Search Results
On the signal contribution function with respect to different norms
2021, Neymeyr, Klaus, Sawall, Mathias, Olivieri, Alejandro C.
The signal contribution function (SCF) in multivariate curve resolution evaluates signal portions of specific components either in absolute or in relative form related to the integrated signal of all components. In 1999, Gemperline used the summed signal data, and in 2001, Tauler worked with the square-summed relative signal in order to determine the profiles that minimize, respectively maximize, the signal contribution. These profiles approximate the bands of all feasible profiles. Here, Gemperline's approach using the entrywise 1-matrix norm is proved to provide accurate bounds for two-component systems. This revives the approach of summed mass or absorption values with its potentially better chemical interpretability.
Modified PCA and PLS: Towards a better classification in Raman spectroscopy–based biological applications
2020, Guo, Shuxia, Rösch, Petra, Popp, Jürgen, Bocklitz, Thomas
Raman spectra of biological samples often exhibit variations originating from changes of spectrometers, measurement conditions, and cultivation conditions. Such unwanted variations make a classification extremely challenging, especially if they are more significant compared with the differences between groups to be separated. A classifier is prone to such unwanted variations (ie, intragroup variations) and can fail to learn the patterns that can help separate different groups (ie, intergroup differences). This often leads to a poor generalization performance and a degraded transferability of the trained model. A natural solution is to separate the intragroup variations from the intergroup differences and build the classifier based on merely the latter information, for example, by a well-designed feature extraction. This forms the idea of this contribution. Herein, we modified two commonly applied feature extraction approaches, principal component analysis (PCA) and partial least squares (PLS), in order to extract merely the features representing the intergroup differences. Both of the methods were verified with two Raman spectral datasets measured from bacterial cultures and colon tissues of mice, respectively. In comparison to ordinary PCA and PLS, the modified PCA was able to improve the prediction on the testing data that bears significant difference to the training data, while the modified PLS could help avoid overfitting and lead to a more stable classification. © 2019 The Authors. Journal of Chemometrics published by John Wiley & Sons Ltd
On the avoidance of crossing of singular values in the evolving factor analysis
2020, Neymeyr, Klaus, Sawall, Mathias, Rasouli, Zahra, Maeder, Marcel
Evolving factor analysis (EFA) investigates the evolution of the singular values of matrices formed by a series of measured spectra, typically, resulting from the spectral observation of an ongoing chemical process. In the original EFA, the logarithms of the singular values are plotted for submatrices that include an increasing number of spectra. A typical observation in these plots is that pairs of trajectories of the singular values are on a collision course, but finally, the curves seem to repel each other and then run in different directions. For parameter-dependent square matrices, such a behaviour is known for the eigenvalues under the keyword of an avoidance of crossing. Here, we adjust the explanation of this avoidance of crossing to the curves of singular values of EFA. Further, a condition is studied that breaks this avoidance of crossing. We demonstrate that the understanding of this noncrossing allows us to design model data sets with a predictable crossing behaviour. © 2020 John Wiley & Sons, Ltd.