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binary matrix factorization via Dictionary Learning

IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING 2018年第6期12卷 1253-1262页

作者： Ramirez, Ignacio Univ Republica Dept Signal Proc Inst Elect Engn Fac Engn Montevideo 11200 Uruguay

matrix factorization is a key tool in data analysis;its applications include recommender systems, correlation analysis, signal processing, among others. binary matrices are a particular case, which has received significant attention for over 30 years, especially within the field of data mining. Dictionary learning refers to a family of methods for learning overcomplete basis (also called frames) in order to efficiently encode samples of a given type;this area, now also about 20 years old, was mostly developed within the signal processing field. In this work, we propose two binary matrix factorization methods based on a binary adaptation of the dictionary learning paradigm to binary matrices. The proposed algorithms focus on speed and scalability;they work with binary factors combined with bit-wise operations and a few auxiliary integer ones. Furthermore, the methods are readily applicable to online binary matrix factorization. Another important issue in matrix factorization is the choice of rank for the factors;we address this model selection problem with an efficient method based on the minimum description length principle. Our preliminary results show that the proposed methods are effective at producing interpretable factorizations of various data types of different nature.

关键词： binary matrix factorization binary dictionary learning data mining

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binary matrix factorization applied to Netflix dataset analysis 5th

Binary Matrix Factorization applied to Netflix dataset analy...

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5th IFAC Symposium on Telematics Applications (TA)

作者： Diop, Mamadou Miron, Sebastian Larue, Anthony Brie, David Univ Lorraine CRAN UMR 7039 F-54506 Vandoeuvre Les Nancy France CEA LIST F-91191 Gif Sur Yvette France

In this paper we aim at assessing the potential of binary matrix factorization (BMF) in the implementation of recommendation systems, by analyzing a Netflix dataset. In particular, we study the explanatory power and the prediction capability of a particular BMF algorithm based on a post non-linear mixture model, namely the Post NonLinear Penalty Function (PNL-PF) algorithm. Unlike the majority of BMF methods, PNL-PF is capable of efficiently handling the difficult case of correlated rank-1 binary terms. We show that BMF represents an interesting alternative to classical matrix factorization methods in terms of explanatory power and prediction capability. Copyright (C) 2019. The Authors. Published by Elsevier Ltd. All rights reserved.

关键词： binary matrix factorization Recommendation system

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binary matrix factorization Discretization 22nd

Binary Matrix Factorization Discretization

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22nd International Conference on Artificial Intelligence and Soft Computing (ICAISC)

作者： Spyrides, Georges Poggi, Marcus Lopes, Helio Potificia Univ Catolica Rio de Janeiro Rio De Janeiro Brazil

ISBN: (纸本)9783031425073;9783031425080

binary matrix factorization can be used at the core of many data analysis pipelines. It is used for clustering items, categorical characteristics of observations, and recommendation systems for users interacting with itemsets. The most common algorithms approximate the factorization through gradient descent. However, the results are approximately binary. When thresholded, the reconstruction error is so high that the matrices are no longer representative of the original. Therefore, the analyst must always choose between precision and explainability. We achieved theoretical results that greatly improve solving the exact subproblem of this factorization. These results enable a backtracking approach that can solve the linearized formulation of the subproblem in large binary matrices taking advantage of their sparsity in real settings. Finally, we test this new approach post-processing matrices yielded by gradient descent algorithms using the new backtracking to obtain actually binary factorized matrices with a diminished reconstruction error, close the level of what gradient descent is capable of finding. We tested our algorithm using gene expression datasets, and could find a error rate comparable to the relaxed continuous problem before discretization. The discretized matrices allow for domain experts to question biclusters of gene-expressions and samples taken.

关键词： binary matrix factorization Gene Expression Algorithms

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Efficient local search for L₁ and L₂ binary matrix factorization

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INTELLIGENT DATA ANALYSIS 2016年第4期20卷 783-807页

作者： Mirisaee, Hamid Gaussier, Eric Termier, Alexandre Univ Grenoble Alps CNRS Grenoble France Univ Rennes 1 F-35014 Rennes France

Rank K binary matrix factorization (BMF) approximates a binary matrix by the product of two binary matrices of lower rank, K. Several researchers have addressed this problem, focusing on either approximations of rank 1 or higher, using either the L-1 or L-2-norms for measuring the quality of the approximation. The rank 1 problem (for which the L-1 and L-2-norms are equivalent) has been shown to be related to the Integer Linear Programming (ILP) problem. We first show here that the alternating strategy with the L-2-norm, at the core of several methods used to solve BMF, can be reformulated as an Unconstrained binary Quadratic Programming (UBQP) problem. This reformulation allows us to use local search procedures designed for UBQP in order to improve the solutions of BMF. We then introduce a new local search dedicated to the BMF problem. We show in particular that this solution is in average faster than the previously proposed ones. We then assess its behavior on several collections and methods and show that it significantly improves methods targeting the L-2-norms on all the datasets considered;for the L-1-norm, the improvement is also significant for real, structured datasets and for the BMF problem without the binary reconstruction constraint.

关键词： binary matrix factorization local search heuristic

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Knowledge structure generation and modularization based on binary matrix factorization in engineering design

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JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY 2020年第11期34卷 4657-4673页

作者： Zhao, Shubin Xu, Cheng Wang, Ruizhe Nanjing Univ Sci & Technol Sch Mech Engn Nanjing Peoples R China Univ Southern Calif Dept Comp Sci Viterbi Sch Engn Los Angeles CA 90007 USA

Implementing improved effective knowledge reuse and modular design in the earlier stages of engineering design have been the development trend over several decades. However, knowledge capture in the field either remains heavily human involved or is difficult for forming structured knowledge that can be directly utilized by computers. Moreover, modularization is usually performed when system components are fully understood, which fails to influence the design process in an earlier stage. In this paper, we propose a knowledge representation method to capture the knowledge in the design documents intelligently and organize them in a structured manner. A modularization method using binary matrix factorization is also put forward to optimize the design process. Case studies of the design of electro-hydraulic dram brake and power supply are used to exemplify how modularization can be accomplished by matrix factorization and how knowledge structure is generated with computer support. Finally, several research problems are discussed.

关键词： binary matrix factorization Engineering design Knowledge structure Modularization Text mining

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binary matrix factorization and Completion via Integer Programming

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MATHEMATICS OF OPERATIONS RESEARCH 2023年第2期49卷 653-1302, C2页

作者： Gunluk, Oktay Hauser, Raphael Andreas Kovacs, Reka Agnes Cornell Univ Ithaca NY 14850 USA Univ Oxford Oxford OX1 3AZ England Alan Turing Inst London NW1 2DB England

binary matrix factorization is an essential tool for identifying discrete patterns in binary data. In this paper, we consider the rank -k binary matrix factorization problem (k- BMF) under Boolean arithmetic: we are given an n x m binary matrix X with possibly missing entries and need to find two binary matrices A and B of dimension n x k and k x m, respectively, which minimize the distance between X and the Boolean product of A and B in the squared Frobenius distance. We present a compact and two exponential size integer programs (IPs) for k-BMF and show that the compact IP has a weak linear programming (LP) relaxation, whereas the exponential size IPs have a stronger equivalent LP relaxation. We introduce a new objective function, which differs from the traditional squared Frobenius objective in attributing a weight to zero entries of the input matrix that is proportional to the number of times the zero is erroneously covered in a rank -k factorization. For one of the exponential size Ips, we describe a computational approach based on column generation. Experimental results on synthetic and real-world data sets suggest that our integer programming approach is competitive against available methods for k-BMF and provides accurate low-error factorizations.

关键词： binary matrix factorization binary matrix completion column generation integer programming

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binary matrix factorization via collaborative neurodynamic optimization

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NEURAL NETWORKS 2024年 176卷 106348页

作者： Li, Hongzong Wang, Jun Zhang, Nian Zhang, Wei City Univ Hong Kong Dept Comp Sci Hong Kong Peoples R China City Univ Hong Kong Sch Data Sci Hong Kong Peoples R China Univ Dist Columbia Dept Elect & Comp Engn Washington DC USA Chongqing Three Gorges Univ Chongqing Engn Res Ctr Internet Things & Intellige Chongqing Peoples R China

binary matrix factorization is an important tool for dimension reduction for high -dimensional datasets with binary attributes and has been successfully applied in numerous areas. This paper presents a collaborative neurodynamic optimization approach to binary matrix factorization based on the original combinatorial optimization problem formulation and quadratic unconstrained binary optimization problem reformulations. The proposed approach employs multiple discrete Hopfield networks operating concurrently in search of local optima. In addition, a particle swarm optimization rule is used to reinitialize neuronal states iteratively to escape from local minima toward better ones. Experimental results on eight benchmark datasets are elaborated to demonstrate the superior performance of the proposed approach against six baseline algorithms in terms of factorization error. Additionally, the viability of the proposed approach is demonstrated for pattern discovery on three datasets.

关键词： binary matrix factorization Collaborative neurodynamic optimization Discrete Hopfield network Quadratic unconstrained binary optimization Pattern discovery

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binary matrix factorization applied to Netflix dataset analysis

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IFAC-PapersOnLine 2019年第24期52卷 13-17页

作者： Mamadou Diop Sebastian Miron Anthony Larue David Brie Université de Lorraine CRAN UMR 7039 Vandœuvre F-54506 France CEA LIST Gif-sur-Yvette Cedex 91191 France

关键词： binary matrix factorization Recommendation system

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INTERPRETABLE CLUSTERING ENSEMBLES USING binary matrix factorization

INTERPRETABLE CLUSTERING ENSEMBLES USING BINARY MATRIX FACTO...

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IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Sukhanov, S. Debes, C. Zoubir, A. M. AGT Int Darmstadt Germany Tech Univ Darmstadt Signal Proc Grp Darmstadt Germany

ISBN: (纸本)9781538646588

The combination of multiple clustering solutions used to obtain accurate and novel output has attracted attention in data clustering research. Despite the success of clustering ensembles, there are still several fundamental limiting issues including the lack of a unified formalized problem formulation and an intuitive interpretation of the resulting solution. We formulate the clustering ensemble problem as a binary matrix factorization imposing assumptions of a binary structure on the resulting matrices. In such a framework, every data object is assigned to its representative ensemble centroid allowing for interpretation and validation of the consensus clustering results. We demonstrate that the formulated problem can be efficiently solved by means of iterative rank-one binary matrix approximation and apply the Proximus algorithm proposing an effective initialization scheme. The evaluation of the proposed clustering ensemble method demonstrates its efficacy on synthetic and real problems.

关键词： clustering ensembles consensus clustering binary matrix factorization

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Mining Discrete Patterns via binary matrix factorization 09

Mining Discrete Patterns via Binary Matrix Factorization

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15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

作者： Shen, Bao-Hong Ji, Shuiwang Ye, Jieping Arizona State Univ Tempe AZ 85287 USA

ISBN: (纸本)9781605584959

Mining discrete patterns in binary data is important for sub-sampling, compression, and clustering. We consider rank-one binary matrix approximations that identify the dominant patterns of the data, while preserving its discrete property. A best approximation on such data has a minimum set of inconsistent entries, i.e., mismatches between the given binary data and the approximate matrix. Due to the hardness of the problem, previous accounts of such problems employ heuristics and the resulting approximation may be far away from the optimal one. In this paper, we show that the rank-one binary matrix approximation can be reformulated as a 0-1 integer linear program (ILP). However, the ILP formulation is computationally expensive even for small-size matrices. We propose a linear program (LP) relaxation, which is shown to achieve a guaranteed approximation error bound. We further extend the proposed formulations using the regularization technique, which is commonly employed to address overfitting. The LP formulation is restricted to medium-size matrices, due to the large number of variables involved for large matrices. Interestingly, we show that the proposed approximate formulation can be transformed into an instance of the minimum s-t cut problem, which can be solved efficiently by finding maximum flows. Our empirical study shows the efficiency of the proposed algorithm based on the maximum flow. Results also confirm the established theoretical bounds.

关键词： binary matrix factorization rank-one integer linear program regularization minimum cut maximum flow

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