Matrix Factorization Techniques in Machine Learning, Signal Processing, and Statistics

Du, Ke-Lin; Swamy, M.N.S.; Wang, Zhangquan; Mow, Wai Ho

doi:10.3390/math11122674

Cited by 12 publications

(4 citation statements)

References 372 publications

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“…In this regard, the factor structure serves as a filter to gain regularization in estimation. Using factor models this way is common in many signal-processing, genetics, and machine-learning domains (Bhattacharya & Dunson, 2011;Du et al, 2023;Sanyal & Ferreira, 2012). The limitation, however, is that the current development is inappropriate for inference on the latent factor structure.…”

Section: Discussionmentioning

confidence: 99%

Estimating Correlations in Low-Reliability Settings With Constrained Hierarchical Models

Mehrvarz,

Rouder

2024

Preprint

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It is popular to study individual differences in cognition with experimental tasks, and the main goal in such approaches is to analyze the pattern of correlations across a battery of tasks and measures. One difficulty is that experimental tasks are often low in reliability as effects are small relative to trial-by-trial variability. Consequently, it remains difficult to accurately estimate correlations. One approach that seems attractive is hierarchical modeling where trial-by-trial variability and variability across conditions, tasks, and individuals are modeled separately. Here we show that hierarchical models may reduce the error in estimating correlations up to 46%, but only if substantive constraint is imposed. The approach here is Bayesian, and we develop novel Bayesian hierarchical factor models for experiments where trials are nested in conditions, tasks, and individuals. The prior on covariances across tasks can either be unconstrained, in which there is little error reduction, or constrained, in which there is substantial error reduction. The constraints are: 1. There is a low-dimension factor structure underlying the covariation across tasks; and 2. All loadings are nonnegative leading to a positive manifold on correlations. We argue that both of these assumptions are reasonable in cognitive domains, and that with them, researchers may profitably use hierarchical models to estimate correlations across tasks in low-reliability settings.

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Section: Discussionmentioning

confidence: 99%

Estimating Correlations in Low-Reliability Settings With Constrained Hierarchical Models

Mehrvarz,

Rouder

2024

Preprint

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“…The NABBH algorithm improves the convergence speed by simplifying the computational complexity of the inverse operation of Hessian matrix [43]; that is, only the inverse matrix of the first derivative matrix of the function is calculated, and the second derivative matrix of the function is omitted. A step-size selection strategy is designed to speed up the convergence of the algorithm.…”

Section: Performance Analysis Of Adaptive Parameter Selection Methodsmentioning

confidence: 99%

“…By introducing a non-monotonic Wolfe-type strategy into the memory gradient method, the global optimal solution is obtained. The purpose of improving convergence speed is achieved by adding step-size constraints [43]. In theory, the proposed adaptive parameter selection method has better global convergence and convergence speeds.…”

Section: Performance Analysis Of Adaptive Parameter Selection Methodsmentioning

confidence: 99%

A Maximally Split and Adaptive Relaxed Alternating Direction Method of Multipliers for Regularized Extreme Learning Machines

et al. 2023

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One of the significant features of extreme learning machines (ELMs) is their fast convergence. However, in the big data environment, the ELM based on the Moore–Penrose matrix inverse still suffers from excessive calculation loads. Leveraging the decomposability of the alternating direction method of multipliers (ADMM), a convex model-fitting problem can be split into a set of sub-problems which can be executed in parallel. Using a maximally splitting technique and a relaxation technique, the sub-problems can be split into multiple univariate sub-problems. On this basis, we propose an adaptive parameter selection method that automatically tunes the key algorithm parameters during training. To confirm the effectiveness of this algorithm, experiments are conducted on eight classification datasets. We have verified the effectiveness of this algorithm in terms of the number of iterations, computation time, and acceleration ratios. The results show that the method proposed by this paper can greatly improve the speed of data processing while increasing the parallelism.

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“…This decomposition exposes underlying structures and patterns within the data. The primary aim is to approximate the original matrix using these simplified components, which enhances the manageability of data analysis [1].…”

Section: Emotion Detectionmentioning

confidence: 99%

Recommendation system based on facial expression

2023

IRJMETS

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Understanding human emotions relies heavily on interpreting facial expressions, which are a crucial aspect of non-verbal communication. Yet, the intricacies of facial muscle movements make it a formidable task to accurately model these expressions when working with static images, especially when considering different facial poses. To tackle this challenge, we introduce an innovative method that harnesses 3D technology to capture and decode facial expressions more effectively. Moreover, we propose a contour alignment technique designed to enhance modeling precision by autonomously repositioning 3D contour landmarks to align with static images. The acquired input representing facial expressions can be parametrically adjusted, enabling the creation of a diverse range of facial expressions through an expression transfer approach grounded in the Facial Action Coding System (FACS).In an era marked by the explosive growth of the digital landscape and an overwhelming deluge of information, the quest for a reliable method to offer tailored recommendations from this vast sea of data has become an imperative. In response to this challenge, recommendation systems have been engineered. One intriguing avenue involves the utilization of pretrained models such as VGG16, harmoniously amalgamated to forge a tool that could prove immensely advantageous for humanity.We envision that our system will extend its benefits to diverse sectors, encompassing the prediction of films, music selections, and various commodities, among others. The adaptability of this system holds the potential to elevate decision-making processes and furnish invaluable guidance across domains.

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Matrix Factorization Techniques in Machine Learning, Signal Processing, and Statistics

Cited by 12 publications

References 372 publications

Estimating Correlations in Low-Reliability Settings With Constrained Hierarchical Models

Estimating Correlations in Low-Reliability Settings With Constrained Hierarchical Models

A Maximally Split and Adaptive Relaxed Alternating Direction Method of Multipliers for Regularized Extreme Learning Machines

Recommendation system based on facial expression

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