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Dictionary learning is a branch of signal processing and machine learning that aims at finding a frame (called dictionary) in which some training data admits a sparse representation. The sparser the representation, the better the…

Machine Learning · Computer Science 2015-02-27 Luc Le Magoarou , Rémi Gribonval

Machine learning techniques for Recommendation System (RS) and Classification has become a prime focus of research to tackle the problem of information overload. RS are software tools that aim at making informed decisions about the services…

Information Retrieval · Computer Science 2019-07-30 Vikas Kumar

Bayesian matrix factorization (BMF) is a powerful tool for producing low-rank representations of matrices and for predicting missing values and providing confidence intervals. Scaling up the posterior inference for massive-scale matrices is…

Machine Learning · Statistics 2019-02-28 Xiangju Qin , Paul Blomstedt , Eemeli Leppäaho , Pekka Parviainen , Samuel Kaski

Factorization of statistical language models is the task that we resolve the most discriminative model into factored models and determine a new model by combining them so as to provide better estimate. Most of previous works mainly focus on…

Computation and Language · Computer Science 2007-05-23 Wei Wang

Matrix factorization is a widely used approach for top-N recommendation and collaborative filtering. When implemented on implicit feedback data (such as clicks), a common heuristic is to upweight the observed interactions. This strategy has…

Information Retrieval · Computer Science 2025-10-14 Alex Ayoub , Samuel Robertson , Dawen Liang , Harald Steck , Nathan Kallus

Matrix factorization from a small number of observed entries has recently garnered much attention as the key ingredient of successful recommendation systems. One unresolved problem in this area is how to adapt current methods to handle…

Machine Learning · Computer Science 2012-08-07 John Z. Sun , Kush R. Varshney , Karthik Subbian

When factorizing binary matrices, we often have to make a choice between using expensive combinatorial methods that retain the discrete nature of the data and using continuous methods that can be more efficient but destroy the discrete…

Discrete Mathematics · Computer Science 2016-10-07 Stefan Neumann , Rainer Gemulla , Pauli Miettinen

Most data for evaluating and training recommender systems is subject to selection biases, either through self-selection by the users or through the actions of the recommendation system itself. In this paper, we provide a principled approach…

Machine Learning · Computer Science 2016-05-30 Tobias Schnabel , Adith Swaminathan , Ashudeep Singh , Navin Chandak , Thorsten Joachims

In this paper, the task-related fMRI problem is treated in its matrix factorization formulation, focused on the Dictionary Learning (DL) approach. The new method allows the incorporation of a priori knowledge associated both with the…

Machine Learning · Statistics 2019-08-20 Manuel Morante , Yannis Kopsinis , Sergios Theodoridis , Athanassios Protopapas

Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing…

Numerical Analysis · Computer Science 2016-05-09 Yuan Lu , Jie Yang

Given labeled data represented by a binary matrix, we consider the task to derive a Boolean matrix factorization which identifies commonalities and specifications among the classes. While existing works focus on rank-one factorizations…

Machine Learning · Computer Science 2019-06-25 Sibylle Hess , Katharina Morik

Predicting user affinity to items is an important problem in applications like content optimization, computational advertising, and many more. While bilinear random effect models (matrix factorization) provide state-of-the-art performance…

Machine Learning · Computer Science 2012-03-26 Rajiv Khanna , Liang Zhang , Deepak Agarwal , Beechung Chen

The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…

Numerical Analysis · Mathematics 2019-02-08 Per-Gunnar Martinsson

This paper is on improving the training of binary neural networks in which both activations and weights are binary. While prior methods for neural network binarization binarize each filter independently, we propose to instead parametrize…

Computer Vision and Pattern Recognition · Computer Science 2019-04-17 Adrian Bulat , Jean Kossaifi , Georgios Tzimiropoulos , Maja Pantic

Classical computing has borne witness to the development of machine learning. The integration of quantum technology into this mix will lead to unimaginable benefits and be regarded as a giant leap forward in mankind's ability to compute.…

Quantum Physics · Physics 2023-11-03 Hinako Asaoka , Kazue Kudo

Many modern tools in machine learning and signal processing, such as sparse dictionary learning, principal component analysis (PCA), non-negative matrix factorization (NMF), $K$-means clustering, etc., rely on the factorization of a matrix…

Machine Learning · Statistics 2015-04-10 Rémi Gribonval , Rodolphe Jenatton , Francis Bach , Martin Kleinsteuber , Matthias Seibert

Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience and signal processing. For signals such as natural images that admit such sparse…

Machine Learning · Statistics 2013-09-10 Julien Mairal , Francis Bach , Jean Ponce

Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…

Methodology · Statistics 2022-12-14 Lorenzo Schiavon , Bernardo Nipoti , Antonio Canale

We give a number of explicit matrix-algorithms for analysis/synthesis in multi-phase filtering; i.e., the operation on discrete-time signals which allow a separation into frequency-band components, one for each of the ranges of bands, say…

Functional Analysis · Mathematics 2014-12-10 Palle Jorgensen , Myung-Sin Song

Factorization Machines (FM), a general predictor that can efficiently model feature interactions in linear time, was primarily proposed for collaborative recommendation and have been broadly used for regression, classification and ranking…

Machine Learning · Computer Science 2021-08-18 Yu Geng , Liang Lan