High-dimensional Clustering and Signal Recovery under Block Signals

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.