Regression Coefficient Derivation via Fractional Calculus Framework

Awadalla, Muath; Noupoue, Yves Yannick Yameni; Tandoğdu, Yücel; Abuasbeh, Kinda

doi:10.1155/2022/1144296

Cited by 2 publications

(2 citation statements)

References 13 publications

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“…It is shown that models not considering fractional derivatives can be outperformed using the presented concepts. Awadalla et al [67] presented a similar approach where the same idea is used for fractional linear and fractional squared regression, i.e., the derivatives to derive the minimum are fractionalized. This approach also shows the applicability of the proposed ideas to standard datasets.…”

Section: Fractional Gradient-based Optimizationmentioning

confidence: 99%

Combining Fractional Derivatives and Machine Learning: A Review

Raubitzek

Mallinger²,

Neubauer³

2022

Entropy

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Fractional calculus has gained a lot of attention in the last couple of years. Researchers have discovered that processes in various fields follow fractional dynamics rather than ordinary integer-ordered dynamics, meaning that the corresponding differential equations feature non-integer valued derivatives. There are several arguments for why this is the case, one of which is that fractional derivatives inherit spatiotemporal memory and/or the ability to express complex naturally occurring phenomena. Another popular topic nowadays is machine learning, i.e., learning behavior and patterns from historical data. In our ever-changing world with ever-increasing amounts of data, machine learning is a powerful tool for data analysis, problem-solving, modeling, and prediction. It has provided many further insights and discoveries in various scientific disciplines. As these two modern-day topics hold a lot of potential for combined approaches in terms of describing complex dynamics, this article review combines approaches from fractional derivatives and machine learning from the past, puts them into context, and thus provides a list of possible combined approaches and the corresponding techniques. Note, however, that this article does not deal with neural networks, as there is already extensive literature on neural networks and fractional calculus. We sorted past combined approaches from the literature into three categories, i.e., preprocessing, machine learning and fractional dynamics, and optimization. The contributions of fractional derivatives to machine learning are manifold as they provide powerful preprocessing and feature augmentation techniques, can improve physically informed machine learning, and are capable of improving hyperparameter optimization. Thus, this article serves to motivate researchers dealing with data-based problems, to be specific machine learning practitioners, to adopt new tools, and enhance their existing approaches.

show abstract

Section: Fractional Gradient-based Optimizationmentioning

confidence: 99%

Combining Fractional Derivatives and Machine Learning: A Review

Raubitzek

Mallinger²,

Neubauer³

2022

Entropy

View full text Add to dashboard Cite

show abstract

“…It is shown that models not considering fractional derivatives can be outperformed using the presented concepts. Awadalla et al [66] present a similar approach where the same idea is used for fractional linear and fractional squared regression, i.e., the derivatives to derive the minimum are fractionalized. This approach also shows the applicability of the proposed ideas to standard data sets.…”

Section: Fractional Gradient Based Optimizationmentioning

confidence: 99%

Combining Fractional Derivatives and Supervised Machine Learning: A Review

Raubitzek¹,

Mallinger²,

Neubauer³

2022

Preprint

View full text Add to dashboard Cite

Fractional calculus gained a lot of attention in the last couple of years. Researchers discovered that processes in various fields follow rather fractional dynamics than ordinary integer-ordered dynamics, meaning the corresponding differential equations feature non-integer valued derivatives. There are several arguments for why this is the case, one of them being that fractional derivatives’ inherit spatiotemporal memory and/or the ability to express complex naturally occurring phenomena. Another popular topic nowadays is machine learning, i.e., learning behavior and patterns from historical data. In our ever-changing world with ever-increasing amounts of data, machine learning is a powerful tool for data analysis, problem-solving, modeling, and prediction. It further provides many insights and discoveries in various scientific disciplines. As these two modern-day topics provide a lot of potential for combined approaches to describe complex dynamics, this article reviews combined approaches of fractional derivatives and machine learning from the past, puts them into context, and thus provides a list of possible combined approaches and the corresponding techniques. Note, however, that this article does not deal with neural networks, as there already is profound literature on neural networks and fractional calculus. We sorted past combined approaches from the literature into three categories, i.e., preprocessing, machine learning &amp; fractional dynamics, and optimization. The contributions of fractional derivatives to machine learning are manifold as they provide powerful preprocessing and feature augmentation techniques, can improve physically informed machine learning, and are capable of improving hyperparameter optimization. Thus, this article serves to motivate researchers dealing with data-based problems, to be specific machine learning practitioners, to adopt new tools and enhance their existing approaches.

show abstract

Regression Coefficient Derivation via Fractional Calculus Framework

Cited by 2 publications

References 13 publications

Combining Fractional Derivatives and Machine Learning: A Review

Combining Fractional Derivatives and Machine Learning: A Review

Combining Fractional Derivatives and Supervised Machine Learning: A Review

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