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Matrix factorization (MF) is a classical collaborative filtering algorithm for recommender systems. It decomposes the user-item interaction matrix into a product of low-dimensional user representation matrix and item representation matrix.…

Information Retrieval · Computer Science 2023-08-15 Shangde Gao , Ke Liu , Yichao Fu

The Nonnegative Matrix Factorization (NMF) of the rating matrix has shown to be an effective method to tackle the recommendation problem. In this paper we propose new methods based on the NMF of the rating matrix and we compare them with…

Machine Learning · Computer Science 2019-08-30 Gianna M. Del Corso , Francesco Romani

Multiresolution Matrix Factorization (MMF) was recently introduced as an alternative to the dominant low-rank paradigm in order to capture structure in matrices at multiple different scales. Using ideas from multiresolution analysis (MRA),…

Numerical Analysis · Mathematics 2019-10-14 Pramod Kaushik Mudrakarta , Shubhendu Trivedi , Risi Kondor

Large language model (LLM)-enhanced recommendation models inject LLM representations into backbone recommenders to exploit rich item text without inference-time LLM cost. However, we find that existing LLM-enhanced methods significantly…

Information Retrieval · Computer Science 2026-04-23 Zhangchi Zhu , Wei Zhang

Fine-tuning large-scale pre-trained models is prohibitively expensive in terms of computation and memory costs. Low-Rank Adaptation (LoRA), a popular Parameter-Efficient Fine-Tuning (PEFT) method, offers an efficient solution by optimizing…

Machine Learning · Computer Science 2025-05-27 Tao Li , Zhengbao He , Yujun Li , Yasheng Wang , Lifeng Shang , Xiaolin Huang

We propose a symmetric low-rank representation (SLRR) method for subspace clustering, which assumes that a data set is approximately drawn from the union of multiple subspaces. The proposed technique can reveal the membership of multiple…

Computer Vision and Pattern Recognition · Computer Science 2015-11-24 Jie Chen , Haixian Zhang , Hua Mao , Yongsheng Sang , Zhang Yi

With the rapid development of large language models (LLMs) and the growing demand for personalized content, recommendation systems have become critical in enhancing user experience and driving engagement. Collaborative filtering algorithms,…

Artificial Intelligence · Computer Science 2024-12-30 Haowei Yang , Longfei Yun , Jinghan Cao , Qingyi Lu , Yuming Tu

This paper investigates the computational and statistical limits in clustering matrix-valued observations. We propose a low-rank mixture model (LrMM), adapted from the classical Gaussian mixture model (GMM) to treat matrix-valued…

Statistics Theory · Mathematics 2023-06-08 Zhongyuan Lyu , Dong Xia

Low-rank adaptation (LoRA) and its variants have recently gained much interest due to their ability to avoid excessive inference costs. However, LoRA still encounters the following challenges: (1) Limitation of low-rank assumption; and (2)…

Computation and Language · Computer Science 2024-09-26 Qibin Wang , Xiaolin Hu , Weikai Xu , Wei Liu , Jian Luan , Bin Wang

Interest in unsupervised methods for joint analysis of heterogeneous data sources has risen in recent years. Low-rank latent factor models have proven to be an effective tool for data integration and have been extended to a large number of…

Methodology · Statistics 2024-05-20 Felix Held , Jacob Lindbäck , Rebecka Jörnsten

Social recommendation, which utilizes social relations to enhance recommender systems, has been gaining increasing attention recently with the rapid development of online social network. Existing social recommendation methods are based on…

Information Retrieval · Computer Science 2018-09-06 Tzu-Heng Lin , Chen Gao , Yong Li

Factorization machines (FM) are a popular model class to learn pairwise interactions by a low-rank approximation. Different from existing FM-based approaches which use a fixed rank for all features, this paper proposes a Rank-Aware FM…

Machine Learning · Computer Science 2019-05-21 Xiaoshuang Chen , Yin Zheng , Jiaxing Wang , Wenye Ma , Junzhou Huang

The application of large language models (LLMs) in recommendation systems has recently gained traction. Traditional recommendation systems often lack explainability and suffer from issues such as popularity bias. Previous research has also…

Information Retrieval · Computer Science 2025-12-04 Yaqi Wang , Haojia Sun , Shuting Zhang

Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and…

Machine Learning · Computer Science 2023-10-18 Rajarshi Saha , Varun Srivastava , Mert Pilanci

Large Language Models (LLMs) have transformed both everyday life and scientific research. However, adapting LLMs from general-purpose models to specialized tasks remains challenging, particularly in resource-constrained environments.…

Machine Learning · Computer Science 2025-09-12 Hao Zhang , Bo Huang , Zhenjia Li , Xi Xiao , Hui Yi Leong , Zumeng Zhang , Xinwei Long , Tianyang Wang , Hao Xu

With the incredibly growing amount of multimedia data shared on the social media platforms, recommender systems have become an important necessity to ease users' burden on the information overload. In such a scenario, extensive amount of…

Information Retrieval · Computer Science 2016-04-26 Xianming Liu , Min-Hsuan Tsai , Thomas Huang

Matrix completion and approximation are popular tools to capture a user's preferences for recommendation and to approximate missing data. Instead of using low-rank factorization we take a drastically different approach, based on the simple…

Machine Learning · Computer Science 2015-01-05 Alex Beutel , Amr Ahmed , Alexander J. Smola

The problem of approximating a matrix by a low-rank one has been extensively studied. This problem assumes, however, that the whole matrix has a low-rank structure. This assumption is often false for real-world matrices. We consider the…

Data Structures and Algorithms · Computer Science 2025-11-05 Martino Ciaperoni , Aristides Gionis , Heikki Mannila

Involving collaborative information in Large Language Models (LLMs) is a promising technique for adapting LLMs for recommendation. Existing methods achieve this by concatenating collaborative features with text tokens into a unified…

Information Retrieval · Computer Science 2024-10-28 Yuting Liu , Jinghao Zhang , Yizhou Dang , Yuliang Liang , Qiang Liu , Guibing Guo , Jianzhe Zhao , Xingwei Wang

Unsupervised integrative analysis of multiple data sources has become common place and scalable algorithms are necessary to accommodate ever increasing availability of data. Only few currently methods have estimation speed as their focus,…

Methodology · Statistics 2024-05-17 Felix Held