Tootfinder

Determined Multichannel Blind Source Separation with Clustered Source Model
Jianyu Wang, Shanzheng Guan
https://arxiv.org/abs/2405.03118 https://

Determined Multichannel Blind Source Separation with Clustered Source Model
The independent low-rank matrix analysis (ILRMA) method stands out as a prominent technique for multichannel blind audio source separation. It leverages nonnegative matrix factorization (NMF) and nonnegative canonical polyadic decomposition (NCPD) to model source parameters. While it effectively captures the low-rank structure of sources, the NMF model overlooks inter-channel dependencies. On the other hand, NCPD preserves intrinsic structure but lacks interpretable latent factors, making it ch…

CALRec: Contrastive Alignment of Generative LLMs For Sequential Recommendation
Yaoyiran Li, Xiang Zhai, Moustafa Alzantot, Keyi Yu, Ivan Vuli\'c, Anna Korhonen, Mohamed Hammad
https://arxiv.org/abs/2405.02429

CALRec: Contrastive Alignment of Generative LLMs For Sequential Recommendation
Traditional recommender systems such as matrix factorization methods rely on learning a shared dense embedding space to represent both items and user preferences. Sequence models such as RNN, GRUs, and, recently, Transformers have also excelled in the task of sequential recommendation. This task requires understanding the sequential structure present in users' historical interactions to predict the next item they may like. Building upon the success of Large Language Models (LLMs) in a variety o…

This https://arxiv.org/abs/2404.17496 has been replaced.
initial toot: https://mastoxiv.page/@a…

From STEM-EDXS data to phase separation and quantification using physics-guided NMF
We present the development of a new algorithm which combines state-of-the-art energy-dispersive X-ray (EDX) spectroscopy theory and a suitable machine learning formulation for the hyperspectral unmixing of scanning transmission electron microscope EDX spectrum images. The algorithm is based on non-negative matrix factorization (NMF) incorporating a physics-guided factorization model. It optimizes a Poisson likelihood, under additional simplex constraint together with user-chosen sparsity-induci…

This https://arxiv.org/abs/2404.02656 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCV_…

Non-negative Subspace Feature Representation for Few-shot Learning in Medical Imaging
Unlike typical visual scene recognition domains, in which massive datasets are accessible to deep neural networks, medical image interpretations are often obstructed by the paucity of data. In this paper, we investigate the effectiveness of data-based few-shot learning in medical imaging by exploring different data attribute representations in a low-dimensional space. We introduce different types of non-negative matrix factorization (NMF) in few-shot learning, addressing the data scarcity issue…

The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$
J. Ablinger, A. Behring, J. Bl\"umlein, A. De Freitas, A. von Manteuffel, C. Schneider, K. Sch\"onwald
https://arxiv.org/abs/2403.00513…

The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements $A_{Qg}^{(3)}$ and $ΔA_{Qg}^{(3)}$
The non-first-order-factorizable contributions (The terms 'first-order-factorizable contributions' and 'non-first-order-factorizable contributions' have been introduced and discussed in Refs. \cite{Behring:2023rlq,Ablinger:2023ahe}. They describe the factorization behaviour of the difference- or differential equations for a subset of master integrals of a given problem.) to the unpolarized and polarized massive operator matrix elements to three-loop order, $A_{Qg}^{(3)}$ and $ΔA_{Qg}^{(3)}$, a…

Privacy-Preserving Distributed Nonnegative Matrix Factorization
Ehsan Lari, Reza Arablouei, Stefan Werner
https://arxiv.org/abs/2403.18326 https://<…

Privacy-Preserving Distributed Nonnegative Matrix Factorization
Nonnegative matrix factorization (NMF) is an effective data representation tool with numerous applications in signal processing and machine learning. However, deploying NMF in a decentralized manner over ad-hoc networks introduces privacy concerns due to the conventional approach of sharing raw data among network agents. To address this, we propose a privacy-preserving algorithm for fully-distributed NMF that decomposes a distributed large data matrix into left and right matrix factors while sa…

Dual Simplex Volume Maximization for Simplex-Structured Matrix Factorization
Maryam Abdolali, Giovanni Barbarino, Nicolas Gillis
https://arxiv.org/abs/2403.20197

Dual Simplex Volume Maximization for Simplex-Structured Matrix Factorization
Simplex-structured matrix factorization (SSMF) is a generalization of nonnegative matrix factorization, a fundamental interpretable data analysis model, and has applications in hyperspectral unmixing and topic modeling. To obtain identifiable solutions, a standard approach is to find minimum-volume solutions. By taking advantage of the duality/polarity concept for polytopes, we convert minimum-volume SSMF in the primal space to a maximum-volume problem in the dual space. We first prove the iden…

A Distance Metric Learning Model Based On Variational Information Bottleneck
YaoDan Zhang, Zidong Wang, Ru Jia, Ru Li
https://arxiv.org/abs/2403.02794 http…

A Distance Metric Learning Model Based On Variational Information Bottleneck
In recent years, personalized recommendation technology has flourished and become one of the hot research directions. The matrix factorization model and the metric learning model which proposed successively have been widely studied and applied. The latter uses the Euclidean distance instead of the dot product used by the former to measure the latent space vector. While avoiding the shortcomings of the dot product, the assumption of Euclidean distance is neglected, resulting in limited recommend…

This https://arxiv.org/abs/2404.02656 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCV_…

Non-negative Subspace Feature Representation for Few-shot Learning in Medical Imaging
Unlike typical visual scene recognition domains, in which massive datasets are accessible to deep neural networks, medical image interpretations are often obstructed by the paucity of data. In this paper, we investigate the effectiveness of data-based few-shot learning in medical imaging by exploring different data attribute representations in a low-dimensional space. We introduce different types of non-negative matrix factorization (NMF) in few-shot learning, addressing the data scarcity issue…

Symmetric bilinear forms, superalgebras and integer matrix factorization
Dan Fretwell, Jenny Roberts
https://arxiv.org/abs/2404.17881 https://

Symmetric bilinear forms, superalgebras and integer matrix factorization
We construct and investigate certain (unbalanced) superalgebra structures on $\text{End}_K(V)$, with $K$ a field of characteristic $0$ and $V$ a finite dimensional $K$-vector space (of dimension $n\geq 2$). These structures are induced by a choice of non-degenerate symmetric bilinear form $B$ on $V$ and a choice of non-zero base vector $w\in V$. After exploring the construction further, we apply our results to certain questions concerning integer matrix factorization and isometry of integral la…

Adaptive Retrieval and Scalable Indexing for k-NN Search with Cross-Encoders
Nishant Yadav, Nicholas Monath, Manzil Zaheer, Rob Fergus, Andrew McCallum
https://arxiv.org/abs/2405.03651

Adaptive Retrieval and Scalable Indexing for k-NN Search with Cross-Encoders
Cross-encoder (CE) models which compute similarity by jointly encoding a query-item pair perform better than embedding-based models (dual-encoders) at estimating query-item relevance. Existing approaches perform k-NN search with CE by approximating the CE similarity with a vector embedding space fit either with dual-encoders (DE) or CUR matrix factorization. DE-based retrieve-and-rerank approaches suffer from poor recall on new domains and the retrieval with DE is decoupled from the CE. While C…

Efficient Mixed-Precision Matrix Factorization of the Inverse Overlap Matrix in Electronic Structure Calculations with AI-Hardware and GPUs
Adela Habib, Joshua Finkelstein, Anders M. N. Niklasson
https://arxiv.org/abs/2404.19163

Efficient Mixed-Precision Matrix Factorization of the Inverse Overlap Matrix in Electronic Structure Calculations with AI-Hardware and GPUs
In recent years, a new kind of accelerated hardware has gained popularity in the Artificial Intelligence (AI) and Machine Learning (ML) communities which enables extremely high-performance tensor contractions in reduced precision for deep neural network calculations. In this article, we exploit Nvidia Tensor cores, a prototypical example of such AI/ML hardware, to develop a mixed precision approach for computing a dense matrix factorization of the inverse overlap matrix in electronic structure …

This https://arxiv.org/abs/2304.13940 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

A Majorization-Minimization Gauss-Newton Method for 1-Bit Matrix Completion
In 1-bit matrix completion, the aim is to estimate an underlying low-rank matrix from a partial set of binary observations. We propose a novel method for 1-bit matrix completion called MMGN. Our method is based on the majorization-minimization (MM) principle, which converts the original optimization problem into a sequence of standard low-rank matrix completion problems. We solve each of these sub-problems by a factorization approach that explicitly enforces the assumed low-rank structure and t…

This https://arxiv.org/abs/2311.04855 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Algorithms for Non-Negative Matrix Factorization on Noisy Data With Negative Values
Non-negative matrix factorization (NMF) is a dimensionality reduction technique that has shown promise for analyzing noisy data, especially astronomical data. For these datasets, the observed data may contain negative values due to noise even when the true underlying physical signal is strictly positive. Prior NMF work has not treated negative data in a statistically consistent manner, which becomes problematic for low signal-to-noise data with many negative values. In this paper we present two…

This https://arxiv.org/abs/2303.17992 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A fast Multiplicative Updates algorithm for Non-negative Matrix Factorization
Nonnegative Matrix Factorization is an important tool in unsupervised machine learning to decompose a data matrix into a product of parts that are often interpretable. Many algorithms have been proposed during the last three decades. A well-known method is the Multiplicative Updates algorithm proposed by Lee and Seung in 2002. Multiplicative updates have many interesting features: they are simple to implement and can be adapted to popular variants such as sparse Nonnegative Matrix Factorization…

Applying Non-negative Matrix Factorization with Covariates to the Longitudinal Data as Growth Curve Model
Kenichi Satoh
https://arxiv.org/abs/2403.05359 ht…

Applying Non-negative Matrix Factorization with Covariates to the Longitudinal Data as Growth Curve Model
Using Non-negative Matrix Factorization (NMF), the observed matrix can be approximated by the product of the basis and coefficient matrices. Moreover, if the coefficient vectors are explained by the covariates for each individual, the coefficient matrix can be written as the product of the parameter matrix and the covariate matrix, and additionally described in the framework of Non-negative Matrix tri-Factorization (tri-NMF) with covariates. Consequently, this is equal to the mean structure of …

Efficient Algorithms for Regularized Nonnegative Scale-invariant Low-rank Approximation Models
Jeremy E. Cohen, Valentin Leplat
https://arxiv.org/abs/2403.18517

Efficient Algorithms for Regularized Nonnegative Scale-invariant Low-rank Approximation Models
Regularized nonnegative low-rank approximations such as sparse Nonnegative Matrix Factorization or sparse Nonnegative Tucker Decomposition are an important branch of dimensionality reduction models with enhanced interpretability. However, from a practical perspective, the choice of regularizers and regularization coefficients, as well as the design of efficient algorithms, is challenging because of the multifactor nature of these models and the lack of theory to back these choices. This paper a…

This https://arxiv.org/abs/2404.07862 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Emergent factorization of Hilbert space at large $N$ and black hole
We investigate the emergent factorization of Hilbert space in the low-energy description of matrix models, addressing key aspects of the black hole information paradox. We examine the collective description for the low-energy sector of $SU(N)$ matrix model, characterized by a factorized Hilbert space composed of a finite number of boxes and anti-boxes. This factorization leads us to examine the emergence of thermofield dynamics (TFD) state in the low energy sector from a fine-tuned state. In ad…

A multiscale cavity method for sublinear-rank symmetric matrix factorization
Jean Barbier, Justin Ko, Anas A. Rahman
https://arxiv.org/abs/2403.07189 https…

A multiscale cavity method for sublinear-rank symmetric matrix factorization
We consider a statistical model for symmetric matrix factorization with additive Gaussian noise in the high-dimensional regime where the rank $M$ of the signal matrix to infer scales with its size $N$ as $M = o(N^{1/10})$. Allowing for a $N$-dependent rank offers new challenges and requires new methods. Working in the Bayesian-optimal setting, we show that whenever the signal has i.i.d. entries the limiting mutual information between signal and data is given by a variational formula involving a…

Non-negative matrix underapproximation as optimal frequency band selector
Mateusz Gabor, Rafal Zdunek, Radoslaw Zimroz, Agnieszka Wylomanska
https://arxiv.org/abs/2403.12547

Non-negative matrix underapproximation as optimal frequency band selector
Time-frequency representation (TFR) is often used for non-stationary signal analysis. The most intuitive and interpretable TFR is the spectrogram. Recently, a concept of non-negative matrix factorization (NMF) has been successfully applied to local damage detection in rolling elements of bearings via spectrogram factorization. NMF applied to the spectrogram allows one to find an informative frequency band, which could be further used as a filter characteristic. However, the obtained filter char…

This https://arxiv.org/abs/2308.02058 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIR_…

Incorporating Recklessness to Collaborative Filtering based Recommender Systems
Recommender systems are intrinsically tied to a reliability/coverage dilemma: The more reliable we desire the forecasts, the more conservative the decision will be and thus, the fewer items will be recommended. This leads to a significant drop in the novelty of these systems, since instead of recommending uncertain unusual items, they focus on predicting items with guaranteed success. In this paper, we propose the inclusion of a new term in the learning process of matrix factorization-based rec…

A numerical algorithm for matrix spectral factorization on the real line
Lasha Ephremidze
https://arxiv.org/abs/2402.06381 https://ar…

A numerical algorithm for matrix spectral factorization on the real line
In this paper, the Janashia-Lagvilava matrix spectral factorization algorithm, which is designed for power spectral density functions defined on the unit circle, is extended to the real line. The proposed algorithm can be used directly for continuous-time models

H3DFact: Heterogeneous 3D Integrated CIM for Factorization with Holographic Perceptual Representations
Zishen Wan, Che-Kai Liu, Mohamed Ibrahim, Hanchen Yang, Samuel Spetalnick, Tushar Krishna, Arijit Raychowdhury
https://arxiv.org/abs/2404.04173

H3DFact: Heterogeneous 3D Integrated CIM for Factorization with Holographic Perceptual Representations
Disentangling attributes of various sensory signals is central to human-like perception and reasoning and a critical task for higher-order cognitive and neuro-symbolic AI systems. An elegant approach to represent this intricate factorization is via high-dimensional holographic vectors drawing on brain-inspired vector symbolic architectures. However, holographic factorization involves iterative computation with high-dimensional matrix-vector multiplications and suffers from non-convergence probl…

This https://arxiv.org/abs/2304.06100 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Tridiagonal and single-pair matrices and the inverse sum of two single-pair matrices
A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent factorizations are established, leading to semi-closed-form formulas for the inverse sum of two single-pair matrices. An application to derive the symbolic inverse of a particular Gram matrix is presented, and the numerical stability of the formulas is studied.

This https://arxiv.org/abs/2304.03887 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Matrix weights, singular integrals, Jones factorization and Rubio de Francia extrapolation
In this article we give an overview of the problem of finding sharp constants in matrix weighted norm inequalities for singular integrals, the so-called matrix A2 conjecture. We begin by reviewing the history of the problem in the scalar case, including a sketch of the proof of the scalar A2 conjecture. We then discuss the original, qualitative results for singular integrals with matrix weights and the best known quantitative estimates. We give an overview of new results by the author and Bowni…

This https://arxiv.org/abs/2303.02566 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

MFAI: A Scalable Bayesian Matrix Factorization Approach to Leveraging Auxiliary Information
In various practical situations, matrix factorization methods suffer from poor data quality, such as high data sparsity and low signal-to-noise ratio (SNR). Here, we consider a matrix factorization problem by utilizing auxiliary information, which is massively available in real-world applications, to overcome the challenges caused by poor data quality. Unlike existing methods that mainly rely on simple linear models to combine auxiliary information with the main data matrix, we propose to integ…

This https://arxiv.org/abs/2403.05359 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Applying Non-negative Matrix Factorization with Covariates to the Longitudinal Data as Growth Curve Model
Using Non-negative Matrix Factorization (NMF), the observed matrix can be approximated by the product of the basis and coefficient matrices. Moreover, if the coefficient vectors are explained by the covariates for each individual, the coefficient matrix can be written as the product of the parameter matrix and the covariate matrix, and additionally described in the framework of Non-negative Matrix tri-Factorization (tri-NMF) with covariates. Consequently, this is equal to the mean structure of …

Emergent factorization of Hilbert space at large $N$ and black hole
Antal Jevicki, Debangshu Mukherjee, Junggi Yoon
https://arxiv.org/abs/2404.07862 https:…

Emergent factorization of Hilbert space at large $N$ and black hole
We investigate the emergent factorization of Hilbert space in the low-energy description of matrix models, addressing key aspects of the black hole information paradox. We examine the collective description for the low-energy sector of $SU(N)$ matrix model, characterized by a factorized Hilbert space composed of a finite number of boxes and anti-boxes. This factorization leads us to examine the emergence of thermofield dynamics (TFD) state in the low energy sector from a fine-tuned state. In ad…

Consistency of matrix decomposition factor analysis
Yoshikazu Terada
https://arxiv.org/abs/2403.06968 https://arxiv.org/pdf/2403.0696…

Consistency of matrix decomposition factor analysis
For factor analysis, many estimators, starting with the maximum likelihood estimator, are developed, and the statistical properties of most estimators are well discussed. In the early 2000s, a new estimator based on matrix factorization, called Matrix Decomposition Factor Analysis (MDFA), was developed. Although the estimator is obtained by minimizing the principal component analysis-like loss function, this estimator empirically behaves like other consistent estimators of factor analysis, not …

This https://arxiv.org/abs/2403.12459 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Non-negative Contrastive Learning
Deep representations have shown promising performance when transferred to downstream tasks in a black-box manner. Yet, their inherent lack of interpretability remains a significant challenge, as these features are often opaque to human understanding. In this paper, we propose Non-negative Contrastive Learning (NCL), a renaissance of Non-negative Matrix Factorization (NMF) aimed at deriving interpretable features. The power of NCL lies in its enforcement of non-negativity constraints on features…

This https://arxiv.org/abs/2401.14592 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Multilayer Simplex-structured Matrix Factorization for Hyperspectral Unmixing with Endmember Variability
Given a hyperspectral image, the problem of hyperspectral unmixing (HU) is to identify the endmembers (or materials) and the abundance (or endmembers' contributions on pixels) that underlie the image. HU can be seen as a matrix factorization problem with a simplex structure in the abundance matrix factor. In practice, hyperspectral images may exhibit endmember variability (EV) effects -- the endmember matrix factor varies from one pixel to another. In this paper we consider a multilayer simplex…

Rethinking Non-Negative Matrix Factorization with Implicit Neural Representations
Krishna Subramani, Paris Smaragdis, Takuya Higuchi, Mehrez Souden
https://arxiv.org/abs/2404.04439

Rethinking Non-Negative Matrix Factorization with Implicit Neural Representations
Non-negative Matrix Factorization (NMF) is a powerful technique for analyzing regularly-sampled data, i.e., data that can be stored in a matrix. For audio, this has led to numerous applications using time-frequency (TF) representations like the Short-Time Fourier Transform. However extending these applications to irregularly-spaced TF representations, like the Constant-Q transform, wavelets, or sinusoidal analysis models, has not been possible since these representations cannot be directly stor…

This https://arxiv.org/abs/2211.15850 has been replaced.
link: https://scholar.google.com/scholar?q=a

Colored Bosonic Models and Matrix Coefficients
We develop the theory of colored bosonic models (initiated by Borodin and Wheeler). We will show how a family of such models can be used to represent the values of Iwahori vectors in the "spherical model" of representations of $GL_r(F)$, where $F$ is a nonarchimedean local field. Among our results are a monochrome factorization, which is the realization of the Boltzmann weights by fusion of simpler weights, a local lifting property relating the colored models with uncolored models, and an actio…

This https://arxiv.org/abs/2310.00636 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A DEIM-CUR factorization with iterative SVDs
A CUR factorization is often utilized as a substitute for the singular value decomposition (SVD), especially when a concrete interpretation of the singular vectors is challenging. Moreover, if the original data matrix possesses properties like nonnegativity and sparsity, a CUR decomposition can better preserve them compared to the SVD. An essential aspect of this approach is the methodology used for selecting a subset of columns and rows from the original matrix. This study investigates the eff…

This https://arxiv.org/abs/2309.04923 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On improvements of the Hardy, Copson and Rellich inequalities
Using a method of factorization and by introducing a generalized discrete Dirichlet's Laplacian matrix $(-Δ_Λ)$, we establish an extended improved discrete Hardy's inequality and Rellich inequality in one dimension. We prove that the discrete Copson inequality (E.T. Copson, \emph{Notes on a series of positive terms}, J. London Math. Soc., 2 (1927), 9-12.) in one-dimension admits an improvement. We also prove that the improved Copson's weights are optimal (in fact \emph{critical}). It is shown…

This https://arxiv.org/abs/2311.13277 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIR_…

Hierarchical Matrix Factorization for Interpretable Collaborative Filtering
Matrix factorization (MF) is a simple collaborative filtering technique that achieves superior recommendation accuracy by decomposing the user-item interaction matrix into user and item latent matrices. Because the model typically learns each interaction independently, it may overlook the underlying shared dependencies between users and items, resulting in less stable and interpretable recommendations. Based on these insights, we propose "Hierarchical Matrix Factorization" (HMF), which incorpor…

This https://arxiv.org/abs/2401.13807 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csET_…

Depth-Optimal Addressing of 2D Qubit Array with 1D Controls Based on Exact Binary Matrix Factorization
Reducing control complexity is essential for achieving large-scale quantum computing. However, reducing control knobs may compromise the ability to independently address each qubit. Recent progress in neutral atom-based platforms suggests that rectangular (row-column) addressing may strike a balance between control granularity and flexibility for 2D qubit arrays. This scheme allows addressing qubits on the intersections of a set of rows and columns each time. While quadratically reducing contro…

Compressive Bayesian non-negative matrix factorization for mutational signatures analysis
Alessandro Zito, Jeffrey W. Miller
https://arxiv.org/abs/2404.10974

Compressive Bayesian non-negative matrix factorization for mutational signatures analysis
Non-negative matrix factorization (NMF) is widely used in many applications for dimensionality reduction. Inferring an appropriate number of factors for NMF is a challenging problem, and several approaches based on information criteria or sparsity-inducing priors have been proposed. However, inference in these models is often complicated and computationally challenging. In this paper, we introduce a novel methodology for overfitted Bayesian NMF models using "compressive hyperpriors" that force …

A sublinear-time randomized algorithm for column and row subset selection based on strong rank-revealing QR factorizations
Alice Cortinovis, Lexing Ying
https://arxiv.org/abs/2402.13975

A sublinear-time randomized algorithm for column and row subset selection based on strong rank-revealing QR factorizations
In this work, we analyze a sublinear-time algorithm for selecting a few rows and columns of a matrix for low-rank approximation purposes. The algorithm is based on an initial uniformly random selection of rows and columns, followed by a refinement of this choice using a strong rank-revealing QR factorization. We prove bounds on the error of the corresponding low-rank approximation (more precisely, the CUR approximation error) when the matrix is a perturbation of a low-rank matrix that can be fa…

Towards Cohesion-Fairness Harmony: Contrastive Regularization in Individual Fair Graph Clustering
Siamak Ghodsi, Seyed Amjad Seyedi, Eirini Ntoutsi
https://arxiv.org/abs/2402.10756

Towards Cohesion-Fairness Harmony: Contrastive Regularization in Individual Fair Graph Clustering
Conventional fair graph clustering methods face two primary challenges: i) They prioritize balanced clusters at the expense of cluster cohesion by imposing rigid constraints, ii) Existing methods of both individual and group-level fairness in graph partitioning mostly rely on eigen decompositions and thus, generally lack interpretability. To address these issues, we propose iFairNMTF, an individual Fairness Nonnegative Matrix Tri-Factorization model with contrastive fairness regularization that…

Projected Gradient Descent for Spectral Compressed Sensing via Symmetric Hankel Factorization
Jinsheng Li, Wei Cui, Xu Zhang
https://arxiv.org/abs/2403.09031

Projected Gradient Descent for Spectral Compressed Sensing via Symmetric Hankel Factorization
Current spectral compressed sensing methods via Hankel matrix completion employ symmetric factorization to demonstrate the low-rank property of the Hankel matrix. However, previous non-convex gradient methods only utilize asymmetric factorization to achieve spectral compressed sensing. In this paper, we propose a novel nonconvex projected gradient descent method for spectral compressed sensing via symmetric factorization named Symmetric Hankel Projected Gradient Descent (SHGD), which updates on…

This https://arxiv.org/abs/2305.17744 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Heterogeneous Matrix Factorization: When Features Differ by Datasets
In myriad statistical applications, data are collected from related but heterogeneous sources. These sources share some commonalities while containing idiosyncratic characteristics. One of the most fundamental challenges in such scenarios is to recover the shared and source-specific factors. Despite the existence of a few heuristic approaches, a generic algorithm with theoretical guarantees has yet to be established. In this paper, we tackle the problem by proposing a method called Heterogeneou…

This https://arxiv.org/abs/2108.02119 has been replaced.
link: https://scholar.google.com/scholar?q=a

Low-complexity Scaling Methods for DCT-II Approximations
This paper introduces a collection of scaling methods for generating $2N$-point DCT-II approximations based on $N$-point low-complexity transformations. Such scaling is based on the Hou recursive matrix factorization of the exact $2N$-point DCT-II matrix. Encompassing the widely employed Jridi-Alfalou-Meher scaling method, the proposed techniques are shown to produce DCT-II approximations that outperform the transforms resulting from the JAM scaling method according to total error energy and me…

This https://arxiv.org/abs/2305.17744 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Heterogeneous Matrix Factorization: When Features Differ by Datasets
In myriad statistical applications, data are collected from related but heterogeneous sources. These sources share some commonalities while containing idiosyncratic characteristics. One of the most fundamental challenges in such scenarios is to recover the shared and source-specific factors. Despite the existence of a few heuristic approaches, a generic algorithm with theoretical guarantees has yet to be established. In this paper, we tackle the problem by proposing a method called Heterogeneou…

MARec: Metadata Alignment for cold-start Recommendation
Julien Monteil, Volodymyr Vaskovych, Wentao Lu, Anirban Majumder, Anton van den Hengel
https://arxiv.org/abs/2404.13298

MARec: Metadata Alignment for cold-start Recommendation
For many recommender systems the primary data source is a historical record of user clicks. The associated click matrix which is often very sparse, however, as the number of users x products can be far larger than the number of clicks, and such sparsity is accentuated in cold-start settings. The sparsity of the click matrix is the reason matrix factorization and autoencoders techniques remain highly competitive across collaborative filtering datasets. In this work, we propose a simple approach …

Employing semi-supervised learning for high-resolution segmentation of crystal defects
Ashish Chauniyal, Pascal Thome, Markus Stricker
https://arxiv.org/abs/2403.13673

Employing semi-supervised learning for high-resolution segmentation of crystal defects
Materials characterization using electron backscatter diffraction (EBSD) requires indexing the orientation of the measured region from Kikuchi patterns. In the presence of defects the quality of the Kikuchi patterns can degrade. Or if the measured region contains a grain boundary, two or more orientations can cause pattern overlap which may lead to erroneous orientation calculations. In this work we show that constrained non-negative matrix factorization can be successfully employed to characte…

This https://arxiv.org/abs/2305.18436 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Statistically Optimal K-means Clustering via Nonnegative Low-rank Semidefinite Programming
$K$-means clustering is a widely used machine learning method for identifying patterns in large datasets. Semidefinite programming (SDP) relaxations have recently been proposed for solving the $K$-means optimization problem that enjoy strong statistical optimality guarantees, but the prohibitive cost of implementing an SDP solver renders these guarantees inaccessible to practical datasets. By contrast, nonnegative matrix factorization (NMF) is a simple clustering algorithm that is widely used b…

Low-rank generalized alternating direction implicit iteration method for solving matrix equations
Juan Zhang, Wenlu Xun
https://arxiv.org/abs/2404.06034 ht…

Low-rank generalized alternating direction implicit iteration method for solving matrix equations
This paper presents an effective low-rank generalized alternating direction implicit iteration (R-GADI) method for solving large-scale sparse and stable Lyapunov matrix equations and continuous-time algebraic Riccati matrix equations. The method is based on generalized alternating direction implicit iteration (GADI), which exploits the low-rank property of matrices and utilizes the Cholesky factorization approach for solving. The advantage of the new algorithm lies in its direct and efficient l…

Accelerating Matrix Factorization by Dynamic Pruning for Fast Recommendation
Yining Wu, Shengyu Duan, Gaole Sai, Chenhong Cao, Guobing Zou
https://arxiv.org/abs/2404.04265

Accelerating Matrix Factorization by Dynamic Pruning for Fast Recommendation
Matrix factorization (MF) is a widely used collaborative filtering (CF) algorithm for recommendation systems (RSs), due to its high prediction accuracy, great flexibility and high efficiency in big data processing. However, with the dramatically increased number of users/items in current RSs, the computational complexity for training a MF model largely increases. Many existing works have accelerated MF, by either putting in additional computational resources or utilizing parallel systems, intro…

Module factorizations and Gorenstein projective modules
Xiao Wu Chen
https://arxiv.org/abs/2402.11613 https://arxiv.org/pdf/2402.1161…

Module factorizations and Gorenstein projective modules
For a regular normal element in an arbitrary ring, we study the category of its module factorizations. The cokernel functor relates module factorizations with Gorenstein projective components to Gorenstein projective modules over the quotient ring. The results are vast extensions of Eisenbud's matrix factorization theorem.

This https://arxiv.org/abs/2305.18436 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Statistically Optimal K-means Clustering via Nonnegative Low-rank Semidefinite Programming
$K$-means clustering is a widely used machine learning method for identifying patterns in large datasets. Semidefinite programming (SDP) relaxations have recently been proposed for solving the $K$-means optimization problem that enjoy strong statistical optimality guarantees, but the prohibitive cost of implementing an SDP solver renders these guarantees inaccessible to practical datasets. By contrast, nonnegative matrix factorization (NMF) is a simple clustering algorithm that is widely used b…

Bearing damage detection with orthogonal and non-negative low-rank feature extraction
Mateusz Gabor, Rafal Zdunek, Agnieszka Wylomanska, Radoslaw Zimroz
https://arxiv.org/abs/2403.12564

Bearing damage detection with orthogonal and non-negative low-rank feature extraction
Local damage of bearings can be detected as a weak cyclic and impulsive component in a highly noisy measured signal. A key problem is how to extract the signal of interest (SOI) from the raw signal, i.e., how to identify and design an optimal filter. To tackle this problem, we propose to use stochastic sampled orthogonal non-negative matrix factorization for extracting frequency-based features from a spectrogram of the measured signal. The proposed algorithm finds a selective filter that is tai…

This https://arxiv.org/abs/2404.12155 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Low-rank alternating direction doubling algorithm for solving large-scale continuous time algebraic Riccati equations
This paper proposes an effective low-rank alternating direction doubling algorithm (R-ADDA) for computing numerical low-rank solutions to large-scale sparse continuous-time algebraic Riccati matrix equations. The method is based on the alternating direction doubling algorithm (ADDA), utilizing the low-rank property of matrices and employing Cholesky factorization for solving. The advantage of the new algorithm lies in computing only the $2^k$-th approximation during the iterative process, inste…

This https://arxiv.org/abs/2305.18436 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Statistically Optimal K-means Clustering via Nonnegative Low-rank Semidefinite Programming
$K$-means clustering is a widely used machine learning method for identifying patterns in large datasets. Semidefinite programming (SDP) relaxations have recently been proposed for solving the $K$-means optimization problem that enjoy strong statistical optimality guarantees, but the prohibitive cost of implementing an SDP solver renders these guarantees inaccessible to practical datasets. By contrast, nonnegative matrix factorization (NMF) is a simple clustering algorithm that is widely used b…