# UPGCN: User Perception-Guided Graph Convolutional Network for Multimodal Recommendation
## 3 Methods
### User Perception-Guided Representation Enhancement Module  
To effectively leverage the multimodal features of the item and mine user preferences across various modalities, we developed the user perception-guided representation enhancement module, which enriches user representations and enhances recommendation performance. First of all, given that the original modal features of items vary in dimensionality, a multilayer perceptron (MLP) is employed to map these different modal features into a unified, low-dimensional space:  
\[h_{m}=x_{m}W_{m}+b_{m} \tag{7}\]  
where \(W_{m}\in\mathbb{R}^{d_{m}\times d}\) and \(b_{m}\in\mathbb{R}^{d}\) represent the learnable transformation matrix and bias in the MLP, respectively. Here, \(d_{m}\) denotes the dimensionality of the item features in \(m\) modality, while \(d\) corresponds to the dimension of the embedding vector. After applyingthe dimensionality transformation, all modal features are in the same dimension as the embedding vector. After acquiring the modal features of the item following dimensionality transformation, we derive the user features of different modalities by aggregating the item modal features on the user-item interaction graph. Analogous to MMGCN [13], we employ the item modal features to conduct GCN on the interaction graph between users and items in order to capture the user features across different modalities. Similarly, upon acquiring the user modal features, these features can be employed as inputs to conduct GCN on the same interaction graph in order to derive the item features of different modalities. This approach effectively leverages user modality information and integrates it with item modality data, thereby facilitating the capture of user preferences across various modalities. Additionally, LightGCN [4] posits that the feature transformation and nonlinear transformation inherent in traditional GCN do not yield significant benefits for collaborative filtering tasks. Building on this premise, it streamlines the graph convolution operation for multimodal recommendation. In alignment with LightGCN [4], we eliminated the circular propagation of self-information, as well as the nonlinear transformation and feature transformation of neighboring nodes during the graph convolution operation. This approach aims to simplify the model while enhancing both inference speed and training efficiency. Consequently, the GCN operation can be defined as follows:  
\[h_{u,m}^{(l+1)}=\sum_{i\in\mathcal{N}_{u}}\frac{1}{\sqrt{|\mathcal{N}_{u}|} \sqrt{|\mathcal{N}_{i}|}}h_{i,m}^{(l)} \tag{8}\]  
Figure 1: Overview of the proposed UPGCN model. \[h_{i,m}^{(l+1)}=\sum_{u\in\mathcal{N}_{i}}\frac{1}{\sqrt{|\mathcal{N}_{u}|}\sqrt{| \mathcal{N}_{i}|}}h_{u,m}^{(l)} \tag{9}\]  
where \(\mathcal{N}_{u}\) and \(\mathcal{N}_{i}\) denote the neighborhoods of \(u\) and \(i\) within the interaction graph between users and items, respectively. \(h_{u,m}^{(l)}\in\mathbb{R}^{d}\) and \(h_{i,m}^{(l)}\in\mathbb{R}^{d}\), respectively, denote the representations of users and items derived from the modalities \(m\) in the preceding layer. It is crucial to emphasize that \(h_{i,m}^{(0)}=h_{m}\). Following the acquisition of user representations across various modalities, the subsequent task involves inputting these representations into the UPEM to extract users' preferences for different modalities of information and to incorporate this preference data into the embedding of user ID. Initially, based on the user representations for each modality, the attention weights corresponding to the user's preferences across different modalities are computed using the following formula:  
\[\gamma_{u}^{m}=softmax(q_{m}^{T}\text{tanh}(V_{m}H_{m}^{u}+b_{m})) \tag{10}\]  
where \(q_{m}\in\mathbb{R}^{d}\) is the attention vector, and \(V_{m}\in\mathbb{R}^{d\times d}\) and \(b_{m}\in\mathbb{R}^{d}\), respectively, represent the transformation matrix and bias vector; all of these are learnable parameters within a particular modality.