隨著數位平台中產品與資訊量快速增加，推薦系統已成為提升使用者體驗與協助使用者找到感興趣內容的重要技術。傳統協同過濾方法，特別是矩陣分解，能透過低維度潛在因子表示使用者與項目，並預測使用者偏好。然而，矩陣分解主要依賴線性交互假設，難以完整捕捉真實情境中複雜的非線性使用者—項目關係，也較難處理隱式回饋、動態偏好與時間脈絡等問題。

為改善上述限制，神經協同過濾（Neural Collaborative Filtering, NCF）利用多層感知機取代傳統內積運算，使模型能學習更彈性的非線性交互關係。然而，標準 NCF 仍主要建立於靜態的使用者—項目二維空間，未能充分考慮時間因素對使用者偏好的影響。特別是在電影推薦情境中，使用者對電影的興趣可能會受到電影上映時間與實際觀看時間之間差距的影響。

因此，本研究提出三維神經協同過濾（Three-Dimensional Neural Collaborative Filtering, 3D-NCF）框架，將觀看延遲作為第三個獨立維度納入模型。透過將觀看延遲離散化為不同等級，並為其學習嵌入向量，模型能同時捕捉使用者、電影與時間脈絡之間的非線性交互作用。此方法有助於提升推薦模型對時間偏好差異的表示能力，並提供更具個人化的電影推薦結果。

With the rapid growth of products and information on digital platforms, recommender systems have become an important technology for improving user experience and helping users find content that may interest them. Traditional collaborative filtering methods, especially Matrix Factorization (MF), represent users and items through low-dimensional latent factors and use them to predict user preferences. However, MF mainly depends on the assumption of linear interaction, so it is difficult to fully capture the complex nonlinear relationships between users and items in real situations. It also has limited ability to deal with implicit feedback, dynamic preferences, and temporal context.

To improve these limitations, Neural Collaborative Filtering (NCF) replaces the traditional inner product operation with a Multi-Layer Perceptron (MLP), allowing the model to learn more flexible nonlinear interactions. However, standard NCF is still mainly built on a static two-dimensional user--item space and does not fully consider the influence of time on user preferences. In movie recommendation, a user's interest in a movie may be affected by the time difference between the movie's release and the actual viewing time.

Therefore, this study proposes a Three-Dimensional Neural Collaborative Filtering (3D-NCF) framework, which introduces watch delay as an independent third dimension in the model. By dividing watch delay into different levels and learning a separate embedding vector for each level, the model can capture the nonlinear interactions among users, movies, and temporal context at the same time. This method improves the model's ability to represent different temporal preferences and provides more personalized movie recommendations.

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