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**Type all equations using latex code between <nowiki> <math> </math> </nowiki> tags. | **Type all equations using latex code between <nowiki> <math> </math> </nowiki> tags. | ||
**You may include links to other [https://www.projectrhea.org/learning/about_Rhea.php Project Rhea] pages. | **You may include links to other [https://www.projectrhea.org/learning/about_Rhea.php Project Rhea] pages. | ||
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| + | Euclidean distance: <br> <math>D(\vec{x_1},\vec{x_2})=||\vec{x_1}-\vec{x_2}||_{L_2}=\sqrt{\sum_{i=1}^n ({x_1}^i-{x_2}^i)^2}</math> | ||
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| + | Manhattan (cab driver) distance: <br><math>D(\vec{x_1},\vec{x_2})=||\vec{x_1}-\vec{x_2}||_{L_1}=\sum_{i=1}^n |{x_1}^i-{x_2}^i|</math> | ||
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| + | Minkowski metric: <br><math>D(\vec{x_1},\vec{x_2})=||\vec{x_1}-\vec{x_2}||_{L_p}=(\sum_{i=1}^n ({x_1}^i-{x_2}^i)^p)^{\frac{1}{p}}</math> | ||
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| + | Riemannian metric: <br><math>D(\vec{x_1},\vec{x_2})=\sqrt{(\vec{x_1}-\vec{x_2})^\top \mathbb{M}(\vec{x_1}-\vec{x_2})}</math> | ||
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| + | Infinite norm: <br><math>D(\vec{x_1},\vec{x_2})=||\vec{x_1}-\vec{x_2}||_{\infty}=max_i |{x_1}^i-{x_2}^i|</math> | ||
Revision as of 19:00, 30 April 2014
From KNN to Nearest Neighbor Classification
A slecture by ECE student Jonathan Manring
Partly based on the ECE662 Spring 2014 lecture material of Prof. Mireille Boutin.
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Euclidean distance:
$ D(\vec{x_1},\vec{x_2})=||\vec{x_1}-\vec{x_2}||_{L_2}=\sqrt{\sum_{i=1}^n ({x_1}^i-{x_2}^i)^2} $
Manhattan (cab driver) distance:
$ D(\vec{x_1},\vec{x_2})=||\vec{x_1}-\vec{x_2}||_{L_1}=\sum_{i=1}^n |{x_1}^i-{x_2}^i| $
Minkowski metric:
$ D(\vec{x_1},\vec{x_2})=||\vec{x_1}-\vec{x_2}||_{L_p}=(\sum_{i=1}^n ({x_1}^i-{x_2}^i)^p)^{\frac{1}{p}} $
Riemannian metric:
$ D(\vec{x_1},\vec{x_2})=\sqrt{(\vec{x_1}-\vec{x_2})^\top \mathbb{M}(\vec{x_1}-\vec{x_2})} $
Infinite norm:
$ D(\vec{x_1},\vec{x_2})=||\vec{x_1}-\vec{x_2}||_{\infty}=max_i |{x_1}^i-{x_2}^i| $
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Questions and comments
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