Information Technology Reference
In-Depth Information
W
T
⊗
(1)
X
i
+ b = 0
Where
denotes the scalar product and
W
is a weight vector perpendicular to
hyper-plane and
b
is the bias. W is also called perpendicular vector or normal
vector. It is used to specify hyper-plane.
⊗
b
The value
is the offset of the hyper-plane from the origin along the
|
W
|
weight vector W.
To calculate the margin, two parallel hyper-planes are constructed, one on each
side of the maximum-margin hyper-plane. Such two parallel hyper-planes are
represented by two following equations:
W
T
⊗
X
i
+ b = 1
W
T
⊗
X
i
+ b = -1
To prevent vectors falling into the margin, all vectors belonging to two class y
i
=1,
y
i
=-1 have two following constraints respectively:
W
T
⊗
X
i
+ b
≥
1 (for X
i
of class y
i
=1)
W
T
⊗
X
i
+ b
≤
-1 (for X
i
of class y
i
=-1)
These constraints can be re-written as:
Y
i
(
W
T
⊗
(2)
X
i
+ b
)
≥
1
For any new vector
X
, the rule for classifying it is computed as below:
⊗
∈
{
≤
−
1
≥
1
(3)
f
(
X
i
) = sign(
W
T
X
i
+ b
)
Fig. 2
Maximum-margin hyper-plane
