Latent Geometry of Taste: Scalable Low-Rank Matrix Factorization for Recommender Systems
African Institute for Mathematical Sciences (AIMS) South Africa（非洲数学科学研究所（AIMS）南非）
Joshua Salako
备注：
Added a new figure on page 5, updated the title to include recommender systems, updated keywords, updated captions for all figures, and cited all figures in the text
Scalability and data sparsity remain critical bottlenecks for collaborative filtering on massive interaction datasets. This work investigates the latent geometry of user preferences using the MovieLens 32M dataset, implementing a high-performance, parallelized Alternating Least Squares (ALS) framework. Through extensive hyperparameter optimization, we demonstrate that constrained low-rank models significantly outperform higher dimensional counterparts in generalization, achieving an optimal balance between Root Mean Square Error (RMSE) and ranking precision. We visualize the learned embedding space to reveal the unsupervised emergence of semantic genre clusters, confirming that the model captures deep structural relationships solely from interaction data. Finally, we validate the system's practical utility in a cold-start scenario, introducing a tunable scoring parameter to manage the trade-off between popularity bias and personalized affinity effectively. The codebase for this research can be found here: https://github.com/joshsalako/recommender.git
Georgia Institute of Technology（佐治亚理工学院）；Health at Scale；INOVA；Sutter Health（萨特医疗）；Emory University（埃默里大学）
Phenotyping electronic health records (EHR) focuses on defining meaningful patient groups (e.g., heart failure group and diabetes group) and identifying the temporal evolution of patients in those groups. Tensor factorization has been an effective tool for phenotyping. Most of the existing works assume either a static patient representation with aggregate data or only model temporal data. However, real EHR data contain both temporal (e.g., longitudinal clinical visits) and static information (e.g., patient demographics), which are difficult to model simultaneously. In this paper, we propose Te…
School of Computer Science and Statistics, Trinity College（都柏林圣三一学院计算机科学与统计学院）
We propose a privacy-enhanced matrix factorization recommender that exploits the fact that users can often be grouped together by interest. This allows a form of "hiding in the crowd" privacy. We introduce a novel matrix factorization approach suited to making recommendations in a shared group (or nym) setting and the BLC algorithm for carrying out this matrix factorization in a privacy-enhanced manner. We demonstrate that the increased privacy does not come at the cost of reduced recommendation accuracy.
University College London（伦敦大学学院）；University of Waterloo（滑铁卢大学）
Many businesses are using recommender systems for marketing outreach. Recommendation algorithms can be either based on content or driven by collaborative filtering. We study different ways to incorporate content information directly into the matrix factorization approach of collaborative filtering. These content-boosted matrix factorization algorithms not only improve recommendation accuracy, but also provide useful insights about the contents, as well as make recommendations more easily interpretable.
IRIT, Université de Toulouse, CNRS（图卢兹大学 IRIT 研究所、法国国家科学研究中心）
We introduce negative binomial matrix factorization (NBMF), a matrix factorization technique specially designed for analyzing over-dispersed count data. It can be viewed as an extension of Poisson matrix factorization (PF) perturbed by a multiplicative term which models exposure. This term brings a degree of freedom for controlling the dispersion, making NBMF more robust to outliers. We show that NBMF allows to skip traditional pre-processing stages, such as binarization, which lead to loss of information. Two estimation approaches are presented: maximum likelihood and variational Bayes infere…
Regularization is a popular technique to solve the overfitting problem of machine learning algorithms. Most regularization technique relies on parameter selection of the regularization coefficient. Plug-in method and cross-validation approach are two most common parameter selection approaches for regression methods such as Ridge Regression, Lasso Regression and Kernel Regression. Matrix factorization based recommendation system also has heavy reliance on the regularization technique. Most people select a single scalar value to regularize the user feature vector and item feature vector independ…
China University of Petroleum（中国石油大学）；East China Jiaotong University（华东交通大学）；Federation University Australia（澳大利亚联邦大学）
Sparsity of user-to-item rating data becomes one of challenging issues in the recommender systems, which severely deteriorates the recommendation performance. Fortunately, context-aware recommender systems can alleviate the sparsity problem by making use of some auxiliary information, such as the information of both the users and items. In particular, the visual information of items, such as the movie poster, can be considered as the supplement for item description documents, which helps to obtain more item features. In this paper, we focus on movie recommender system and propose a probabilist…
University of Hyderabad（海得拉巴大学）；Central University of Rajasthan（拉贾斯坦中央大学）
With the abundance of data in recent years, interesting challenges are posed in the area of recommender systems. Producing high quality recommendations with scalability and performance is the need of the hour. Singular Value Decomposition(SVD) based recommendation algorithms have been leveraged to produce better results. In this paper, we extend the SVD technique further for scalability and performance in the context of 1) multi-threading 2) multiple computational units (with the use of Graphical Processing Units) and 3) distributed computation. We propose block based matrix factorization (BMF…
Beyond accuracy, quality measures are gaining importance in modern recommender systems, with reliability being one of the most important indicators in the context of collaborative filtering. This paper proposes Bernoulli Matrix Factorization (BeMF), which is a matrix factorization model, to provide both prediction values and reliability values. BeMF is a very innovative approach from several perspectives: a) it acts on model-based collaborative filtering rather than on memory-based filtering, b) it does not use external methods or extended architectures, such as existing solutions, to provide …
Decentralized Matrix Factorization with Heterogeneous Differential Privacy
Research Institute for Interdisciplinary Sciences（交叉科学研究院）；School of Information Management and Engineering（信息管理与工程学院）；Shanghai University of Finance and Economics（上海财经大学）
Real-world item recommenders commonly suffer from a persistent cold-start problem which is caused by dynamically changing users and items. In order to overcome the problem, several context-aware recommendation techniques have been recently proposed. In terms of both feasibility and performance, factorization machine (FM) is one of the most promising methods as generalization of the conventional matrix factorization techniques. However, since online algorithms are suitable for dynamic data, the static FMs are still inadequate. Thus, this paper proposes incremental FMs (iFMs), a general online f…
Does Weighting Improve Matrix Factorization for Recommender Systems?
University of Alberta Edmonton, AB Canada；Netflix, Inc. Los Gatos, CA USA；Netflix, Inc. \& Cornell University New York, NY USA；University of Alberta；Netflix, Inc.；Netflix, Inc. \& Cornell University
ContentWise（ContentWise公司）；Politecnico di Milano（米兰理工大学）
Proposed in 2014, Generative Adversarial Networks (GAN) initiated a fresh interest in generative modelling. They immediately achieved state-of-the-art in image synthesis, image-to-image translation, text-to-image generation, image inpainting and have been used in sciences ranging from medicine to high-energy particle physics. Despite their popularity and ability to learn arbitrary distributions, GAN have not been widely applied in recommender systems (RS). Moreover, only few of the techniques that have introduced GAN in RS have employed them directly as a collaborative filtering (CF) model. In…
Recommender systems are emerging technologies that nowadays can be found in many applications such as Amazon, Netflix, and so on. These systems help users to find relevant information, recommendations, and their preferred items. Slightly improvement of the accuracy of these recommenders can highly affect the quality of recommendations. Matrix Factorization is a popular method in Recommendation Systems showing promising results in accuracy and complexity. In this paper we propose an extension of matrix factorization which adds general neighborhood information on the recommendation model. Users …
Matrix Factorization is one of the most successful recommender system techniques over the past decade. However, the classic probabilistic theory framework for matrix factorization is modeled using normal distributions. To find better probabilistic models, algorithms such as RankMat, ZeroMat and DotMat have been invented in recent years. In this paper, we model the user rating behavior in recommender system as a Poisson process, and design an algorithm that relies on no input data to solve the recommendation problem and the cold start issue at the same time. We prove the superiority of our algo…
Recommender systems leverage user demographic information, such as age, gender, etc., to personalize recommendations and better place their targeted ads. Oftentimes, users do not volunteer this information due to privacy concerns, or due to a lack of initiative in filling out their online profiles. We illustrate a new threat in which a recommender learns private attributes of users who do not voluntarily disclose them. We design both passive and active attacks that solicit ratings for strategically selected items, and could thus be used by a recommender system to pursue this hidden agenda. Our…
Shandong University（山东大学）；University of Amsterdam（阿姆斯特丹大学）；Ahold Delhaize（皇家阿霍德德尔海兹集团）
Federated recommender systems have distinct advantages in terms of privacy protection over traditional recommender systems that are centralized at a data center. However, previous work on federated recommender systems does not fully consider the limitations of storage, RAM, energy and communication bandwidth in a mobile environment. The scales of the models proposed are too large to be easily run on mobile devices. And existing federated recommender systems need to fine-tune recommendation models on each device, making it hard to effectively exploit collaborative filtering information among us…
University of Cambridge（剑桥大学）；University of Science and Technology of China（中国科学技术大学）；Microsoft Research（微软研究院）
The success of recommender systems in modern online platforms is inseparable from the accurate capture of users' personal tastes. In everyday life, large amounts of user feedback data are created along with user-item online interactions in a variety of ways, such as browsing, purchasing, and sharing. These multiple types of user feedback provide us with tremendous opportunities to detect individuals' fine-grained preferences. Different from most existing recommender systems that rely on a single type of feedback, we advocate incorporating multiple types of user-item interactions for better rec…
Joint analysis of data from multiple information repositories facilitates uncovering the underlying structure in heterogeneous datasets. Single and coupled matrix-tensor factorization (CMTF) has been widely used in this context for imputation-based recommendation from ratings, social network, and other user-item data. When this side information is in the form of item-item correlation matrices or graphs, existing CMTF algorithms may fall short. Alleviating current limitations, we introduce a novel model coined coupled graph-tensor factorization (CGTF) that judiciously accounts for graph-related…
Despite the prominence of neural network approaches in the field of recommender systems, simple methods such as matrix factorization with quadratic loss are still used in industry for several reasons. These models can be trained with alternating least squares, which makes them easy to implement in a massively parallel manner, thus making it possible to utilize billions of events from real-world datasets. Large-scale recommender systems need to account for severe popularity skew in the distributions of users and items, so a lot of research is focused on implementing sparse, mixed dimension or s…
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 some classical algorithms such as the SVD and the regularized and unregularized non-negative matrix factorization approach. In particular a new algorithm is obtained changing adaptively the function to be minimized at each step, realizing a sort of dynamic prior strategy. Another algorithm is obtained modifying the function to be minimized in the NMF formulati…
China University of Petroleum（中国石油大学）；Minjiang University（闽江学院）；Dalian University of Technology（大连理工大学）；Federation University Australia（澳大利亚联邦大学）
The rapid growth of edge data generated by mobile devices and applications deployed at the edge of the network has exacerbated the problem of information overload. As an effective way to alleviate information overload, recommender system can improve the quality of various services by adding application data generated by users on edge devices, such as visual and textual information, on the basis of sparse rating data. The visual information in the movie trailer is a significant part of the movie recommender system. However, due to the complexity of visual information extraction, data sparsity c…
Shahid Beheshti University, G.C.（沙希德·贝赫什提大学）；Michigan State University（密歇根州立大学）；University of Minnesota（明尼苏达大学）
With the advent of online social networks, recommender systems have became crucial for the success of many online applications/services due to their significance role in tailoring these applications to user-specific needs or preferences. Despite their increasing popularity, in general recommender systems suffer from the data sparsity and the cold-start problems. To alleviate these issues, in recent years there has been an upsurge of interest in exploiting social information such as trust relations among users along with the rating data to improve the performance of recommender systems. The mai…
Microsoft（微软）；Xidian University（西安电子科技大学）；Emory University（埃默里大学）；Health Science Center of University of Texas（德克萨斯大学健康科学中心）；Emory School of Medicine（埃默里医学院）
Tensor factorization has received increasing interest due to its intrinsic ability to capture latent factors in multi-dimensional data with many applications such as recommender systems and Electronic Health Records (EHR) mining. PARAFAC2 and its variants have been proposed to address irregular tensors where one of the tensor modes is not aligned, e.g., different users in recommender systems or patients in EHRs may have different length of records. PARAFAC2 has been successfully applied on EHRs for extracting meaningful medical concepts (phenotypes). Despite recent advancements, current models…
National Chiao Tung Univ.（国立交通大学）；Inst. of Information Science, Academia Sinica, Taiwan（中央研究院资讯科学研究所）；The Pennsylvania State Univ.（宾夕法尼亚州立大学）
In contrast to traditional online videos, live multi-streaming supports real-time social interactions between multiple streamers and viewers, such as donations. However, donation and multi-streaming channel recommendations are challenging due to complicated streamer and viewer relations, asymmetric communications, and the tradeoff between personal interests and group interactions. In this paper, we introduce Multi-Stream Party (MSP) and formulate a new multi-streaming recommendation problem, called Donation and MSP Recommendation (DAMRec). We propose Multi-stream Party Recommender System (MARS…
Hong Kong University of Science and Technology（香港科技大学）；Southern University of Science and Technology（南方科技大学）；WeBank Co. Ltd（微众银行）
Matrix Factorization has been very successful in practical recommendation applications and e-commerce. Due to data shortage and stringent regulations, it can be hard to collect sufficient data to build performant recommender systems for a single company. Federated learning provides the possibility to bridge the data silos and build machine learning models without compromising privacy and security. Participants sharing common users or items collaboratively build a model over data from all the participants. There have been some works exploring the application of federated learning to recommender…
This work explores non-negative low-rank matrix factorization based on regularized Poisson models (PF or "Poisson factorization" for short) for recommender systems with implicit-feedback data. The properties of Poisson likelihood allow a shortcut for very fast computations over zero-valued inputs, and oftentimes results in very sparse factors for both users and items. Compared to HPF (a popular Bayesian formulation of the problem with hierarchical priors), the frequentist optimization-based approach presented here tends to produce better top-N recommendations with significantly shorter fitting…
University of Maryland, Baltimore County（马里兰大学巴尔的摩郡分校）；LANL（洛斯阿拉莫斯国家实验室）
Non-negative matrix factorization (NMF) with missing-value completion is a well-known effective Collaborative Filtering (CF) method used to provide personalized user recommendations. However, traditional CF relies on the privacy-invasive collection of users' explicit and implicit feedback to build a central recommender model. One-shot federated learning has recently emerged as a method to mitigate the privacy problem while addressing the traditional communication bottleneck of federated learning. In this paper, we present the first unsupervised one-shot federated CF implementation, named FedSP…
This paper addresses the large-scale acquisition of end-to-end network performance. We made two distinct contributions: ordinal rating of network performance and inference by matrix completion. The former reduces measurement costs and unifies various metrics which eases their processing in applications. The latter enables scalable and accurate inference with no requirement of structural information of the network nor geometric constraints. By combining both, the acquisition problem bears strong similarities to recommender systems. This paper investigates the applicability of various matrix fac…
Much like other learning-based models, recommender systems can be affected by biases in the training data. While typical evaluation metrics (e.g. hit rate) are not concerned with them, some categories of final users are heavily affected by these biases. In this work, we propose using multiple triplet losses terms to extract meaningful and robust representations of users and items. We empirically evaluate the soundness of such representations through several "bias-aware" evaluation metrics, as well as in terms of stability to changes in the training set and agreement of the predictions variance…
Matrix factorization techniques compute low-rank product approximations of high dimensional data matrices and as a result, are often employed in recommender systems and collaborative filtering applications. However, many algorithms for this task utilize an exact least-squares solver whose computation is time consuming and memory-expensive. In this paper we discuss and test a block Kaczmarz solver that replaces the least-squares subroutine in the common alternating scheme for matrix factorization. This variant trades a small increase in factorization error for significantly faster algorithmic p…
University of Notre Dame（圣母大学）；Microsoft Research（微软研究院）
Neural collaborative filtering (NCF) and recurrent recommender systems (RRN) have been successful in modeling user-item relational data. However, they are also limited in their assumption of static or sequential modeling of relational data as they do not account for evolving users' preference over time as well as changes in the underlying factors that drive the change in user-item relationship over time. We address these limitations by proposing a Neural Tensor Factorization (NTF) model for predictive tasks on dynamic relational data. The NTF model generalizes conventional tensor factorization…
This work explores the ability of collective matrix factorization models in recommender systems to make predictions about users and items for which there is side information available but no feedback or interactions data, and proposes a new formulation with a faster cold-start prediction formula that can be used in real-time systems. While these cold-start recommendations are not as good as warm-start ones, they were found to be of better quality than non-personalized recommendations, and predictions about new users were found to be more reliable than those about new items. The formulation pro…
Motivated by the needs of online large-scale recommender systems, we specialize the decoupled extended Kalman filter (DEKF) to factorization models, including factorization machines, matrix and tensor factorization, and illustrate the effectiveness of the approach through numerical experiments on synthetic and on real-world data. Online learning of model parameters through the DEKF makes factorization models more broadly useful by (i) allowing for more flexible observations through the entire exponential family, (ii) modeling parameter drift, and (iii) producing parameter uncertainty estimates…
Department of Mathematics, UC Santa Barbara（加州大学圣巴巴拉分校数学系）；Department of ECE, UC Santa Barbara（加州大学圣巴巴拉分校电气工程与计算机科学系）
Streaming tensor factorization is a powerful tool for processing high-volume and multi-way temporal data in Internet networks, recommender systems and image/video data analysis. Existing streaming tensor factorization algorithms rely on least-squares data fitting and they do not possess a mechanism for tensor rank determination. This leaves them susceptible to outliers and vulnerable to over-fitting. This paper presents a Bayesian robust streaming tensor factorization model to identify sparse outliers, automatically determine the underlying tensor rank and accurately fit low-rank structure. We…
IRIT, Université de Toulouse, CNRS（图卢兹大学 IRIT 研究所、法国国家科学研究中心）；ISAE-SUPAERO, Université de Toulouse（图卢兹大学 ISAE-SUPAERO 高等航空与航天学院）
We introduce a new non-negative matrix factorization (NMF) method for ordinal data, called OrdNMF. Ordinal data are categorical data which exhibit a natural ordering between the categories. In particular, they can be found in recommender systems, either with explicit data (such as ratings) or implicit data (such as quantized play counts). OrdNMF is a probabilistic latent factor model that generalizes Bernoulli-Poisson factorization (BePoF) and Poisson factorization (PF) applied to binarized data. Contrary to these methods, OrdNMF circumvents binarization and can exploit a more informative repr…
Rank minimization is of interest in machine learning applications such as recommender systems and robust principal component analysis. Minimizing the convex relaxation to the rank minimization problem, the nuclear norm, is an effective technique to solve the problem with strong performance guarantees. However, nonconvex relaxations have less estimation bias than the nuclear norm and can more accurately reduce the effect of noise on the measurements. We develop efficient algorithms based on iteratively reweighted nuclear norm schemes, while also utilizing the low rank factorization for semidefi…
Swiss Federal Institute of Technology (EPFL)（瑞士联邦理工学院（洛桑联邦理工学院））
This work formulates a novel song recommender system as a matrix completion problem that benefits from collaborative filtering through Non-negative Matrix Factorization (NMF) and content-based filtering via total variation (TV) on graphs. The graphs encode both playlist proximity information and song similarity, using a rich combination of audio, meta-data and social features. As we demonstrate, our hybrid recommendation system is very versatile and incorporates several well-known methods while outperforming them. Particularly, we show on real-world data that our model overcomes w.r.t. two eva…
Matrix Factorization for Inferring Associations and Missing Links
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）；Institute for Clarity in Documentation（文献清晰度研究所）；Inria Paris-Rocquencourt（法国国家信息与自动化研究所巴黎-罗康校区）；Rajiv Gandhi University（拉吉夫·甘地大学）；Tsinghua University（清华大学）；Palmer Research Laboratories（帕尔默研究实验室）
Universidade da Coruña（科鲁尼亚大学）；Universidad de Oviedo（奥维耶多大学）；CESGA（CESGA（无常见中文名，按原文））；NVIDIA Corporation（英伟达公司（NVIDIA Corporation））
Recommender systems (RS) are increasingly present in our daily lives, especially since the advent of Big Data, which allows for storing all kinds of information about users' preferences. Personalized RS are successfully applied in platforms such as Netflix, Amazon or YouTube. However, they are missing in gastronomic platforms such as TripAdvisor, where moreover we can find millions of images tagged with users' tastes. This paper explores the potential of using those images as sources of information for modeling users' tastes and proposes an image-based classification system to obtain personali…
