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C = { StoneHinge,FO1,FO1M,FO,HingeSeq,TLSMD,NMA,NMB,NMC,NMD,1}
x c (i) = output of predictor c for residue i.
" c = weighting coefficient of predictor c, determined below.
We used least squares fitting to find the " c‘s in Equation 5 corresponding to an optimal
predictor. The procedure follows.
Let
y = a column vector, the components
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y(i) of which are the hinge annotations of the
m residues in the HAG, in the format 1 = hinge, 0 = non-hinge. The index i counts over
all residues in all proteins of the set in question, which in this work will be either the
training, test, or complete HAG set. Order is unimportant as long as the i’s in
the same order as the i’s in
Let
!
x = an
column of
x, below.
m " 9 matrix, the rows of which will be used to predict the ! rows of
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y are in
y. Each
x is a ! an m-component vector xc, such that c " C. Each component xc (i) of
each such column vector is the output of the predictor c for residue i. Correspondingly,
x(i) ! (without a subscript) is a row ! vector with ! 9 components corresponding ! to the output
each of the 9 predictors emitted for residue i.
Let " = a column vector, the components " c of which will give us the weight to be
applied to the various predictors in order to make the composite HingeMaster predictor.
Thus according to our definition of HingeMaster (Equation 5):
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