Open AccessProceedings Article
Collaborative filtering with graph information: consistency and scalable methods
Nikhil Rao,Hsiang-Fu Yu,Pradeep Ravikumar,Inderjit S. Dhillon +3 more
- Vol. 28, pp 2107-2115
TLDR
This work formulate and derive a highly efficient, conjugate gradient based alternating minimization scheme that solves optimizations with over 55 million observations up to 2 orders of magnitude faster than state-of-the-art (stochastic) gradient-descent based methods.Abstract:
Low rank matrix completion plays a fundamental role in collaborative filtering applications, the key idea being that the variables lie in a smaller subspace than the ambient space. Often, additional information about the variables is known, and it is reasonable to assume that incorporating this information will lead to better predictions. We tackle the problem of matrix completion when pairwise relationships among variables are known, via a graph. We formulate and derive a highly efficient, conjugate gradient based alternating minimization scheme that solves optimizations with over 55 million observations up to 2 orders of magnitude faster than state-of-the-art (stochastic) gradient-descent based methods. On the theoretical front, we show that such methods generalize weighted nuclear norm formulations, and derive statistical consistency guarantees. We validate our results on both real and synthetic datasets.read more
Citations
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Geometric Deep Learning: Going beyond Euclidean data
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LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation
TL;DR: This work proposes a new model named LightGCN, including only the most essential component in GCN -- neighborhood aggregation -- for collaborative filtering, and is much easier to implement and train, exhibiting substantial improvements over Neural Graph Collaborative Filtering (NGCF) under exactly the same experimental setting.
Proceedings ArticleDOI
LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation
TL;DR: LightGCN as mentioned in this paper learns user and item embedding by linearly propagating them on the user-item interaction graph, and uses the weighted sum of the embeddings learned at all layers as the final embedding.
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Graph Convolutional Matrix Completion
TL;DR: A graph auto-encoder framework based on differentiable message passing on the bipartite interaction graph that shows competitive performance on standard collaborative filtering benchmarks and outperforms recent state-of-the-art methods.
Journal ArticleDOI
CayleyNets: Graph Convolutional Neural Networks With Complex Rational Spectral Filters
TL;DR: A new spectral domain convolutional architecture for deep learning on graphs with a new class of parametric rational complex functions (Cayley polynomials) allowing to efficiently compute spectral filters on graphs that specialize on frequency bands of interest.
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Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering
Mikhail Belkin,Partha Niyogi +1 more
TL;DR: The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering.
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Graph Regularized Nonnegative Matrix Factorization for Data Representation
TL;DR: In GNMF, an affinity graph is constructed to encode the geometrical information and a matrix factorization is sought, which respects the graph structure, and the empirical study shows encouraging results of the proposed algorithm in comparison to the state-of-the-art algorithms on real-world problems.
Proceedings ArticleDOI
Recommender systems with social regularization
TL;DR: This paper proposes a matrix factorization framework with social regularization, which can be easily extended to incorporate other contextual information, like social tags, etc, and demonstrates that the approaches outperform other state-of-the-art methods.