Riemannian manifold

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• Published Subscription Original Research 28 Aug 2026

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

  By Chethana N S, Markala Karthik, S. Vairachilai

  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 …

  Published in Recent Trends in Mathematics · Vol. 3, Issue 2, 2026 · pp. 49–55 Read article →