- Random forest
In

machine learning , a**random forest**is a classifier that consists of many decision trees and outputs the class that is the mode of the classes output by individual trees. The algorithm for inducing a random forest was developed byLeo Breiman andAdele Cutler , and "Random Forests" is theirtrademark . The term came from**random decision forests**that was first proposed byTin Kam Ho of Bell Labs in 1995. The method combines Breiman's "bagging" idea and Ho's "random subspace method" to construct a collection of decision trees with controlled variations.**Learning algorithm**Each tree is constructed using the following

algorithm :

# Let the number of training cases be "N", and the number of variables in the classifier be "M".

# We are told the number "m" of input variables to be used to determine the decision at a node of the tree; "m" should be much less than "M".

# Choose a training set for this tree by choosing "N" times with replacement from all "N" available training cases (i.e. take a bootstrap sample). Use the rest of the cases to estimate the error of the tree, by predicting their classes.

# For each node of the tree, randomly choose "m" variables on which to base the decision at that node. Calculate the best split based on these m variables in the training set.

# Each tree is fully grown and not pruned (as may be done in constructing a normal tree classifier).**Advantages**The advantages of random forest are:

* For many data sets, it produces a highly accurate classifier.

* It handles a very large number of input variables.

* It estimates the importance of variables in determining classification.

* It generates an internal unbiased estimate of the generalization error as the forest building progresses.

* It includes a good method for estimating missing data and maintains accuracy when a large proportion of the data are missing.

* It provides an experimental way to detect variable interactions.

* It can balance error in class population unbalanced data sets.

* It computes proximities between cases, useful forclustering , detectingoutlier s, and (by scaling) visualizing the data.

* Using the above, it can be extended to unlabeled data, leading to unsupervised clustering, outlier detection and data views.

* Learning is fast.**External links*** [

*http://cm.bell-labs.com/cm/cs/who/tkh/papers/odt.pdf Ho, Tin Kam (1995). "Random Decision Forest". Proc. of the 3rd Int'l Conf. on Document Analysis and Recognition, Montreal, Canada, August 14-18, 1995, 278-282*] (Preceding Work)

* [*http://cm.bell-labs.com/cm/cs/who/tkh/papers/df.pdf Ho, Tin Kam (1998). "The Random Subspace Method for Constructing Decision Forests". IEEE Trans. on Pattern Analysis and Machine Intelligence 20 (8), 832-844*] (Preceding Work)

* [*http://www.cis.jhu.edu/publications/papers_in_database/GEMAN/shape.pdf Amit, Yali and Geman, Donald (1997) "Shape quantization and recognition with randomized trees". Neural Computation 9, 1545-1588.*] (Preceding work)

* [*http://www.ics.uci.edu/~liang/seminars/win05/papers/wald2002-2.pdf Breiman, Leo "Looking Inside The Black Box". Wald Lecture II*] (Lecture)

* [*http://www.springerlink.com/content/u0p06167n6173512/fulltext.pdf Breiman, Leo (2001). "Random Forests". Machine Learning 45 (1), 5-32*] (Original Article)

* [*http://stat-www.berkeley.edu/users/breiman/RandomForests/cc_home.htm Random Forest classifier description*] (Site of Leo Breiman)

* [*http://cran.r-project.org/doc/Rnews/Rnews_2002-3.pdf Liaw, Andy & Wiener, Matthew "Classification and Regression by randomForest" R News (2002) Vol. 2/3 p. 18*] (Discussion of the use of the random forest package for R)

* [*http://cm.bell-labs.com/cm/cs/who/tkh/papers/compare.pdf Ho, Tin Kam (2002). "A Data Complexity Analysis of Comparative Advantages of Decision Forest Constructors". Pattern Analysis and Applications 5, p. 102-112*] (Comparison of bagging and random subspace method)

* [*http://dx.doi.org/10.1007/978-3-540-74469-6_35 Prinzie, A., Van den Poel, D. (2007). Random Multiclass Classification: Generalizing Random Forests to Random MNL and Random NB, Dexa 2007, Lecture Notes in Computer Science, 4653, 349-358.*] Generalizing Random Forest framework to other methods. The paper introduces Random MNL and Random NB as two generalizations of Random Forests.

* [*http://dx.doi.org/10.1016/j.eswa.2007.01.029 Prinzie, A., Van den Poel, D. (2008). Random Forests for multiclass classification: Random MultiNomial Logit, Expert Systems with Applications, 34(3), 1721-1732.*] Generalization of Random Forests to choice models like the Multinomial Logit Model (MNL): Random Multinomial Logit.**See also***

Random multinomial logit

*Random naive bayes

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