In addition, we develop an objective function that calculates the best partitioning for a specific configuration and gives the computing cost of each partition, allowing for a computing balance through a mapping policy.
However, most community finding methods typically look for the "best" partition of a network, disregarding the possible existence of hierarchical structure.
For the example in Figure 2, the recursive partitioning starts by searching for the best partition of Age and Triage Category which results in a region that maximises the departure of the counts from the region's expected value, that is, maximises z t.
A series of experiments revealed that the combination of right- and left-handed coils produced the best partition efficiencies for both lower and upper mobile phases by selecting the revolution direction.
The AIC favored independent gene partitions in the nuclear and the combined data sets, whereas the best partition scheme for the mt data sets was that with all genes analyzed separately except for atp8/atp6 and nad4L/nad4.
This demanded that we recalculate the best partition scheme, for the second codon positions of the 13 PCGs, with PartitionFinder, which gave these four partitions: (atp6_pos2, atp8_pos2, cox2_pos2, cox3_pos2, cytb_pos2) (cox1_pos2) (nad4_pos2, nad4L_pos2 nad5_pos22, nad3_pos2) (nad6_pos2, nad6_pos2, nad6_pos2).
Each retained partition pi is compared with the best partition pb and for each cluster cbi ϵ pb a support value is defined as follows: (i) for each partition pj ϵ P, j≠b, identify the cluster c*jk ϵ pj such as c*jk ∩ cbi is the maximum among all possible intersections cjk ∩ cbi; (ii) calculate the support sbij as sbij = c*jk ∩ cbi/c*jk U cbi.
Algorithm 1 depicts this rationale, where kmax is the largest value of k tested, k∗ is the number of clusters estimated by the method, V is the value of the validity criterion after a single run of k-means, V∗ is the value of the validity criterion for the best partition found and p is the number of different partitions generated for each number k≤kmax of clusters.
The best partitioning schemes for Nuc- and AA-datasets were estimated under the Akaike information criterion (AIC) [ 65] using PartitionFinder v1.0.1 and PartitionFinderProtein v1.0.1, respectively [ 66].
Partitioning by codon position was the best partitioning scheme for the nt123 data set, as indicated by the AIC score in PartitionFinder, and this model was used for all ML analyses that included all three codon positions.
