Inputs. samples and sample labels, where K represents number of feature points (m/z ratios or genes). |
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xcontrol ∈ ℝK and xdisease ∈ ℝK representing control and disease (case) groups of samples. |
Nested two-fold cross-validation. Parameters: single component points (SCPs) selection threshold in radian equivalents of Δ θ {10, 30, 50}; regularization constant λ∈ {10-2λmax, 10-4λmax, 10-6λmax}; number of components M ∈{2, 3, 4, 5}; parameters of selected classifier. |
Components selection from mixture samples. |
1. form a linear mixture models (LMMs) (2a) and (2b). |
2. For LMMs (2a)/(2b) select a set of single component points for a givenΔθ. |
3. On sets of SCPs use hierarchical clustering (other clustering methods can be used also) to estimate mixing matrices Acontrol and Adisease for a given M. |
4. Estimate source matrices Scontrol and Sdisease by solving (3a) and (3b) respectively for a given regularization parameter λ. |
5. Use minimal and maximal mixing angles estimated from mixing matrices A control and A disease to select, following the logic illustrated in Fig. 2a and Fig. 2b, disease and control specific components: , , and . |
End of component selection. |
End of nested two-fold cross-validation. |