Fast Functional Clustering via Closed-Form Covariance Updates
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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BibTeX
@misc{wang2026fast,
title = {{Fast Functional Clustering via Closed-Form Covariance Updates}},
author = {Yu Wang and Jiaze Guo and Yao Chen and Tianxiang Hao and Rongling Wu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08227},
eprint = {2611.08227},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08227},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fast Functional Clustering via Closed-Form Covariance Updates
AU - Yu Wang
AU - Jiaze Guo
AU - Yao Chen
AU - Tianxiang Hao
AU - Rongling Wu
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08227
UR - https://arxiv.org/abs/2611.08227
AB - 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.
ER -