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This assignment is for Artificial Intelligence course. It was assigned by Madam Amrita Ahuja at Central University of Jammu and Kashmir. Its main points are: Fortunate, Choices, Street, Groups, Strategy, Lagrange, Multipliers, Numerical, Methods, Kernel, Gutters
Typology: Exercises
1 / 22
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-^
The constraints require:
-^
So, subtracting:
-^
Dividing by the length of
w
produces the distance betweenthe lines:
2
1 2
b^ b
x w
x w
1
x
(x w
w
x
(x w w
1
-^
-^
separation
2
w
1
)
(^
≥
⋅^
b
y
i
i^
x
w
Using LaGrange’s method, and working through somemathematics, you get to the following problem.
When
solved for the alphas, you then have what you need for theclassification formula.
b
y a
b
f
a
y a
y y a a
a
l ji
i i i
i
l i
i
i i
l ji
j i j i j i
l i
i
≥
=
⋅
−
∑
∑
∑
∑
=
=
=
)
(
) (
of
sign
check
Then
0
and 0
to
Subject
1 2
Maximize
1 ,
1 ,
1
u x
u w
u
x x
What you need
To get
x
1
into the high-dimensional space, you use
To optimize, you need
-^
To use, you need
-^
)( x (^1) So, all you need is a way to compute dot products in high-dimensional space as a function of vectors in originalspace! Φ
) ( ) (^
2
1
x
x^
Φ⋅
Φ
) ( ) 1 (^
u
x^
Φ⋅
Φ
) 2 , 1 ( ) 2 ( ) 1 (^
x x
x
x^
Φ⋅
Φ
) 2 , 1 (^
x x K
Aside: about the hairy mathematics
s
derivative
zero has
where
places
Find
s
constraint
subject to
minimize To
1
2
2
∑=
l i
i i i
i i b
y a
b
y w x
w
w x
w
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Aside: about the hairy mathematics
2
∑
∑
=
=
l i
i i
l i
i i i
1
1
