First-order perturbation analysis of low-rank tensor approximations based on the truncated HOSVD

Emilio Rafael Balda, Sher Ali Cheema, Jens Steinwandt, Martin Haardt, Amir Weiss, Arie Yeredor

פרסום מחקרי: פרק בספר / בדוח / בכנספרסום בספר כנסביקורת עמיתים

תקציר

The truncated version of the higher-order singular value decomposition (HOSVD) has a great significance in multi-dimensional tensor-based signal processing. It allows to extract the principal components from noisy observations in order to find a low-rank approximation of the multi-dimensional data. In this paper, we address the question of how good the approximation is by analytically quantifying the tensor reconstruction error introduced by the truncated HOSVD. We present a first-order perturbation analysis of the truncated HOSVD to obtain analytical expressions for the signal subspace error in each dimension as well as the tensor reconstruction error induced by the low-rank approximation of the noise corrupted tensor. The results are asymptotic in the signal-to-noise ratio (SNR) and expressed in terms of the second-order moments of the noise, such that apart from a zero mean, no assumptions on the noise statistics are required. Empirical simulation results verify the obtained analytical expressions.

שפה מקוריתאנגלית
כותר פרסום המארחConference Record of the 50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016
עורכיםMichael B. Matthews
מוציא לאורIEEE Computer Society
עמודים1723-1727
מספר עמודים5
מסת"ב (אלקטרוני)9781538639542
מזהי עצם דיגיטלי (DOIs)
סטטוס פרסוםפורסם - 1 מרץ 2017
אירוע50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016 - Pacific Grove, ארצות הברית
משך הזמן: 6 נוב׳ 20169 נוב׳ 2016

סדרות פרסומים

שםConference Record - Asilomar Conference on Signals, Systems and Computers

כנס

כנס50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016
מדינה/אזורארצות הברית
עירPacific Grove
תקופה6/11/169/11/16

ASJC Scopus subject areas

  • ???subjectarea.asjc.1700.1711???
  • ???subjectarea.asjc.1700.1705???

טביעת אצבע

להלן מוצגים תחומי המחקר של הפרסום 'First-order perturbation analysis of low-rank tensor approximations based on the truncated HOSVD'. יחד הם יוצרים טביעת אצבע ייחודית.

פורמט ציטוט ביבליוגרפי