Statistical properties of color-signal spaces
2005 (English)In: Journal of the Optical Society of America A: Optics and Image Science, and Vision, ISSN 1084-7529, Vol. 22, no 5, 820-827 p.Article in journal (Refereed) Published
In applications of principal component analysis (PCA) it has often been observed that the eigenvector with the largest eigenvalue has only nonnegative entries when the vectors of the underlying stochastic process have only nonnegative values. This has been used to show that the coordinate vectors in PCA are all located in a cone. We prove that the nonnegativity of the first eigenvector follows from the Perron-Frobenius (and Krein-Rutman theory). Experiments show also that for stochastic processes with nonnegative signals the mean vector is often very similar to the first eigenvector. This is not true in general, but we first give a heuristical explanation why we can expect such a similarity. We then derive a connection between the dominance of the first eigenvalue and the similarity between the mean and the first eigenvector and show how to check the relative size of the first eigenvalue without actually computing it. In the last part of the paper we discuss the implication of theoretical results for multispectral color processing. © 2005 Optical Society of America.
Place, publisher, year, edition, pages
2005. Vol. 22, no 5, 820-827 p.
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-45453DOI: 10.1364/JOSAA.22.000820OAI: oai:DiVA.org:liu-45453DiVA: diva2:266349