Spectral Collaborative Filtering (1808.10523v1)

Abstract: Despite the popularity of Collaborative Filtering (CF), CF-based methods are haunted by the \textit{cold-start} problem, which has a significantly negative impact on users' experiences with Recommender Systems (RS). In this paper, to overcome the aforementioned drawback, we first formulate the relationships between users and items as a bipartite graph. Then, we propose a new spectral convolution operation directly performing in the \textit{spectral domain}, where not only the proximity information of a graph but also the connectivity information hidden in the graph are revealed. With the proposed spectral convolution operation, we build a deep recommendation model called Spectral Collaborative Filtering (SpectralCF). Benefiting from the rich information of connectivity existing in the \textit{spectral domain}, SpectralCF is capable of discovering deep connections between users and items and therefore, alleviates the \textit{cold-start} problem for CF. To the best of our knowledge, SpectralCF is the first CF-based method directly learning from the \textit{spectral domains} of user-item bipartite graphs. We apply our method on several standard datasets. It is shown that SpectralCF significantly outperforms state-of-the-art models. Code and data are available at \url{https://github.com/lzheng21/SpectralCF}.

• The paper introduces SpectralCF, a novel method that uses spectral graph convolution to address cold-start challenges in collaborative filtering.
• It transforms user-item interactions via eigenvector decomposition of the graph Laplacian, employing polynomial approximations for efficient spectral filtering.
• Experimental results demonstrate over 20% improvement in recall and 40% in MAP compared to existing CF and graph-based approaches.

Spectral Collaborative Filtering

In the paper "Spectral Collaborative Filtering," the authors address the persistent cold-start problem in collaborative filtering (CF) based recommender systems (RS), proposing an innovative approach leveraging spectral graph theory to improve performance. Collaborative filtering techniques often grapple with effectively recommending items to users with sparse interaction histories, affecting the user experience negatively in RS applications.

The authors introduce Spectral Collaborative Filtering (SpectralCF), a novel method that formulates the user-item interactions as a bipartite graph and employs spectral convolution operations in the spectral domain. This approach aims to capture not just the proximity information but also the connectivity information inherently present in graph structures, which has proven difficult to model using traditional CF methods.

Key Methodologies

SpectralCF benefits from the connectivity details encapsulated in the spectral domain by directly learning from the user-item bipartite graph. Traditionally, CF-based models such as Matrix Factorization approximate direct connections, often neglecting indirect connectivity information. SpectralCF circumvents this limitation by revealing graph structure connectivity through a spectral perspective, employing eigenvectors of the graph laplacian matrix to transform observed graph signals into the spectral domain.

The proposed spectral convolution operation is approximated by a polynomial, allowing efficient dynamic filtering of contributions from various frequency domains. The polynomial approximation ensures scalability of the spectral convolution, overcoming the computational drawbacks of traditional methods. The authors further enhance the model's capacity by generalizing graph signals to multi-dimensional representations, thus introducing a deep RS model stacked by multiple spectral convolution layers.

Experimental Results

SpectralCF's utility is evidenced through robust experimental results across standard datasets like MovieLens-1M, HetRec, and Amazon Instant Video. SpectralCF significantly outperforms state-of-the-art models, including both CF-based and graph-based approaches.

• Performance Metrics: Compared to various competitive models such as BPR, eALS, and NCF, SpectralCF demonstrates superior performance quantified by Recall@M and MAP@M. SpectralCF displays an improvement of over 20% and 40% in average recall and MAP metrics, respectively.
• Cold-start Problem Alleviation: For users with sparse interaction histories, SpectralCF is particularly promising; it results in more accurate recommendations than established methods like BPR, improving recall and ranking efficacy substantially.

Future Directions

SpectralCF provides a compelling alternative by leveraging spectral graph theory to capture deep connectivity within user-item graphs, opening avenues for more sophisticated RS that exploit spectral properties. This method encourages the exploration of spectral domains for other RS challenges, potentially steering future research towards graph-based techniques that can be optimized further with side information or expanded to accommodate multiple graph modalities.

Overall, SpectralCF is an insightful contribution to the field of collaborative filtering, offering a new perspective and methodology for RS that could effectively tackle fundamental issues like the cold-start problem, marking progress in both practical implementations and theoretical understanding of graph analytics within recommender systems.