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

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

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<strong>Neuro</strong>-<strong>Fuzzy</strong> <strong>and</strong> S<strong>of</strong>t <strong>Computing</strong>: <strong>Fuzzy</strong> <strong>Sets</strong><br />

Least-Square Estimators<br />

Theorem [least-squares estimator]<br />

The squared error is minimized when θ =<br />

(called the least-squares estimators LSE) satisfies<br />

the normal equation A T A = A T y, if A T A is<br />

nonsingular, is unique & is given by<br />

θˆ<br />

θˆ<br />

= (A T A) -1 A T y<br />

θˆ<br />

θˆ<br />

17

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