First, ATLD gives matrices A and B randomly and alternately updates A * B * C in the three separate directions of the three-dimensional data matrix, which are as follows:
The residual sum of squares (SSR) is the loss function defined by ATLD, which is
As a result, ATLD could decompose the three-dimension fluorescence spectrum matrix X(I x J x K) to three low-dimension matrices, which are known as relative excitation matrix A(I x N), relative emission matrix BJ x N), and relative concentration matrix C(K x N).
Model parameters are obtained with ATLD algorithm, which is known as relative excitation matrix A, relative emission matrix B, and relative concentration matrix C of the background sample.
Known by formula (4), if the background sample matrix X(I x J), the relative excitation matrix A, and the relative emission matrix B of the background sample are substituted into formula (4), the relative concentration C-pre of each component of the sample X could be obtained based on the ATLD model.
Qualitative Determination Based on ATLD and Threshold.
ATLD algorithm focuses on extracting the trilinear part in the three-way data and makes the iterative procedure more efficiency.
SWATLD is derived from ATLD and is based on the same ideology.
In addition, the build-in way of updating [a.sub.(i)] makes the final solution more stable than ATLD.
Three kinds of second-order calibration algorithms, that is, ATLD, SWATLD, and APTLD, were used to resolve the spectral and concentration profiles.
As can be seen, on average, ATLD models containing 4-7 factors exhibit the same recovery, and the recovery of either APTLD or SWATLD model is highest when using five factors.
Mean of Mean of COS recovery F ATLD APTLD SWATLD ATLD APTLD SWATLD 4 0.9697 0.9841 0.9841 0.9399 0.9363 0.9364 5 0.9639 0.9853 0.9853 0.9377 0.9850 0.9850 6 0.9630 0.9850 0.9847 0.9388 0.9801 0.8828 7 0.9320 0.9852 0.8799 0.9388 0.9801 0.8828 8 0.9312 0.8703 0.9780 0.9557 0.9671 0.9399