Blessing of randomness against the curse of dimensionality. (9th November 2017)

• Record Type: Journal Article
• Authors: Kucheryavskiy, Sergey
• Other Names: Ruckebusch Cyril guestEditor.
• Is Part Of: Journal of chemometrics. Volume 32:Number 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2017-11-09
• Subjects: hyperspectral images -- matrix decomposition -- principal component analysis -- probabilistic algorithms -- randomization; Chemistry -- Mathematics -- Periodicals; Chemistry -- Statistical methods -- Periodicals; 542.85
• DOI: 10.1002/cem.2966
• Languages: English
• ISSNs: 0886-9383

Abstract

Abstract : Modern hyperspectral images, especially acquired in remote sensing and from on‐field measurements, can easily contain from hundreds of thousands to several millions of pixels. This often leads to a quite long computational time when, eg, the images are decomposed by Principal Component Analysis (PCA) or similar algorithms. In this paper, we are going to show how randomization can tackle this problem. The main idea is described in detail by Halko et al in 2011 and can be used for speeding up most of the low‐rank matrix decomposition methods. The paper explains this approach using visual interpretation of its main steps and shows how the use of randomness influences the speed and accuracy of PCA decomposition of hyperspectral images. Abstract : This paper shows how randomization can speed up principal component analysis of hyperspectral images and how it influences the speed and accuracy of the decomposition.