English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Let $C$ be a real-valued $M\times M$ matrix with singular values$\lambda_1\ge...\ge\lambda_M$ and $E$ a random matrix of centered i.i.d.entries with finite fourth moment. In this paper we give a universal upperbound on the expectation of $||\hat\pi_rX||_{S_2}^2-||\pi_rX||^2_{S_2}$, where$X:=C+E$ and $\hat\pi_r$ (resp. $\pi_r$) is a rank-$r$ projection maximizingthe Hilbert-Schmidt norm $||\tilde\pi_rX||_{S_2}$ (resp.$||\tilde\pi_rC||_{S_2}$) over the set $\S_{M,r}$ of all orthogonal rank-$r$projections. This result is a generalization of a theorem for Gaussian matricesdue to Rohde (2012). Our approach differs substantially from the techniques ofthe mentioned article. We analyze $||\hat\pi_rX||_{S_2}^2-||\pi_rX||^2_{S_2}$from a rather deterministic point of view by an upper bound on$||\hat\pi_rX||_{S_2}^2-||\pi_rX||^2_{S_2}$, whose randomness is totallydetermined by the largest singular value of $E$.

A universal expectation bound on empirical projections of deformed random matrices