Title: sparseGeoHOPCA: A Geometric Solution to Sparse Higher-Order PCA Without Covariance Estimation
Primary area: optimization
Keywords: Sparse Higher-Order Principal Component Analysis, Tensor Optimization

Abstract: This paper proposes sparseGeoHOPCA, a geometric framework for sparse higher-order principal component analysis (SHOPCA). 
 The method unfolds the input tensor along each mode and reformulates the resulting subproblems as binary linear programs, transforming the nonconvex sparse objective into a tractable geometric form. 
 This eliminates covariance estimation and iterative deflation, leading to improved efficiency and interpretability in high-dimensional and unbalanced settings. 
 Theoretical equivalence with the original SHOPCA formulation is established, and error bounds linked to PCA residuals are derived, providing data-dependent guarantees. 
 The algorithm has total complexity $O(\sum_{n=1}^{N} (k_n^3 + J_n k_n^2))$, scaling linearly with tensor size.
 Extensive experiments demonstrate accurate sparse support recovery, stable classification under 10× compression, and high-quality ImageNet reconstruction, highlighting robustness and versatility.