Slides for Fuzzy Sets, Ch. 2 of Neuro-Fuzzy and Soft Computing

Neuro-Fuzzy and Soft Computing: Fuzzy Sets
Least-Square Estimators
The task of fitting data using a linear model is referred
to as linear regression
We collect a training data set
{(u i ;y i ), i = 1, …, m}
Equation (*) becomes:
⎧f
⎪
f
⎨
⎪M
⎪⎩
f
1
1
1
(u
(u
(u
1
2
m
) θ
) θ
1
1
) θ
1
+ f
+ f
+ f
) θ
) θ
) θ
+ ... + f
+ ... + f
+ ... + f
which is equivalent to: A θ = y
2
2
(u
2
(u
1
(u
2
m
2
2
2
n
n
(u
(u
n
1
2
(u
) θ
) θ
m
n
n
) θ
=
=
n
y
y
=
1
2
y
m
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