387
12 Consensus Drug Design Using IT Microcosm
(12.12)
where B ijC is the number of descriptors ij in compound С; and
B ijl is the number of descriptors ij in compound H l .
Therefore, the subclass of class k compounds that is structurally similar to compound C in the space of i-type descriptors appears as
(12.13)
where {Hʹ 1 , Hʹ 2 , Hʹ 3 , Hʹ 4 } are the first four members of a set of compounds H l arranged in descending order of the Q i (H l ) value, l = 1, … N.
In other words, four structures that are similar to the predicted compound C,
compounds with a minimal value of Q i (H l ), and compounds with a similarity coefficient for compound C of no less than 0.8 are selected in each class a and n.
Applying the formulas of the Bayesian approach (1–4) to the constructed local
training set k i = {a i , n i }, we obtain
(12.14)
Compound C is defined as active for the i-type descriptor if
(12.15)
otherwise it is classified as inactive.
In the local distribution method, the membership function for compound C belonging to activity class k for the i-type descriptor is
(12.16)
The classification metric (14) and membership function (16) for compound C are
only calculated for compounds of the local training set.
The central parametric methods of classification are based on generalized information about all of the objects in the training set, so when applying these methods,
one generally takes the most significant regularities that are typical of this type of
activity into consideration. Conversely, local nonparametric methods consider the
characteristics of objects that are closest to the predicted structure, so they mostly
1
min{ , }
1
( )
·
,
max{ ,
1, ..., ,
}
i
j C H l
d
ijC
ijl
i
l
j
i
ijC
ijl
l
B B
Q H
d
B
N
B
∈ ∪
=
=
=
∑
{ ,
,
,
} {
|
( )
( )} {
|
( ) 0.8},
1
2
3
4
4
k
H H H H
H k Q H
Q H
H k Q H
i
l
i l
i
l
i l
′
′
′
′
′
=
∪
∈
=
∪
∈
≥
[
]
0
1
Pr (
) log (
)
log ( |
) .
i
d
i
i
i
ij
i
j
C k
P C k
P B C k
=
∈ =
∈
+
∈
∑
Pr (
) Pr (
);
i
i
i
i
C a
C n
∈ ≥
∈
Pr (
)
.
(
)
Pr (
) Pr (
) 2
i
i
i
i
i
i
i
C k
Fb C k
C a
C n
β
β
∈
+
∈ =
∈
+
∈
+ ⋅
12 Consensus Drug Design Using IT Microcosm
(12.12)
where B ijC is the number of descriptors ij in compound С; and
B ijl is the number of descriptors ij in compound H l .
Therefore, the subclass of class k compounds that is structurally similar to compound C in the space of i-type descriptors appears as
(12.13)
where {Hʹ 1 , Hʹ 2 , Hʹ 3 , Hʹ 4 } are the first four members of a set of compounds H l arranged in descending order of the Q i (H l ) value, l = 1, … N.
In other words, four structures that are similar to the predicted compound C,
compounds with a minimal value of Q i (H l ), and compounds with a similarity coefficient for compound C of no less than 0.8 are selected in each class a and n.
Applying the formulas of the Bayesian approach (1–4) to the constructed local
training set k i = {a i , n i }, we obtain
(12.14)
Compound C is defined as active for the i-type descriptor if
(12.15)
otherwise it is classified as inactive.
In the local distribution method, the membership function for compound C belonging to activity class k for the i-type descriptor is
(12.16)
The classification metric (14) and membership function (16) for compound C are
only calculated for compounds of the local training set.
The central parametric methods of classification are based on generalized information about all of the objects in the training set, so when applying these methods,
one generally takes the most significant regularities that are typical of this type of
activity into consideration. Conversely, local nonparametric methods consider the
characteristics of objects that are closest to the predicted structure, so they mostly
1
min{ , }
1
( )
·
,
max{ ,
1, ..., ,
}
i
j C H l
d
ijC
ijl
i
l
j
i
ijC
ijl
l
B B
Q H
d
B
N
B
∈ ∪
=
=
=
∑
{ ,
,
,
} {
|
( )
( )} {
|
( ) 0.8},
1
2
3
4
4
k
H H H H
H k Q H
Q H
H k Q H
i
l
i l
i
l
i l
′
′
′
′
′
=
∪
∈
=
∪
∈
≥
[
]
0
1
Pr (
) log (
)
log ( |
) .
i
d
i
i
i
ij
i
j
C k
P C k
P B C k
=
∈ =
∈
+
∈
∑
Pr (
) Pr (
);
i
i
i
i
C a
C n
∈ ≥
∈
Pr (
)
.
(
)
Pr (
) Pr (
) 2
i
i
i
i
i
i
i
C k
Fb C k
C a
C n
β
β
∈
+
∈ =
∈
+
∈
+ ⋅