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arXiv · 2611.08227

Fast Functional Clustering via Closed-Form Covariance Updates

Yu Wang·Jiaze Guo·Yao Chen·Tianxiang Hao·Rongling Wu
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Abstract

Functional clustering identifies coordinated molecular profiles, but repeated numerical covariance optimization can make mixture-model fitting computationally demanding. We develop a fast functional clustering procedure for joint analysis across conditions, combining linear mean profiles on a standardized log niche coordinate with first-order structured antedependence (SAD(1)) covariance. Weighted residual statistics yield closed-form conditional covariance updates under four parameter-sharing specifications, while an innovation representation simplifies likelihood evaluation. In same-R comparisons with numerical optimization of identical conditional objectives, the closed-form solver was 91.5--201.4 times as fast, with objective agreement in all 60 targets. Under matched complete mixture fits, it achieved a 1.87--2.37-fold speedup with identical cluster assignments. Recovery simulations showed higher module classification accuracy and lower mean-curve error than $K$-means and a Gaussian mixture with shared full covariance when the mean structure was correctly specified. SAD(1) provided an additional recovery gain under strong residual correlation, whereas curved-mean controls identified the importance of an appropriate mean family. Applications to single-condition gut microbiota, paired leaf--root microbiota and three-visit human gut multi-omics illustrate the framework across different numbers of conditions. Closed-form covariance estimation makes joint functional clustering substantially faster while retaining the fitted model's likelihood and assignments.

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Yu Wang, Jiaze Guo, Yao Chen, Tianxiang Hao, Rongling Wu. 2026-11-05. Fast Functional Clustering via Closed-Form Covariance Updates. https://arxiv.org/abs/2611.08227

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