Fractional Riemannian Fuzzy C-Means with Time-Series Regularization for Economic Manifold Forecasting

Year : 2026 | Volume : 03 | Issue : 02 | Page : 49 55
By

Chethana N S,

Markala Karthik,

S. Vairachilai,

  1. Student, Department of Mathematics, Department of Mathematics, Central University of Karnataka, Kalaburagi, Karnataka, India
  2. Assistant Professor, Department of Electrical and Electronics Engineering, SR University, Warangal, Telangana, India
  3. Associate Professor, School of Computer Science and Artificial Intelligence, SR University, Warangal, Telangana, India

Abstract

A fractional Riemannian fuzzy c-means framework is proposed for uncertain economic forecasting on non-Euclidean data domains. Observations are represented on a Riemannian manifold, cluster centres are intrinsic prototypes, and a latent fuzzy regime signal is regularised by both autoregressive and fractional-memory penalties. The resulting objective couples geometric clustering with time-series consistency, thereby discouraging partitions that are locally plausible but temporally incoherent. Closed-form membership updates, exponential-map centre updates, normal equations for the predictive coefficients, and a monotone descent property are derived. A manifold-valued forecasting rule is then obtained from predicted fuzzy memberships and intrinsic barycentres. Numerical experiments on stylised quarterly economic compositions show improved regime smoothness and lower forecast error relative to Euclidean fuzzy c-means baselines. The paper contributes a mathematically dense RTM-style model that integrates fuzzy clustering, manifold optimisation, and fractional time-series analysis.

Keywords: Fuzzy c-means, Riemannian manifold, fractional memory, economic forecasting, intrinsic clustering, time series.

[This article belongs to Recent Trends in Mathematics ]

How to cite this article: Chethana N S, Markala Karthik, S. Vairachilai. Fractional Riemannian Fuzzy C-Means with Time-Series Regularization for Economic Manifold Forecasting. Recent Trends in Mathematics. 2026; 03(02):49-55.
How to cite this URL: Chethana N S, Markala Karthik, S. Vairachilai. Fractional Riemannian Fuzzy C-Means with Time-Series Regularization for Economic Manifold Forecasting. Recent Trends in Mathematics. 2026; 03(02):49-55. Available from: https://journals.stmjournals.com/rtm/article=2026/view=254996

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Regular Issue Subscription Original Research
Volume 03
Issue 02
Received 14/03/2026
Accepted 13/08/2026
Published 28/08/2026
Publication Time 167 Days

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