| Title |
On the problem of eigenvector sign ambiguity: ad-hoc solution for eigenvector decomposition-based signal and image analysis / |
| Authors |
Kriščiukaitis, Algimantas ; Alves Dos Santos Rodrigues, Ana Rita ; Petrolis, Robertas ; Marozas, Vaidotas |
| DOI |
10.15388/DAMSS.12.2021 |
| ISBN |
9786090706732 |
| eISBN |
9786090706749 |
| Full Text |
|
| Is Part of |
DAMSS 2021: 12th conference on data analysis methods for software systems, Druskininkai, Lithuania, December 2–4, 2021 / Lithuanian computer society, Vilnius university Institute of data science and digital technologies, Lithuanian academy of sciences.. Vilnius : Vilnius university press, 2021. p. 35.. ISBN 9786090706732. eISBN 9786090706749 |
| Abstract [eng] |
Although eigenvalue decomposition based multivariate analysis methods as Principal Component Analysis or Singular Value Decomposition are wellestablished and can be performed using state-of-the-art algorithms, users still face the methods’ inherent problem - eigenvector sign ambiguity. It can significantly impact the conclusions and interpretations drawn from the methods’ results. Yet, no standardized mathematical method exists to resolve this problem, with only a few ad-hoc solutions published thus far. We have been facing this problem in two cases: (i) electrocardiosignal analysis: to determine the main spacial direction of depolarization and repolarization in the heart muscle. (ii) protein antibody array image analysis: to determine the weak chemiluminescence signal over background illumination. In both cases the direction of first eigenvector of covariation matrix is carrying essential information for further analysis. We propose an ad-hoc solution, based on intrinsic features of the original data. The method is based on the feature that its’ distribution is always skewed to one predominant side. The electrical activity of the heart muscle during de- and re-polarization has a predominant polarity. Similarly, the chemiluminescence signal reflecting pixel values are always scattered from background illumination to the positive direction. Thus, we align the polarity of the first eigenvector coefficients with the polarity of the skewness of the corresponding original data. Testing this approach on more than 200 recordings of electrocardiosignals showed that only a few uncertainties remain in low amplitude signals with a biphasic shape. In 150 series of protein antibody array images, this approach showed no failure to determine the polarity. Both testings showed no errors in eigenvector calculations. |
| Published |
Vilnius : Vilnius university press, 2021 |
| Type |
Conference paper |
| Language |
English |
| Publication date |
2021 |
| CC license |
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