PMC:4331678 / 22246-23498 JSONTXT

{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/4331678","sourcedb":"PMC","sourceid":"4331678","source_url":"https://www.ncbi.nlm.nih.gov/pmc/4331678","text":"Complexity analysis\nSeveral components in Eq. (8) (i.e., VWTVW∈RM×M, VWTVK∈RM×1 and (Wm1)TWm2∈Rn×n) can be computed before the iterative process. The time complexity of tr(FTWF ) is O(Cn2). Θ is an M × M symmetric matrix, in each iteration there are M (M + 1)/2 elements to be computed, so the time complexity of computing Θ is O(M (M + 1) × Cn2). The complexity of matrix inverse in Eq. (3) is O(n3). To avoid large matrix inverse, iterative approximation algorithms (i.e. Conjugate Gradient) can be applied. Since the computation complexity of matrix inverse in Eq. (8), and the complexity of μ is smaller than Θ, the overall time complexity of MNet is max{O(M2TCn2), O(Tn3)}. T is the number of iterations for convergency. In practice, T is no more than 10. In our study, the association matrices of the individual networks and the composite network are all sparse with O(n) non-zero elements. For this reason, the time complexity of the above operations can be greatly reduced. The main difference between MNet and ProMK is that ProMK just uses μ, so its time complexity is max{O(MTCn2), O(Tn3)}. Given that the number of individual networks is much smaller than the number of proteins and functional labels, MNet has similar complexity with ProMK.","divisions":[{"label":"title","span":{"begin":0,"end":19}}],"tracks":[]}