Leave-one-out Singular Subspace Perturbation Analysis for Spectral Clustering

Understand

The singular subspaces perturbation theory is of fundamental importance in probability and statistics.

• It has various applications across different fields.
• We consider two arbitrary matrices where one is a leave-one-column-out submatrix of the other one and establish a novel perturbation upper bound for the distance between the two corresponding singular subspaces.
• It is well-suited for mixture models and results in a sharper and finer statistical analysis than classical perturbation bounds such as Wedin's Theorem.