Comparison of PARAFAC and PARALIND in modeling three‐way fluorescence data array with special linear dependences in three modes: a case study in 2‐naphthol

Abstract

aOwing to excited-state proton transfer in 2-naphthol solutions, the fluorescence excitation-emission matrices (EEMs) have factors that are highly dependent in three modes. For the first time such EEMs are used to compare the capability of PARALIND (PARAFAC with linear dependence) and conventional PARAFAC in modeling three-way EEMs having linearly dependent factors in three modes. Two primary conclusions have been drawn. First, the results indicate that a 3-factor PARAFAC model fit the data better than two PARALIND models (type 1 and 2) in this case while equally well with a specially PARALIND model (type 3); second, a negative core consistency (CC) in the 3-factor PARAFAC model is reported but the type 3 PARALIND model reports a nearly 100 CC. This work has demonstrated that a properly constrained PARALIND can fit the very special EEMs of 2-naphthol. The presence of negative CC associated with a perfect PARAFAC model would imply the presence of very special linear dependences in EEMs, which would be used as an ''alarm'' for the investigators to interpret the data more carefully when dealing with complicated environmental EEMs in the absence of a priori knowledge.

Combination of a Copper-Ion Selective Electrode and Fluorometric Titration for the Determination of Copper(II) Ion Conditional Stability Constants of Humic Substances

“…Fluorescence intensities in the EEM were corrected for inner-filtering effects (IFEs) based on the approach employed in our earlier studies. 30,31 Scattering light removal from EEMs and PARAFAC modeling of the data were conducted following the protocols elaborated elsewhere. 18,30,31 In brief, the scattering light intensity in EEMs was replaced by not a number (NaN), and the PARAFAC modeling was achieved using a PLS 3.0 tool package running in the software of Matlab 7.1.…”

“…30,31 Scattering light removal from EEMs and PARAFAC modeling of the data were conducted following the protocols elaborated elsewhere. 18,30,31 In brief, the scattering light intensity in EEMs was replaced by not a number (NaN), and the PARAFAC modeling was achieved using a PLS 3.0 tool package running in the software of Matlab 7.1. The appropriateness of an n -component model was evaluated by a combinational check of the core consistency value, 18,30,31 modeling residuals and the spectral features of the resolved components.…”

On rotational ambiguity in parallel profiles with linear dependencies

“…The actual profiles for simulating the data set are illustrated in Figure , third row. Complex photo‐physical processes, eg, Förster resonance energy transfer (FRET) or excited‐state reactions such as excited‐state proton transfer (ESPT), are experimental systems with proportional profiles in 2 modes. This example is specially designed to show the interaction matrix effect and reveal the difference between the PARAFAC model and PARALIND model in case of complex rank‐deficient data.…”

“…Leitao et al used the PARALIND model for the analysis of carbon dot nano particle's fluorescence. Chen et al used the PARALIND model for the analysis of a complex photophysical process named excited state proton transfer that shows rank overlap in 2 modes. De Almeida et al applied the PARALIND algorithm to model multiple‐antenna transmissions in the context of wireless telecommunications and signal processing.…”

Visualization and establishment of partial uniqueness and uniqueness rules in parallel factor analysis

“…When the results complicate with rotational ambiguity, quantitative or qualitative information of loadings are less useful because they differ from true profiles significantly . By the aid of uniqueness, PARAFAC could be applied as an exploratory data analysis tool to different kind of data sets and chemical systems . For three‐way trilinear data curve resolution results are unique, but in two‐way data sets, unambiguous recovery is not possible in most cases.…”