Why Do Big Data and Machine Learning Entail the Fractional Dynamics?

Niu, Haoyu; Chen, YangQuan; West, Bruce J.

doi:10.3390/e23030297

Cited by 24 publications

(10 citation statements)

References 154 publications

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“…Thus we describe our findings in this context and consider the results of another article by Niu. et al [85], titled "Why Do Big Data and Machine Learning Entail the Fractional Dynamics?" in which the researchers further discuss ideas on the overlap between machine learning and fractional calculus, specifically for big data.…”

Section: Bringing It All Togethermentioning

confidence: 99%

“…al. [85], variability is the central aspect of big data where employing fractional calculus and machine learning can be beneficial. Thus we recommend considering approaches combining fractional derivatives and machine learning when dealing with variability in data and further recommend considering these for big data approaches.…”

Section: Variabilitymentioning

confidence: 99%

“…Thus we recommend considering approaches combining fractional derivatives and machine learning when dealing with variability in data and further recommend considering these for big data approaches. As the topic of big data would unnecessarily blow up this discussion, we refer the interested reader to [85,87].…”

Section: Variabilitymentioning

confidence: 99%

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Combining Fractional Derivatives and Supervised Machine Learning: A Review

Raubitzek¹,

Mallinger²,

Neubauer³

2022

Preprint

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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.

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Section: Bringing It All Togethermentioning

confidence: 99%

Section: Variabilitymentioning

confidence: 99%

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Combining Fractional Derivatives and Supervised Machine Learning: A Review

Raubitzek¹,

Mallinger²,

Neubauer³

2022

Preprint

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“…That strategy has proven to be extraordinarily successful, even surviving the introduction of fractals into its modeling, until quite recently. The true complexity of medical networks has been revealed with the development and implementation of ever more sensitive sensors and mathematically sophisticated data processing techniques (Niu et al, 2021). These developments have led to a divergence of the modeling strategies appropriate for the physical sciences from those for the life sciences.…”

Section: Introductionmentioning

confidence: 99%

The Fractal Tapestry of Life: II Entailment of Fractional Oncology by Physiology Networks

West

2022

Front. Netw. Physiol.

Self Cite

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This is an essay advocating the efficacy of using the (noninteger) fractional calculus (FC) for the modeling of complex dynamical systems, specifically those pertaining to biomedical phenomena in general and oncological phenomena in particular. Herein we describe how the integer calculus (IC) is often incapable of describing what were historically thought to be simple linear phenomena such as Newton’s law of cooling and Brownian motion. We demonstrate that even linear dynamical systems may be more accurately described by fractional rate equations (FREs) when the experimental datasets are inconsistent with models based on the IC. The Network Effect is introduced to explain how the collective dynamics of a complex network can transform a many-body noninear dynamical system modeled using the IC into a set of independent single-body fractional stochastic rate equations (FSREs). Note that this is not a mathematics paper, but rather a discussion focusing on the kinds of phenomena that have historically been approximately and improperly modeled using the IC and how a FC replacement of the model better explains the experimental results. This may be due to hidden effects that were not anticapated in the IC model, or to an effect that was acknowledged as possibly significant, but beyond the mathematical skills of the investigator to Incorporate into the original model. Whatever the reason we introduce the FRE used to describe mathematical oncology (MO) and review the quality of fit of such models to tumor growth data. The analytic results entailed in MO using ordinary diffusion as well as fractional diffusion are also briefly discussed. A connection is made between a time-dependent fractional-order derivative, technically called a distributed-order parameter, and the multifractality of time series, such that an observed multifractal time series can be modeled using a FRE with a distributed fractional-order derivative. This equivalence between multifractality and distributed fractional derivatives has not received the recognition in the applications literature we believe it warrants.

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“…Big Data (BD) and Machine Learning (ML) are two of the more visible areas of research in which investigators are working to span the gap separating the understanding based on modeling in social and life sciences from the more quantitative models of physics and engineering. Niu et al (NCW) [ 7 ] maintain that the future success of these research activities is tied to the successful application of the FC and fractional order thinking (FOT) to the understanding of complex systems, to improving the processing and control of those systems and even to extending the enabling of creativity itself. The heart of the matter is that BD and ML seek to characterize complexity and of the ten characteristics used to describe BD variability is selected by NCW as the most important.…”

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confidence: 99%