PMC:4996402 / 18648-20010 JSONTXT

{"project":"2_test","denotations":[{"id":"27600242-17044167-69476456","span":{"begin":342,"end":344},"obj":"17044167"},{"id":"27600242-17044167-69476457","span":{"begin":1074,"end":1076},"obj":"17044167"},{"id":"27600242-17044167-69476458","span":{"begin":1358,"end":1360},"obj":"17044167"}],"text":"3.4. Generalized-Framework NCA\nThe original NCA work requires the biological system to satisfy all three criteria to ensure a unique decomposition up to a scaling factor. However, NCA only checks the compliance for the initialized matrix A. It may occur that the derived matrix A at certain iterations violates the NCA criteria. The work in [28] generalizes the NCA criteria, such that the system identification can be determined directly from the connectivity (topology) information, rather than checking the rank properties of the unknown connectivity matrix A. In other words, if a certain connectivity topology, i.e., A(I0), meets the newly-derived conditions, then all matrices A∈A(I0) satisfy the first and second criterion of NCA, and thus, they guarantee the feasibility of A during each iteration of the NCA algorithm. To deal with the issue that the connectivity topology does not satisfy the newly-derived conditions or the TF matrix does not satisfy the third criterion of NCA (for example, when M\u003eK, the linear independence of TFs is violated), the authors in [28] alternatively seek to infer subnetworks by removing the selected TF node together with all of its associated genes until all of the system identification criteria of the reduced subnetwork are verified. The resulting algorithm is referred to as generalized-framework NCA (gfNCA) [28]."}