A Theoretical Guarantees for FINE Algorithm

This section provides the detailed proof for Theorem 1 and the lower bounds of the precision and recall. We derive such theorems with the concentration inequalities in probabilistic theory. In this section, we frequently use the spectral norm. U = I when U is an orthogonal matrix). A.2 Proof of Theorem 1 We deal with some require lemmas which are used for the proof of Theorem 1. Lemma 1. Lemma 3. (David-Kahan sin Theorem) F or given symmetric matrices A, B R Assume that A and A + B have non-negative eigenvalues.