A Provably Correct and Robust Algorithm for Convolutive Nonnegative Matrix Factorization

Degleris, Anthony; Gillis, Nicolas

doi:10.1109/tsp.2020.2984163

Cited by 6 publications

(3 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then we fill h init q: with zeros and place a one at t * . Note that this initialization procedure mimics a recently proposed algorithm for separable CNMF 2 [16] but is less computationally intensive. A total of 500 outer iterations are performed to learn a single note template.…”

Section: Learning Note-wise Templatesmentioning

confidence: 99%

Semi-Supervised Convolutive NMF for Automatic Piano Transcription

Wu¹,

Marmoret²,

Cohen³

2022

Preprint

View full text Add to dashboard Cite

Automatic Music Transcription, which consists in transforming an audio recording of a musical performance into symbolic format, remains a difficult Music Information Retrieval task. In this work, we propose a semi-supervised approach using low-rank matrix factorization techniques, in particular Convolutive Nonnegative Matrix Factorization. In the semi-supervised setting, only a single recording of each individual notes is required. We show on the MAPS dataset that the proposed semisupervised CNMF method performs better than state-ofthe-art low-rank factorization techniques and a little worse than supervised deep learning state-of-the-art methods, while however suffering from generalization issues.

show abstract

Section: Learning Note-wise Templatesmentioning

confidence: 99%

Semi-Supervised Convolutive NMF for Automatic Piano Transcription

Wu¹,

Marmoret²,

Cohen³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…After entering Security Layer 1 to Bravias System, two vectors will get generated based on height and width of the plain image by TLCG, and the Bravias lattice will get produced according to these vectors. The next step (Non-negative Matrix Factorization) is to extract the points generated in Bravais Crystal System, and assign them into a 2D matrix V ∈ R m×n , then it will get factorized into two matrices W ∈ R m×r F ); finally, h is the product of mixing ratio and saturated mixing ratio [37,38]. The output of factorization for lattice in fig.…”

Section: Fig 2 Procedures Of Primary Security Layermentioning

confidence: 99%

PiouCrypt: Decentralized Lattice-based Method for Visual Symmetric Cryptography

Abapour¹,

Ebadpour²

2022

Preprint

View full text Add to dashboard Cite

In recent years, establishing secure visual communications has turned into one of the essential problems for security engineers and researchers. However, only limited novel solutions are provided for image encryption, and limiting the visual cryptography to only limited schemes can bring up negative consequences, especially with emerging quantum computational systems. This paper presents a novel algorithm for establishing secure private visual communication. The proposed method has a layered architecture with several cohesive components, and corresponded with an NP-hard problem, despite its symmetric structure. This two-step technique is not limited to gray-scale pictures, and furthermore, utilizing a lattice structure causes to proposed method has optimal resistance for the post-quantum era, and is relatively secure from the theoretical dimension.

show abstract

“…Studies have been conducted to seek unique and exact solutions to NMF, despite the non-convexity nature of the problem. Most of these studies are based on the separability assumption (Chen et al 2019;Degleris and Gillis 2019). This condition states that the columns of the bases W , which should be a subset of dataset X, i.e., W ⊆ X, span a convex hull/simplex/conical hull/cone which includes all data points X (Zhou, Bian, and Tao 2013).…”

Section: Introductionmentioning

confidence: 99%

Diversified Bayesian Nonnegative Matrix Factorization

Qiao¹,

Liu

et al. 2020

AAAI

View full text Add to dashboard Cite

Nonnegative matrix factorization (NMF) has been widely employed in a variety of scenarios due to its capability of inducing semantic part-based representation. However, because of the non-convexity of its objective, the factorization is generally not unique and may inaccurately discover intrinsic “parts” from the data. In this paper, we approach this issue using a Bayesian framework. We propose to assign a diversity prior to the parts of the factorization to induce correctness based on the assumption that useful parts should be distinct and thus well-spread. A Bayesian framework including this diversity prior is then established. This framework aims at inducing factorizations embracing both good data fitness from maximizing likelihood and large separability from the diversity prior. Specifically, the diversity prior is formulated with determinantal point processes (DPP) and is seamlessly embedded into a Bayesian NMF framework. To carry out the inference, a Monte Carlo Markov Chain (MCMC) based procedure is derived. Experiments conducted on a synthetic dataset and a real-world MULAN dataset for multi-label learning (MLL) task demonstrate the superiority of the proposed method.

show abstract

A Provably Correct and Robust Algorithm for Convolutive Nonnegative Matrix Factorization

Cited by 6 publications

References 29 publications

Semi-Supervised Convolutive NMF for Automatic Piano Transcription

Semi-Supervised Convolutive NMF for Automatic Piano Transcription

PiouCrypt: Decentralized Lattice-based Method for Visual Symmetric Cryptography

Diversified Bayesian Nonnegative Matrix Factorization

Contact Info

Product

Resources

About