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

نتاج البحث: فصل من :كتاب / تقرير / مؤتمرمنشور من مؤتمرمراجعة النظراء

ملخص

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.

اللغة الأصليةالإنجليزيّة
عنوان منشور المضيفConference Record of the 50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016
المحررونMichael B. Matthews
ناشرIEEE Computer Society
الصفحات1723-1727
عدد الصفحات5
رقم المعيار الدولي للكتب (الإلكتروني)9781538639542
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - 1 مارس 2017
الحدث50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016 - Pacific Grove, الولايات المتّحدة
المدة: ٦ نوفمبر ٢٠١٦٩ نوفمبر ٢٠١٦

سلسلة المنشورات

الاسمConference Record - Asilomar Conference on Signals, Systems and Computers

!!Conference

!!Conference50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016
الدولة/الإقليمالولايات المتّحدة
المدينةPacific Grove
المدة٦/١١/١٦٩/١١/١٦

All Science Journal Classification (ASJC) codes

  • !!Signal Processing
  • !!Computer Networks and Communications

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