# Research on Learning Resource Recommendation Based on Knowledge Graph and Collaborative Filtering
## 3 Combining Knowledge Graph and Collaborative Filtering Recommendation Algorithm
### Collaborative Filtering Similarity Calculation  
#### 3.2.1 Implicit Feedback Model  
This paper builds an implicit feedback model based on learning information from online courses. The learning information includes the user's video-watching progress and text-reading progress for each chapter. According to this feature, it assumes that user \(i\) has a preference value \(V_{ij}\) for the video content of chapter \(j\) and a preference value \(P_{ij}\) for the text content. In the implicit feedback, the overall preference value \(M_{ij}\) for this chapter is calculated using \(V_{ij}\) and \(P_{ij}\). The formula is defined as follows:  
In this paper, an implicit feedback model is constructed by utilizing learning information obtained from online courses. This learning information includes the user's progress in watching videos and reading text materials for each chapter. Given this context, it assumes that user \(i\) holds a preference value \(V_{ij}\) for the video content of chapter \(j\) and a preference value \(P_{ij}\) for the text content of chapter \(j\). Within the framework of implicit feedback, the combined preference value \(M_{ij}\) for this chapter is computed by considering both \(V_{ij}\) and \(P_{ij}\). The formula for this calculation is defined as follows:  
\[V_{ij}=\frac{N_{\triangledown}}{A_{\triangledown}} \tag{7}\]  
\[P_{ij}=\frac{N_{\triangledown}}{A_{\triangledown}} \tag{8}\]  
\[M_{ij}=V_{ij}*r_{\triangledown}+P_{ij}*r_{\triangledown} \tag{9}\]  
In the formula, \(N_{\triangledown}\) represents the total duration of videos that user \(i\) has watched in chapter \(j\), while \(N_{\triangledown}\) represents the total duration of text content that user \(i\) has studied in chapter \(j\). \(A_{\triangledown}\) signifies the total duration of videos available in chapter \(j\), and \(A_{\triangledown}\) denotes the total amount of text content within chapter \(j\). Furthermore, \(r_{\triangledown}\) represents the predetermined preference ratio for video content while \(r_{\triangledown}\) indicates the predetermined preference ratio for text content.  
In the information age, video and text formats constitute the primary multimedia learning resources. These multimedia formats integrate visual, auditory, and textual components to offer learners vivid, intuitive, and diverse learning experiences, which exert a profound influence on learning outcomes. To assess the significance of these two formats in learning resource recommendations, this paper formulates the following preference rules:  
1. Video Dominance  
In this configuration, the weight \(r_{v}\) for video resources is established as 1, while the weight \(r_{p}\) for text resources is designated as 0.5. This weight assignment is intended to underscore the significance and relatively higher priority attributed to video resources in learning resource recommendations.
2. Text Dominance  
In this configuration, the weight \(r_{p}\) for text resources is defined as 1, while the weight \(r_{v}\) for video resources is assigned a value of 0.5. This weight arrangement is intended to highlight the significance and relatively higher priority assigned to text resources in learning resource recommendations.