Assuming that the measured spectra are linear superpositions of constituent spectra, then each abundance is effectively a percentage spectral weight, with the coefficients summing to one.
Individuals are placed in K clusters and can be members of multiple clusters, with membership coefficients summing to 1 across all K clusters.
The individuals can have membership coefficients summing 1 across clusters.
The above combination is convex if all coefficients p i are non-negative and the coefficient sum is equal to 1.
Let ( {displaystyle sum_{k=i}^K{delta}_kleft(i=1,2,dots, Mright)} ) denotes the generalized mixing coefficient, sum of which must be 1.
A combination c = ∑ i = 1 n p i x i (1.1). of points x i and real coefficients p i is affine if the coefficient sum ∑ i = 1 n p i = 1.
A constant-coefficient sum (Sigma _{j}c_{j}B^{j}) is a (linear, time-invariant) filter, a symmetric filter if the same filter results when B is replaced by (B^{-1}), as with the intermediate time filters (33) and (38).
The HEIP of tumour internal enhancement could not be replicated with a reasonable degree of accuracy using CEIP of tumour enhancement; the AUC associated with the best model as identified through ten-fold cross-validation, which involved energy, entropy, information measure of correlation, maximum correlation coefficient, sum of average, sum of entropy, and sum of squares, was 0.551 (p = 0.263).
For example, the percentage of variation explained by maternal preconception concentrations was estimated as the preconception PCB coefficient sum of squares (0.15) divided by the total model sum of squares (0.679) = 22%.
The linear test for trend [degrees of freedom (df) = 1] across exposure categories was conducted by assigning the quartiles of exposure values of 0, 1, 2, 3 (ordinal variable) and specifying an appropriate linear combination vector (with a coefficient sum that equals 0) in a contrast statement.
