For this purpose, a Euclidean distance metric between consecutive solutions was employed as described in [25].
We now state the second situation one can find when estimating the difference of two consecutive solutions.
The next results provide estimates of the difference of two consecutive solutions of equation (72) with respect to the perturbation parameter.
Set d i contains the Euclidean distance between consecutive solutions in the obtained non-dominated set of solutions; d f and d l are the Euclidean distances between the extreme solutions and the boundary solutions of the obtained non-dominated set; (bar {d}) is the average of all distances d i.
where, d i represents the Euclidean distance between the consecutive solutions of the obtained Pareto solution set, d ¯ Open image in new window is the mean value of all Euclidean distances, and N denotes the number of the final obtained Pareto solutions.
Sorting the solutions E i ∈ P by their cardinality so that i = |E i |, the Occam razor condition is specified in Equation (9) for a given selection threshold ε on the difference of relative errors between consecutive solutions according to the number of endmembers: E * = arg min P f RMSE ( E i + 1 ) f RMSE ( E i ) - f RMSE ( E i ) f RMSE ( E i - 1 ) < ε. (9).
Remarkably, the required computation time between two consecutive solutions is polynomial in the input size.
Arrays were hybridized at 42°C overnight and washed with two consecutive solutions (0.2% SDS, 2× SSC at 42°C for 5 min, and 0.2× SSC for 5 min at room temperature).
In terms of complexity, DME belongs to the class of polynomial-delay algorithms, which means that, independently of the size of the results, the computation time between two consecutive solutions is polynomial in the input size (see Supplementary Material).
Agilent human lncRNA + mRNA Array V3.0 was hybridized in an Agilent Hybridization Oven overnight at 42°C and washed with two consecutive solutions (0.2% SDS, 2x SSC for 5 min at 42°C, and 0.2x SSC for 5 min at room temperature).
