A Generalized Model of Complex Allometry I: Formal Setup, Identification Procedures and Applications to Non-Destructive Estimation of Plant Biomass Units

Abstract

(1) Background: We previously demonstrated that customary regression protocols for curvature in geometrical space all derive from a generalized model of complex allometry combining scaling parameters expressing as continuous functions of covariate. Results highlighted the relevance of addressing suitable complexity in enhancing the accuracy of allometric surrogates of plant biomass units. Nevertheless, examination was circumscribed to particular characterizations of the generalized model. Here we address the general identification problem. (2) Methods: We first suggest a log-scales protocol composing a mixture of linear models weighted by exponential powers. Alternatively, adopting an operating regime-based modeling slant we offer mixture regression or Takagi–Sugeno–Kang arrangements. This last approach allows polyphasic identification in direct scales. A derived index measures the extent on what complexity in arithmetic space drives curvature in arithmetical space. (3) Results: Fits on real and simulated data produced proxies of outstanding reproducibility strength indistinctly of data scales. (4) Conclusions: Presented analytical constructs are expected to grant efficient allometric projection of plant biomass units and also for the general settings of allometric examination. A traditional perspective deems log-transformation and allometry inseparable. Recent views assert that this leads to biased results. The present examination suggests this controversy can be resolved by addressing adequately the complexity of geometrical space protocols

Assessment of a Takagi–Sugeno-Kang fuzzy model assembly for examination of polyphasic loglinear allometry

“…Each subdivision associates to a linear sub model. Brokenline regression (Beckman & Cook, 1979;Ertel & Fowlkes, 1976;Tsuboi et al, 2018;Ramírez-Ramírez et al, 2019;Muggeo, 2003;Echavarria-Heras et al, 2019b). Forbes & López (1989) furnish an empirical approach to identification of PLA patterns.…”

“…In particular, soft computing techniques entail modelling procedures, which are supplemental to customary statistics and probability approaches and that bear tolerance to imprecision, uncertainty, partial truth and approximation (Baldwin, Martin & Azvine, 1998). For instance, identification and control of nonlinear systems exemplifies a subject that has greatly benefited by adoption of related hybrid modeling schemes (Bonissone et al, 1999;Kawaji, 2002;Vrkalovic, Lunca & Borlea, 2018;Chen, 2001;Echavarria-Heras et al, 2019b). Implementation of soft computing protocols include techniques of fuzzy set theory, neural networks, probabilistic reasoning, rough sets, machine learning, and evolutionary computing (Zadeh, 1993;Oduguwa, Tiwari & Roy, 2005;Bello & Verdegay, 2012;Ibrahim, 2016;Al-Kaysi et al, 2017;Herrera-Viedma & López-Herrera, 2010).…”

“…Local models valid over restricted domains are combined by smooth interpolation into an overall general output (Johansen & Foss, 1997). Therefore, this structure naturally hosts heterogeneity as conceived by PLA (Echavarria-Heras et al, 2019b). One example of a hybrid-operating regime based modeling is the Takagi-Sugeno-Kang fuzzy model (Sugeno & Kang, 1988;Takagi & Sugeno, 1985) (TSK in what follows).…”

“…The outstanding approximation capabilities of a TSK fuzzy model entail reliable identification of whatever MPCA functional form renders necessary in arithmetical space (Echavarría-Heras et al, 2018a;Echavarria-Heras et al, 2019b). Adaptation of the TSK fuzzy model for that aim will be forward designated by means of the TSK-MPCA abbreviation.…”

“…Moreover, from a theoretical standpoint a TSK-PLA representation implies an allometric model in arithmetical space that seemingly fits MPCA. This expresses the response as a generalized power function including scaling parameters expressed as functions of the covariate (Bervian, Fontoura & Haimovici, 2006;Echavarría-Heras et al, 2019a;Echavarria-Heras et al, 2019b). But, above all, present fuzzy approach contributes by offering a way of overcoming the controversy between a school considering analysis in geometrical space as a must in allometry, and critics claiming that consistent results can only come along by using a MPCA formulation followed by nonlinear regression protocol in the original scale of data.…”