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Although extreme learning machines (ELM) are widely used, they also suffer from multicollinearity. This work integrates ridge and Liu estimators into ELM theory to improve robustness. Two two-parameter algorithms (TP1-ELM and TP2-ELM) are proposed to combine both estimators within ELM. Extensive benchmarking on seven datasets shows consistent superiority over ELM-focused methods and traditional techniques for regression and classification, especially under multicollinearity.",{"@graph":69,"@context":114},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/novel-statistical-regularized-extreme-learning-algorithm-to-address-the-multicollinearity-in-machine-learning/290606/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/novel-statistical-regularized-extreme-learning-algorithm-to-address-the-multicollinearity-in-machine-learning/290606.png","ImageObject",300,407,{"name":92,"@type":93},"Ezra","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-09-17",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108],{"name":109,"@type":110,"acceptedAnswer":111},"What evidence is used to validate the algorithms’ effectiveness?","Question",{"text":112,"@type":113},"The algorithms are benchmarked against ELM, ELM-based algorithms, and other commonly used machine learning techniques across seven diverse datasets. 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This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10. 1109/ACCESS.2024.3432490  \nDate of publication xxxx 00, 0000, date of current version xxxx 00, 0000.  \nDigital Object Identifier 10.1109/ACCESS.2023.0322000  \nNovel statistical regularized extreme learning algorithm to address the multicollinearity in machine learning  \nHASAN YILDIRIM 1  \n1Karamanoğlu Mehmetbey University, Karaman, 70100, Turkey ([e-mail: hasanyildirim@kmu.edu.tr](e-mail: hasanyildirim@kmu.edu.tr))  \nCorresponding author: Hasan YILDIRIM ([e-mail: hasanyildirim@kmu.edu.tr](e-mail: hasanyildirim@kmu.edu.tr)).  \n ABSTRACT The multicollinearity problem is a common phenomenon in data-driven studies, significantly affecting the performance of machine learning algorithms during the process of extracting information from data. Despite its widespread use across various fields, the extreme learning machine (ELM) also suffers from multicollinearity issues. To address this challenge, the ridge and Liu estimators, drawn from statistics literature, have been integrated into ELM theory, resulting in a notable advancement. This study aims to further enhance the capabilities of ridge and Liu estimators within the ELM framework by introducing two innovative two-parameter algorithms (TP1-ELM and TP2-ELM) that simultaneously incorporate both estimators. The proposed algorithms undergo comprehensive benchmarking against ELM, ELM-based algorithms, and other commonly used machine learning techniques across seven diverse datasets. Benchmark results demonstrate that the proposed algorithms consistently outperform both ELM-focused approaches and traditional machine learning algorithms on most datasets, yielding more generalizable and stable results. These findings suggest that the proposed algorithms offer a promising alternative to traditional machine learning techniques for regression and classification tasks, particularly in scenarios where multicollinearity is a concern.  \n INDEX TERMS Extreme learning machine, Liu estimator, machine learning, multicollinearity, ridge estimator, Tikhonov regularization.  \nI. INTRODUCTION  \nIn parallel with the facilitation of the acquisition of data, the need to make sense of it and transform it into valuable insights has emerged. For this purpose, numerous algorithms have been developed in the field of artificial intelligence, especially in the branch of machine learning. Artificial neural networkoriented algorithms stand out among these algorithms and continue to be intensively developed in the academic field.  \nArtificial neural networks have been used in practically every field due to its capabilities such as i) capturing complex patterns, ii) creating non-linear models, iii) flexibility. In general, artificial neural networks are classified into feedforward and feed-back neural networks, with feed-forward networks leading the way with its simplicity [1], [2] . Feedforward networks, studied first in the literature, have a number of parameters to be determined, such as learning rate, momentum, period, stopping criteria, input weights and biases. Huang et al. [3], [4], proposed the extreme learning machine (ELM) algorithm as a single-layer feed-forward neural network capable of being used in both regression and classifica-  \ntion tasks, essentially eliminating the process of determining such parameters and avoiding risks related to slowness, local optimum and over-fitting.  \nThe ELM algorithm assigns input layer weights and hidden layer parameters (e.g. biases) randomly and provides a closed-form solution, thereby achieving i) faster trainability, ii) reasonable generalization performance, iii) universal approximation capability, iv) applicability in machine learning domains such as regression, classification and clustering, and v) relatively low human intervention [5] . Due to the consequence o","cbCaiaMsMPhhHCZz","https://ap.wps.com/l/cbCaiaMsMPhhHCZz","pdf",1236110,13,"English","# Introduction\n## Literature Review of Related Works","[{\"question\":\"What evidence is used to validate the algorithms’ effectiveness?\",\"answer\":\"The algorithms are benchmarked against ELM, ELM-based algorithms, and other commonly used machine learning techniques across seven diverse datasets. Results show better performance and more stable, generalizable outcomes on most datasets.\"}]","Novel Statistical Regularized Extreme Learning Algorithm to Address the Multicollinearity in Machine Learning | PDF",1789642186,33]