Difference between revisions of "Foo"

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~~[[Category:slecture]]~~

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~~[[Category:ECE662Spring2014Boutin]]~~

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~~[[Category:ECE]]~~

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~~[[Category:ECE662]]~~

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~~[[Category:pattern recognition]]~~

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~~<center><font size= 4>~~

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~~K Nearest Neighbors~~

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~~</font size>~~

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~~A [https://www.projectrhea.org/learning/slectures.php slecture] by [[ECE]] student~~

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~~Partly based on the [[2014_Spring_ECE_662_Boutin|ECE662 Spring 2014 lecture]] material of [[user:mboutin|Prof. Mireille Boutin]].~~

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~~</center>~~

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~~----~~

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~~----~~

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~~Post your slecture material here. Guidelines:~~

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*If you are making a text slecture

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**Type text using wikitext markup languages

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**Type all equations using latex code between <nowiki> <math> </math> </nowiki> tags.

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**You may include links to other [https://www.projectrhea.org/learning/about_Rhea.php Project Rhea] pages.

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~~K Nearest Neighbors is a classification algorithm based on local density estimation.~~

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The goal of a classifier is to take a data-point <math> x_{0} </math>, usually represented as a vector, and assign it a class label from some set of <math> C </math> classes <math> w_1,w_2,...w_C</math>

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If the data-points from each class are random variables, then it can be proven that the optimal decision rule to classify a point <math> x_0 </math> is Bayes Rule, which is to choose the class for which <math> P(w_i|x_0) </math>, the is highest.

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~~Therefore, it is desirable to assume that the data-points are random variables, and attempt to estimate <math> P(w_i|x_0) </math>, in order to use it to classify the points.~~

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By Bayes Theorem, <math> P(w_i|x_0) = P(x_o|w_i)P(w_i)</math>. This is advantageous because it is often easier to estimate <math> P(x_o|w_i)</math> and <math>P(w_i)</math> separately than to estimate <math> P(w_i|x_0) </math> directly.

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K Nearest Neighbors does not explicitly estimate <math> P(w_i|x_0) = P(x_o|w_i)P(w_i)</math>, but instead does so implicitly, and chooses the class with the highest estimated <math> P(w_i|x_0) </math>.

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This method belongs to the class of local density estimation methods because it forms a separate density estimate locally around each test point <math> x_0</math>. This is in contrast to non-local methods which assume a symbolic form (for example gaussian) for the distributions and estimate the entire distribution by finding the parameters (the mean and variance for the gaussian example) of that distribution.

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~~The classifier is given a set of <math> N </math> data-points <math> x_{1}, x_{2}, ..., x_{N} </math> along with corresponding labels <math> y_{1}, y_{2}, ..., y_{N} </math>~~

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~~Together these are often called the training set, because they are used to "train" the classifier, i.e. estimate the distributions.~~

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~~<math> \alpha = \sum_{i=1}^{N} \beta_{i}</math>~~

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~~----~~

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~~----~~

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~~----~~

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~~==[[slecture_title_of_slecture_review|Questions and comments]]==~~

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~~If you have any questions, comments, etc. please post them on [[slecture_title_of_slecture_review|this page]].~~

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~~----~~

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~~[[2014_Spring_ECE_662_Boutin|Back to ECE662, Spring 2014]]~~

Difference between revisions of "Foo" - Rhea

Latest revision as of 18:03, 30 April 2014

Alumni Liaison

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-[[Category:slecture]]
-[[Category:ECE662Spring2014Boutin]]
-[[Category:ECE]]
-[[Category:ECE662]]
-[[Category:pattern recognition]]
-<center><font size= 4>
-K Nearest Neighbors
-</font size>
-A [https://www.projectrhea.org/learning/slectures.php slecture] by [[ECE]] student
-Partly based on the [[2014_Spring_ECE_662_Boutin|ECE662 Spring 2014 lecture]] material of [[user:mboutin|Prof. Mireille Boutin]].
-</center>
-----
-----
-Post your slecture material here. Guidelines:
-*If you are making a text slecture
-**Type text using wikitext markup languages
-**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.
-K Nearest Neighbors is a classification algorithm based on local density estimation.
-The goal of a classifier is to take a data-point <math> x_{0} </math>, usually represented as a vector, and assign it a class label from some set of <math> C </math> classes <math> w_1,w_2,...w_C</math>
-If the data-points from each class are random variables, then it can be proven that the optimal decision rule to classify a point <math> x_0 </math> is Bayes Rule, which is to choose the class for which <math> P(w_i|x_0) </math>, the  is highest.
-Therefore, it is desirable to assume that the data-points are random variables, and attempt to estimate <math> P(w_i|x_0) </math>, in order to use it to classify the points.
-By Bayes Theorem, <math> P(w_i|x_0) = P(x_o|w_i)P(w_i)</math>. This is advantageous because it is often easier to estimate <math> P(x_o|w_i)</math> and <math>P(w_i)</math> separately than to estimate  <math> P(w_i|x_0) </math> directly.
-K Nearest Neighbors does not explicitly estimate <math> P(w_i|x_0) = P(x_o|w_i)P(w_i)</math>, but instead does so implicitly, and chooses the class with the highest estimated <math> P(w_i|x_0) </math>.
-This method belongs to the class of local density estimation methods because it forms a separate density estimate locally around each test point <math> x_0</math>. This is in contrast to non-local methods which assume a symbolic form (for example gaussian) for the distributions and estimate the entire distribution by finding the parameters (the mean and variance for the gaussian example) of that distribution.
-The classifier is given a set of <math> N </math> data-points <math> x_{1}, x_{2}, ..., x_{N} </math> along with corresponding labels <math> y_{1}, y_{2}, ..., y_{N} </math>
-Together these are often called the training set, because they are used to "train" the classifier, i.e. estimate the distributions.
- <math> \alpha = \sum_{i=1}^{N} \beta_{i}</math>
-----
-----
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-==[[slecture_title_of_slecture_review|Questions and comments]]==
-If you have any questions, comments, etc. please post them on [[slecture_title_of_slecture_review|this page]].
-----
-[[2014_Spring_ECE_662_Boutin|Back to ECE662, Spring 2014]]