Today, the performance of computers is high enough to perform powerful search requests on large libraries for analytical data in minutes or even seconds. Similar analytical data and related information can be retrieved in a short time. The following search algorithms for spectrum searches on libraries are available in the software:
Scalar product algorithm
This search algorithm calculates the angle between the query spectrum intensity vector and all library spectrum intensity vectors using the scalar product of the two intensity vectors. The closer the angle is to zero, the better is the matching of query and library spectrum. The scalar product is calculated according to the following equation:
Legend
a
angle between query spectrum intensity vector and library spectrum intensity vector
Q
query spectrum intensity vector
L
library spectrum intensity vector
Derivative algorithm
This search algorithm investigates the difference between slopes of a query spectrum and library spectra. This algorithm is nearly independent of the baseline shape, because only the slopes are considered.
The slope is calculated from the derivatives of two adjacent data points, respectively and summed up to get the total absolute difference between both spectra. The smaller the absolute difference between the spectrum slopes will be, the better the correlation.
Legend
D
absolute difference between slopes of query spectrum and library spectra
n
total number of data points to be compared
dQi
slope of query spectrum at ith data point
dLi
slope of library spectrum at ith data point
Squared derivative algorithm
This search algorithm investigates the squared difference between slopes of a query spectrum and library spectra. The slope is calculated from the derivatives of two adjacent data points, respectively. The differences will be squared and summed up to get the total squared difference between both spectra. The smaller the squared difference value between the spectrum slopes will be, the better the accordance.
Legend
D2
squared difference between slopes of query spectrum and library spectra
n
total number of data points to be compared
dQi
slope of query spectrum at ith data point
dLi
slope of library spectrum at ith data point
Difference algorithm
This search algorithm investigates the absolute intensities of the query spectrum and library spectra. The differences between the intensity value of the query spectrum and the library spectra at each data point is determined and summed up to get the total absolute difference value for a spectrum. The smaller the absolute difference will be, the better is the accordance between query and library spectrum.
Legend
D
total difference between intensity values of query spectrum and library spectra
n
total number of data points to be compared
Qi
intensity of query spectrum at ith data point
Li
intensity of library spectrum at ith data point
Normalization and baseline correction are mandatory!
This algorithm strongly depends on a good baseline and normalized intensities. Normalization will be carried out automatically before comparing spectra, but the baseline should be corrected manually before searching. The baseline correction function of the software may be used for this purpose.
Squared difference algorithm
This search algorithm investigates the squared intensity differences of the query spectrum and library spectra according to a least squares fit. Larger differences will be weighted higher than smaller differences by using this algorithm.
The differences between the intensity values of the query spectrum and the library spectra at each data point are determined and squared. The sum of all squared difference values for a spectrum are calculated. The smaller the square difference will be, the better is the accordance between query and library spectrum.
Legend
D2
total squared difference between intensity values of query spectrum and library spectra
n
total number of data points to be compared
Qi
intensity of query spectrum at ith data point
Li
intensity of library spectrum at ith data point
Normalization and baseline correction are mandatory!
This algorithm strongly depends on a good baseline and normalized intensities. Normalization will be carried out automatically before comparing spectra, but the baseline should be corrected manually before searching. The baseline correction function of the software may be used for this purpose.
Correlation coefficient algorithm
This search algorithm facilitates a linear regression of the query spectrum intensities versus the library spectrum intensities. The correlation coefficient of the resulting linear function is very characteristic through deviations from linearity. The closer the correlation coefficient is to 1, the better is the accordance of both spectra.
Derivative correlation coefficient algorithm
This search algorithm facilitates a linear regression of the derivative of the query spectrum intensities versus the library spectrum intensities. The correlation coefficient of the resulting linear function is very characteristic through deviations from linearity. The closer the correlation coefficient is to 1, the better is the accordance of both spectra.
