Lecture 2 Piecewise-linear optimization
Lecture 2 Piecewise-linear optimization
Lecture 2 Piecewise-linear optimization
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Robust curve fitting<br />
• fit affine function f(t) = α+βt to m points (t i ,y i )<br />
• an approximation problem Ax ≈ b with<br />
⎡<br />
A = ⎣ 1 t ⎤<br />
[<br />
1 α<br />
. . ⎦, x =<br />
β<br />
1 t m<br />
]<br />
, b =<br />
⎡<br />
⎣ y ⎤<br />
1<br />
. ⎦<br />
y m<br />
f(t)<br />
25<br />
20<br />
15<br />
10<br />
5<br />
0<br />
¢5<br />
¢10<br />
¢15<br />
¢20<br />
¢10<br />
¢5 0 5 10<br />
t<br />
• dashed: minimize ‖Ax−b‖<br />
• solid: minimize ‖Ax−b‖ 1<br />
l 1 -norm approximation is more<br />
robust against outliers<br />
<strong>Piecewise</strong>-<strong>linear</strong> <strong>optimization</strong> 2–12
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