A Nested $ell_{1}$-penalized Adaptive Normalized Quasi-Newton Algorithm for Sparsity-Aware Generalized Eigen-subspace Extraction

摘要

The sparsity-aware generalized eigen-subspace extraction is a modern strategy to achieve better interpretability than classical statistical data analysis, and has been realized, as sparse PCA, sparse CCA and sparse FDA, etc, in signal processing, machine learning and data sciences. For its broader applications in the scenarios of adaptive signal processing, the generalized orthogonality among the estimates of principal generalized eigenvectors is certainly desired to be exploited in the learning process. However, it seems that such adaptive learning algorithms have not yet been reported so far. In this paper, we present an algorithm by combining the idea of ℓ₁-penalized adaptive normalized quasi-Newton algorithm (Uchida and Yamada, 2018) with Nested orthogonal complement structure (NTY 2013, KYY 2017).