2026-10-14T19:10:35Z https://api.figshare.com/v2/oai

oai:figshare.com:article/34014835 2026-09-28T15:03:13Z category_146 category_7 category_12 category_21 category_46 category_734 category_931 category_811 category_132 portal_87 item_type_3 month_year_09_2026

High-dimensional Clustering and Signal Recovery under Block Signals Wu Su (1499908) Yumou Qiu (823634) Space Science Medicine Cell Biology Biotechnology Immunology Biological Sciences not elsewhere classified Information Systems not elsewhere classified Mathematical Sciences not elsewhere classified Infectious Diseases block signals clustering high dimensionality minimax signal recovery <p>This paper studies computationally efficient methods and minimax optimality for high-dimensional clustering and signal recovery under block signal structures. We propose cross-block feature aggregation PCA (CFA-PCA) and moving average PCA (MA-PCA) for sparse and dense block signals, respectively. Both methods adaptively exploit block structures and apply to non-Gaussian data with heterogeneous variances and non-diagonal covariance matrices. CFA uses a cross-block statistic to aggregate and select signals nonparametrically when cluster labels are unknown. We establish consistency for clustering and signal recovery under mild conditions and weaker signal strengths than methods that ignore block structures. We further derive statistical and computational minimax lower bounds, with the latter restricted to polynomial-time algorithms, thereby characterizing regions of statistical and computational impossibility. CFA-PCA and MA-PCA attain the computational minimax lower bounds in the sparse and dense regimes, respectively, establishing their computational minimax optimality. We also propose a tuning-parameter selection procedure based on post-clustering signal recovery. Simulations demonstrate strong finite-sample performance, and an application to global temperature change illustrates the practical utility of the proposed methods.</p> 2026-09-28T15:03:13Z Dataset Dataset 10.6084/m9.figshare.34014835.v1 https://figshare.com/articles/dataset/High-dimensional_Clustering_and_Signal_Recovery_under_Block_Signals/34014835 CC BY 4.0