Stat841f09 - Wiki Course Notes

# Wikipediaorgwikik neares tneighboralgorithm k nearest

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Unformatted text preview: org/tutorials/dtree18.pdf) Common Node Impurity M e as ure s wikicour senote.com/w/index.php?title= Stat841&pr intable= yes 71/74 10/09/2013 Stat841 - Wiki Cour se Notes Some common node impurity measures are: Misclassification error: Gini Index: Cross- entropy: K-Neares t Neighbours Clas s ification (http://en.wikipedia.org/wiki/K-neares t_neighbor_algorithm) K- nearest neighbours is a very simple algorithm that classifies points based on a majority vote of the nearest points in the feature space, with the object being assigned to the class most common among its nearest neighbors. is a positive integer, typically small which is chosen by cross validation. If , then the object is simply assigned to the class of its nearest neighbor. 1. Ties are broken at random. 2. If we assume the features are real, we can use the Euclidean distance in feature space. 3. Since the features are measured in different units, we can standardize the features to have mean zero and variance 1. Prope rty[42] (http://e n.wikipe dia.org/wiki/K-ne are s t_ne ighbor_algorithm#Prope rtie s ) K- mearest neighbor algorithm has some strong results. As the number of data points goes infinity, the algorithm is guaranteed to yield an error rate no worse than twice the Bayes error rate (the minimum achievable error rate given the distribution of the data). K- nearest neighbor is guaranteed to approach the Bayes error rate, for some value of k (where k increases as a function of the number of data points). Boos ting Boosting (http://en.wikipedia.org/wiki/Boosting) algorithms are a class of machine learning meta- algorithms that can improve weak classifiers. If we have a weak classifier which slightly does better than random classification, then by assigning larger weights to points which are misclassified and trying to minimize the new cost function, we probably can get a new classifier which classifies with less error. This procedure can be repeated for a finite number of times and then a new classifier which is a weighed aggregation of the generat...
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