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Deep matrix factorizations [article]

Pierre De Handschutter, Nicolas Gillis, Xavier Siebert
2020 arXiv   pre-print
Recently, deep matrix factorization (deep MF) was introduced to deal with the extraction of several layers of features and has been shown to reach outstanding performances on unsupervised tasks.  ...  Deep MF was motivated by the success of deep learning, as it is conceptually close to some neural networks paradigms.  ...  A BRIEF SUMMARY ON MATRIX FACTORIZATIONS In this section, we recall the basics of matrix factorizations, which will be key to understand deep MF.  ... 
arXiv:2010.00380v2 fatcat:5d6zleu6w5gh7nmduv2zxu7ep4

Implicit Regularization in Deep Matrix Factorization [article]

Sanjeev Arora, Nadav Cohen, Wei Hu, Yuping Luo
2019 arXiv   pre-print
We study the implicit regularization of gradient descent over deep linear neural networks for matrix completion and sensing, a model referred to as deep matrix factorization.  ...  Secondly, we present theoretical and empirical arguments questioning a nascent view by which implicit regularization in matrix factorization can be captured using simple mathematical norms.  ...  matrix factorization) and 3 (deep matrix factorization).  ... 
arXiv:1905.13655v3 fatcat:xla4gio4kzdtfjwd5ns3un6xua

Bayesian Deep Collaborative Matrix Factorization

Teng Xiao, Shangsong Liang, Weizhou Shen, Zaiqiao Meng
2019 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
In this paper, we propose a Bayesian Deep Collaborative Matrix Factorization (BDCMF) algorithm for collaborative filtering (CF).  ...  matrix.  ...  Bayesian Deep Collaborative Matrix Factorization In this section, we propose a Bayesian Deep Collaborative Matrix Factorization (BDCMF) for recommendation, the goal of which is to infer user latent matrix  ... 
doi:10.1609/aaai.v33i01.33015474 fatcat:osm7xtdrczdl3ppp6a4lqfbyay

Matrix Factorization via Deep Learning [article]

Duc Minh Nguyen and Evaggelia Tsiligianni and Nikos Deligiannis
2018 arXiv   pre-print
This paper addresses these two drawbacks by presenting a deep matrix factorization model and a generic method to allow joint training of the factorization model and the discretization operator.  ...  Matrix completion is one of the key problems in signal processing and machine learning. In recent years, deep-learning-based models have achieved state-of-the-art results in matrix completion.  ...  Deep Matrix Factorization Model Consider a partially observed matrix M ∈ R n×m , and let X i ∈ R m , i = 1, . . . , n, be the i-th row vector and Y j ∈ R n , j = 1, . . . , m, be the j-th column vector  ... 
arXiv:1812.01478v1 fatcat:e5coe7mzwfgsjoo4cju6w55ayy

Sparse Deep Nonnegative Matrix Factorization [article]

Zhenxing Guo, Shihua Zhang
2017 arXiv   pre-print
In this paper, we proposed sparse deep nonnegative matrix factorization models to analyze complex data for more accurate classification and better feature interpretation.  ...  Nonnegative matrix factorization is a powerful technique to realize dimension reduction and pattern recognition through single-layer data representation learning.  ...  SPARSE DEEP NMF Similar to the general multi-layer NMF framework, sparse deep NMF models factorize a nonnegative matrix into L + 1 nonnegative ones: X ≈ W 1 g −1 (W 2 · · · g −1 (W L H L )).  ... 
arXiv:1707.09316v1 fatcat:c6rzyvdmurdjlp6rdzof5fj37u

Exponential Signal Reconstruction with Deep Hankel Matrix Factorization [article]

Yihui Huang, Jinkui Zhao, Zi Wang, Vladislav Orekhov, Di Guo, Xiaobo Qu
2021 arXiv   pre-print
low-rank Hankel matrix factorization.  ...  In this work, we propose a deep learning method whose neural network structure is designed by unrolling the iterative process in the model-based state-of-the-art exponentials reconstruction method with  ...  To reconstruct exponential signals without SVD, we introduce Deep Hankel Matrix Factorization network (DHMF).  ... 
arXiv:2007.06246v4 fatcat:x4ugr2f6ozbwfpxr6baorburia

Deep Collective Matrix Factorization for Augmented Multi-View Learning [article]

Ragunathan Mariappan, Vaibhav Rajan
2019 arXiv   pre-print
Collective Matrix Factorization (CMF) is a technique to learn shared latent representations from arbitrary collections of matrices.  ...  In this paper, we develop the first deep-learning based method, called dCMF, for unsupervised learning of multiple shared representations, that can model such non-linear interactions, from an arbitrary  ...  reconstruction foreach matrix X (m) in V M do X (m) = U (rm) · U (cm) T end return U , X Algorithm 2: Deep Collective Matrix Factorization Time Complexity.  ... 
arXiv:1811.11427v2 fatcat:pzgtvjyafjd7bfxghnhalwagka

Deep Neural Convolutive Matrix Factorization for Articulatory Representation Decomposition [article]

Jiachen Lian and Alan W Black and Louis Goldstein and Gopala Krishna Anumanchipalli
2022 arXiv   pre-print
This work, investigating the speech representations derived from articulatory kinematics signals, uses a neural implementation of convolutive sparse matrix factorization to decompose the articulatory data  ...  The proposed work thus makes a bridge between articulatory phonology and deep neural networks to leverage informative, intelligible, interpretable,and efficient speech representations.  ...  Such auto-encoder based matrix factorization method is compatible with modern deep neural network and the batch-wise optimization improves the convergence rate to the huge extent.  ... 
arXiv:2204.00465v3 fatcat:23pkjaevizfrrfrwp2e4uo6mka

Deep Matrix Factorization Models for Recommender Systems

Hong-Jian Xue, Xinyu Dai, Jianbing Zhang, Shujian Huang, Jiajun Chen
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
With this matrix as the input, we present a deep structure learning architecture to learn a common low dimensional space for the representations of users and items.  ...  In this paper, we propose a novel matrix factorization model with neural network architecture. Firstly, we construct a user-item matrix with explicit ratings and non-preference implicit feedback.  ...  Deep Matrix Factorization Models (DMF) As mentioned in Section 2, we form a matrix Y according to the Equation 2.  ... 
doi:10.24963/ijcai.2017/447 dblp:conf/ijcai/XueDZHC17 fatcat:3a3ozqsghnfw7jwlzrq3zljyia

Multi-View Clustering via Deep Matrix Factorization

Handong Zhao, Zhengming Ding, Yun Fu
2017 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
In this paper, we present a deep matrix factorization framework for MVC, where semi-nonnegative matrix factorization is adopted to learn the hierarchical semantics of multi-view data in a layer-wise fashion  ...  The superior experimental results on three face benchmarks show the effectiveness of the proposed deep matrix factorization model.  ...  Conclusion In this paper, we proposed a deep matrix factorization approach for MVC problem.  ... 
doi:10.1609/aaai.v31i1.10867 fatcat:kuwtbexj2bffdlnpbhbwvh7m7m

Gradient Descent for Deep Matrix Factorization: Dynamics and Implicit Bias towards Low Rank [article]

Hung-Hsu Chou, Carsten Gieshoff, Johannes Maly, Holger Rauhut
2021 arXiv   pre-print
of deep learning.  ...  Wealso provide empirical evidence for implicit bias in more general scenarios, such as matrix sensing andrandom initialization.  ...  Acknowledgements HHC and HR acknowledge funding by the DAAD through the project Understanding stochastic gradient descent in deep learning (project no. 57417829).  ... 
arXiv:2011.13772v4 fatcat:3jmukdilyvcspnozuph67qurju

Deep Approximately Orthogonal Nonnegative Matrix Factorization for Clustering [article]

Yuning Qiu, Guoxu Zhou, Kan Xie
2017 arXiv   pre-print
Nonnegative Matrix Factorization (NMF) is a widely used technique for data representation.  ...  Experiment on two face image datasets showed that the proposed method achieved better clustering performance than other deep matrix factorization methods and state-of-the-art single layer NMF variants.  ...  Based on this novel deep matrix factorizing technique, we proposed deep approximately orthogonal nonnegative matrix factorization (DAONMF) by incorporating the orthogonality penalty on each layer.  ... 
arXiv:1711.07437v1 fatcat:egufgx7dx5ck5l2ifuxqkmnrse

A regularized deep matrix factorized model of matrix completion for image restoration [article]

Zhemin Li, Zhi-Qin John Xu, Tao Luo, Hongxia Wang
2020 arXiv   pre-print
the matrix factorization component.  ...  In this work, we propose a Regularized Deep Matrix Factorized (RDMF) model for image restoration, which utilizes the implicit bias of the low rank of deep neural networks and the explicit bias of total  ...  The second method is also deep matrix factorization (DMF) without TV constraint [10] .  ... 
arXiv:2007.14581v1 fatcat:xefiqdltgvhnvkrt4cogqnsgde

A consistent and flexible framework for deep matrix factorizations [article]

Pierre De Handschutter, Nicolas Gillis
2022 arXiv   pre-print
Deep matrix factorizations (deep MFs) are recent unsupervised data mining techniques inspired by constrained low-rank approximations.  ...  In this paper, we introduce two meaningful loss functions for deep MF and present a generic framework to solve the corresponding optimization problems.  ...  Sparse deep MF Sparse matrix factorizations consist in enforcing some factors of the decomposition to be sparse to foster their interpretability.  ... 
arXiv:2206.10693v1 fatcat:asjfz34lvnhwvbymwyaz2oft3y

Deep Risk Model: A Deep Learning Solution for Mining Latent Risk Factors to Improve Covariance Matrix Estimation [article]

Hengxu Lin, Dong Zhou, Weiqing Liu, Jiang Bian
2021 arXiv   pre-print
In this work, we formulate the quest of mining risk factors as a learning problem and propose a deep learning solution to effectively "design" risk factors with neural networks.  ...  Traditional approaches to estimate the covariance matrix are based on human-designed risk factors, which often require tremendous time and effort to design better risk factors to improve the covariance  ...  In this work, we propose a deep learning solution, Deep Risk Model, to facilitate the design of risk factors.  ... 
arXiv:2107.05201v2 fatcat:jlnl2c63qravpj63r4ox3me7ce
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