Editorial board editor-in-chief

Feature Vectors
In these experiments, the feature vectors developed by Ding and 
Dubchak [5] were used. These feature vectors are based on six 
parameters: Amino acids composition (C), predicted second-
ary structure (S), Hydrophobity (H), Normalized van der Waals 
volume (v), Polarity (P) and Polarizability (Z). Each parameter 
corresponds to 21 features, except Amino acids composition (C), 
which corresponds to 20 features. The data sets including these 
feature vectors are available at http://ranger.uta.edu/~chqding/
protein/. For more concrete details see Dubchak et al. [6], [7]. 
In this study the sequence length was added to the Amino acids 
composition (C) vector and the feature vectors based on these 
parameters were used in the different combinations creating 
vectors from 21D to 126D.
Statistical classiiers
Quadratic discriminant analysis (QDA) models the likelihood of 
a class as a Gaussian distribution and then uses the posterior 
distributions to estimate the class for a given test vector. This 
approach leads to discriminant function: 
d
k
 (x)=(x – μ
k
)
T
 Σ
k
–
1
 (x – μ
k
)+ 
log |Σ
k
| − 2log 
p(k)
(1)
where 
x
is a test vector, 
µ
k
is a mean vector, 
Σ
k
 
is a covariance 
matrix and 
p(k)
is prior probability of the class 
k
. 
The Gaussian 
parameters for each class can be estimated from training vec-
tors, so the values of 
Σ
k
 
and 
µ
k
 
are replaced in the formula (1) 
by its estimates 
Σ
ˆ
k
and
 µ
ˆ
k
.
However, when the number of the training samples 
n
is small 
compared to the number of dimensions of the training vector, 
the covariance estimation can be ill-posed. The approach to 

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69
Bioinf
or
ma
tics
A combined SvM-RDA
 classiier for protein fold recognition…
provides a choice of built-in kernels i.e. Linear, Polynomial, Radial 
Basis Function (RBF) and Gaussian. The RBF kernel:
K(x
i
,x)= –y||x–x
i
||
²,
 y
>0 
(7)
gave the best results in our experiments.
The parameters 
C 
from formula (5) and 
y
must be chosen to 
use the SvM classiier with RBF kernel. It is not known beforehand 
which 
C
and 
y
are the best for the given problem. Both values must 
be experimentally chosen, which was done by using cross-valida-
tion procedure on the training data set. The best recognition ratio 
58.7% was achieved using parameter values 
y
=0.1
and 
C
=128
.
In one-versus-one strategy with max-win voting scheme the 
binary classiiers are trained between all the possible pairs of the 
classes. Every binary classiier votes for the preferred class and 
in this way the voting table is created. Originally a class with the 
maximum number of votes is recognized as the correct class. 
However, some of these binary classiiers are unreliable. The 
votes from these classiiers inluence the inal classiication result. 
In our method there is a strategy proposed to assign a weight 
(which can be treated as a measure of reliability) to each vote. 
The weight is based on the values of the discriminant function 
from an RDA classiier as described below.
In our experiments we decide to use selection algorithm to 
ind better feature vector for an RDA classiier. The best selection 
method is to check all possible feature combinations. However, 
the number of them is far to high to use such an algorithm, but the 
features used in our experiments are based on the parameters 
C, S, H, V, P, Z (as described in section 2) that create six feature 
sets containing 21 values each, so all combinations of these sets 
can be considered. The total number of these combinations is 63, 
so the brute force algorithm can be used. The best combination 
obtained using cross-validation procedure was 63D feature set 
based on C, S and P parameters.
The next step was to ind the best regularization method 
and corresponding parameter value. The method described by 
formula (2) and