PMC:4331678 / 16728-19499
Annnotations
{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/4331678","sourcedb":"PMC","sourceid":"4331678","source_url":"https://www.ncbi.nlm.nih.gov/pmc/4331678","text":"Kernel target alignment\nGiven Wij=∑m=1MαmWijm and the available functional association networks {Wm}m=1M, the accuracy of protein function prediction is determined by α = [α1, α2,⋯,αM]. [24] and [35] have shown that the target aligned kernel (network) can boost the performance of kernel-based classification and regression. To compute the weights to be assigned to the M individual networks, we resort to a form of kernel-target alignment algorithm [24] as follows:\n(4) α = arg min α t r ( ( K - W ) T ( K - W ) ) s . t . W = ∑ m = 1 M α m W m , α m ≥ 0\nwhere K∈ℝn×n is the induced target network of functional labels, defined as K=∑c=1CKc, where Kc is the c-th induced target network computed as:\nK c ( i , j ) = n c - l 2 if y i c = y j c = 1 n c + n c - l 2 if y i c y j c = 0 \u0026 y i c + y j c = 1 \u0026 i , j ≤ 1 0 , otherwise\nwhere nc- is the number of proteins which are not annotated with the c-th function. Since a functional label often has a relatively small number of member proteins nc+\u003cnc- and nc-l2\u003enc+nc-l2. From the definition, the more functions two proteins have in commom, the larger the entry (corresponding to the weight of the edge between them) in the target network is. This idea was adapted to define the target network [15,16] and to reconstruct the functional association network [36]. Mostafavi et al. [15,16] set the entry (corresponding to the edge between two proteins such that one has the c-th function and the other doesn't) in the target network as -nc+nc-n2. In contrast, we set the entry as nc+nc-l2. The reason is that the available GO term annotation of proteins is incomplete, is updated regularly and suffer from a large research bias [3,21,37]. As such, yic = 0 should not be simply interpreted as if the i-th protein does not have the c-th function. Furthermore, for a to be predicted protein j, if W(i; j) is large, from the guilty by association rule, protein j is likely to share some functions with the i-th protein. By minimizing Eq. (4), we aim at crediting larger weights to the networks which consider highly similar proteins which share more functions, and smaller weights to networks which consider highly similar proteins which share fewer or no functions. By doing so, we can assign larger weights to networks that are coherent with functional labels.\nBased on the fact that tr(KW) = vec(K)T vec(W), where vec(K) is the vectorization operator that stacks the columns of K on top of each other, we can rewrite Eq. (4) as a non-negative linear regression problem:\n(5) α = arg min α t r ( ( V K - V W α ) T ( V K - V W α ) ) s . t . α m ≥ 0 , 1 ≤ m ≤ M\nwhere VK = vec(K), VW=[vec(W1),⋯,vec(WM)]∈ℝ(n×n)×M.","divisions":[{"label":"title","span":{"begin":0,"end":23}},{"label":"p","span":{"begin":24,"end":466}},{"label":"p","span":{"begin":467,"end":583}},{"label":"label","span":{"begin":467,"end":470}},{"label":"p","span":{"begin":584,"end":727}},{"label":"p","span":{"begin":728,"end":913}},{"label":"p","span":{"begin":914,"end":2389}},{"label":"p","span":{"begin":2390,"end":2599}},{"label":"p","span":{"begin":2600,"end":2719}},{"label":"label","span":{"begin":2600,"end":2603}}],"tracks":[{"project":"2_test","denotations":[{"id":"25707434-20507895-14839078","span":{"begin":1332,"end":1334},"obj":"20507895"},{"id":"25707434-24149053-14839079","span":{"begin":1391,"end":1393},"obj":"24149053"},{"id":"25707434-20507895-14839080","span":{"begin":1417,"end":1419},"obj":"20507895"},{"id":"25707434-22522134-14839081","span":{"begin":1762,"end":1764},"obj":"22522134"}],"attributes":[{"subj":"25707434-20507895-14839078","pred":"source","obj":"2_test"},{"subj":"25707434-24149053-14839079","pred":"source","obj":"2_test"},{"subj":"25707434-20507895-14839080","pred":"source","obj":"2_test"},{"subj":"25707434-22522134-14839081","pred":"source","obj":"2_test"}]}],"config":{"attribute types":[{"pred":"source","value type":"selection","values":[{"id":"2_test","color":"#eca593","default":true}]}]}}