trees - Classification/Decision Trees(I...

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Classifcation/Decision Trees (I) Classifcation/Decision Trees (I) Jia Li Department of Statistics The Pennsylvania State University Email: [email protected] http://www.stat.psu.edu/ jiali Jia Li http://www.stat.psu.edu/ jiali
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Classifcation/Decision Trees (I) Tree Structured Classifer ° Reference: Classifcation and Regression Trees by L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stone, Chapman & Hall, 1984. ° A Medical Example ( CART ): ° Predict high risk patients who will not survive at least 30 days on the basis of the initial 24-hour data. ° 19 variables are measured during the ±rst 24 hours. These include blood pressure, age, etc. Jia Li http://www.stat.psu.edu/ jiali
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Classifcation/Decision Trees (I) A tree structure classifcation rule For the medical example Jia Li http://www.stat.psu.edu/ jiali
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Classifcation/Decision Trees (I) ° Denote the feature space by X . The input vector X ∈X contains p features X 1 , X 2 , ..., X p , some of which may be categorical. ° Tree structured classiFers are constructed by repeated splits of subsets of X into two descendant subsets, beginning with X itself. ° DeFnitions: node , terminal node (leaf node) , parent node , child node . ° The union of the regions occupied by two child nodes is the region occupied by their parent node. ° Every leaf node is assigned with a class. A query is associated with class of the leaf node it lands in. Jia Li http://www.stat.psu.edu/ jiali
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Classifcation/Decision Trees (I) Notation ° A node is denoted by t . Its left child node is denoted by t L and right by t R . ° The collection of all the nodes is denoted by T ; and the collection of all the leaf nodes by ˜ T . ° A split is denoted by s . The set of splits is denoted by S . Jia Li http://www.stat.psu.edu/ jiali
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Classifcation/Decision Trees (I) Jia Li http://www.stat.psu.edu/ jiali
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Classifcation/Decision Trees (I) The Three Elements ° The construction of a tree involves the following three elements: 1. The selection of the splits. 2. The decisions when to declare a node terminal or to continue splitting it. 3. The assignment of each terminal node to a class. Jia Li http://www.stat.psu.edu/ jiali
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Classifcation/Decision Trees (I) ° In particular, we need to decide the following: 1. A set Q of binary questions of the form { Is X A ? } , A ⊆X . 2. A goodness of split criterion Φ( s , t ) that can be evaluated for any split s of any node t . 3. A stop-splitting rule. 4. A rule for assigning every terminal node to a class. Jia Li http://www.stat.psu.edu/ jiali
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Classifcation/Decision Trees (I) Standard Set of Questions ° The input vector X =( X 1 , X 2 , ..., X p ) contains features of both categorical and ordered types. ° Each split depends on the value of only a unique variable. ° For each ordered variable X j , Q includes all questions of the form { Is X j c ? } for all real-valued c .
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trees - Classification/Decision Trees(I...

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