Abstract

Research on network data with nodal covariates has received increasing attention, yet

few studies have focused on nonlinear patterns among nodal covariates. In this work, we propose a

model-free framework that leverages network information to achieve nonlinear dimension reduction

of nodal covariates. An efficient regularization-based estimation procedure is proposed and the

asymptotic properties of estimated projection directions are studied. For the downstream task of

community detection, we propose a two-step algorithm along with theoretical guarantees. Besides,

we draw connections between our method and three existing kernel methods. Extensive simulations

and a real data analysis support the advantages of the proposed method.

Key words and phrases: Nonlinear dimension reduction, Community detection, Degree-corrected stochastic block-model

Information

Preprint No.SS-2025-0362
Manuscript IDSS-2025-0362
Complete AuthorsZhonghan Wang, Shenbin Zheng, Junlong Zhao
Corresponding AuthorsJunlong Zhao
Emailszhaojunlong928@126.com

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Acknowledgments

Junlong Zhao’s research was supported in part by National Natural Science Foundation

of China grants No.12371288 and 12131006, and the Fundamental Research Funds for the

Central Universities.

Supplementary Materials

The Supplementary Materials include proofs of all the theoretical results in the main text,

additional simulations, discussions and theoretical results.

Supplementary materials are available for download.