Functional and Object-Oriented Data Analysis for Complex Biomedical, Environmental and Socioeconomic Systems
Year: 2026
Type: article
Abstract: : Biomedical, environmental and socioeconomic systems increasingly generate data whose natural observational units are curves, surfaces, images, probability distributions, networks, trees and other structured objects. Conventional vectorisation can destroy temporal continuity, topology, phase variation or intrinsic geometry, thereby producing unstable estimates and scientifically weak interpretations. This paper develops an integrated analytical architecture that combines functional data analysis with object-oriented data analysis for complex, multiscale and dependent systems. The proposed Integrated Functional–Object Systems Analytics (IFOSA) Framework links basis representation, registration, functional principal components, Fréchet means and regression, metric-space learning, graph and tensor operators, dynamic state equations, uncertainty calibration and domain-specific decision criteria. Its mathematical formulation covers Hilbert-space functional models, matrix basis expansions, nonlinear object regression, stochastic dynamics, regularised optimisation and a risk-adjusted master objective. An illustrative numerical model uses normalised 0–10 values for functional fidelity, object-geometry preservation, multiscale integration, predictive performance, interpretability, robustness and data quality, together with bias and uncertainty penalties. The resulting IFOSA score is 7.58, indicating promising analytical capacity under the stated assumptions; the value is demonstrative rather than empirical. Comparative analysis suggests that geometry-aware integration is most valuable when observations are irregular, phase-varying, non-Euclidean or linked across levels, whereas simpler functional models may remain preferable for densely observed homogeneous curves. The paper contributes a coherent methodology for biomedical monitoring, environmental intelligence and socioeconomic policy analysis while emphasising validation, privacy, fairness, computational reproducibility and transportability. It offers a research programme rather than a claim of empirically proven superiority, and it identifies the data and experiments required for substantive validation. Keywords: functional data analysis; object-oriented data analysis; Fréchet regression; metric-space statistics; functional principal component analysis; shape analysis; manifold learning; multilevel functional data; spatiotemporal modelling; biomedical signals; environmental profiles; socioeconomic distributions; graph-valued data; uncertainty quantification; complex systems analytics
Author: Murali Krishna Pasupuleti
Institution: National Education Services
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W7171194566