Improve the performance of independent component analysis by mapping the spectrum to an orthogonal space

Independent Component Analysis (ICA) has attracted chemists recently, for its charm can separate the independent signals from a mixed system and does not need prior knowledge. However, its dissatisfactory performance for the chemical measured signal is still blocking the practicability. Thus, this paper summarized the ICA processing path from the establishment of rectangular coordinates in linear space to the determination of the corresponding relation between the coordinate system and real components. The primary cause of the deviation between the ICA results and the chemical measurements is that the measuring signal was subject to uncertainty. Besides, uncertainty made the deviation of source signal from the statistical independence assumption, or in other words, it appeared to be nonorthogonal. For this key, it proposed to map the measured value to the high-order derivative space, use the derivative to narrow the peak width, reduce the influence of uncertainty, and improve the separation performance of ICA to chemical measurement signal, such as the spectrum. Actual cases of this paper showed that when up to 6th order, the separating results had been perfect for IR spectra, and even for homologs isomers.