Feature selection in weakly coherent matrices
This addresses feature extraction in weakly coherent matrices, which is incremental as it builds on perturbation analysis for specific matrix conditions.
The paper tackles the problem of selecting a submatrix with a smallest singular value above a specified threshold by proposing a perturbation bound for the smallest singular value when appending a column to a matrix with low coherence, and uses this bound to develop a fast algorithm for feature extraction.
A problem of paramount importance in both pure (Restricted Invertibility problem) and applied mathematics (Feature extraction) is the one of selecting a submatrix of a given matrix, such that this submatrix has its smallest singular value above a specified level. Such problems can be addressed using perturbation analysis. In this paper, we propose a perturbation bound for the smallest singular value of a given matrix after appending a column, under the assumption that its initial coherence is not large, and we use this bound to derive a fast algorithm for feature extraction.