserve $other\ block$ for no specific meanings) and we do not explicitly force the independence of different factors. In this way, we could preserve more complicated relations in recommendation system, while achieving proper disentanglement.