Interactive curve resolution by using latent projections in polar coordinates

The problem of resolving bilinear two‐way data into the contributions from the underlying mixture components is of great interest for all hyphenated analytical techniques. The fact that the optimal solution to this problem at least to some extent depends on the nature of the data under study has lead to a numerous different approaches. One of the seminal publications in this area was contributed by Olav M. Kvalheim and Yi‐Zeng Liang in 1992. They not only provided valuable Heuristic Evolving Latent Projections (HELP) but also enlightened many important aspects of curve resolution in this and numerous subsequent publications. Here we extend their key concept of HELP, that is the use of latent projective graphs for identifying one‐component regions, by using polar coordinates for these analyses and thereby creating a simple, intuitive exploratory tool for directly solving the curve resolution problem for two and three components graphically. Our approach is demonstrated with simulated data, an example from reaction monitoring with broadband ultrafast spectroscopy and one chemometric standard data set. Copyright © 2007 John Wiley & Sons, Ltd.