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September 1977 (vol. 26 no. 9)
pp. 905916
ASCII Text  x  
H.J. Payne, W.S. Meisel, "An Algorithm for Constructing Optimal Binary Decision Trees," IEEE Transactions on Computers, vol. 26, no. 9, pp. 905916, September, 1977.  
BibTex  x  
@article{ 10.1109/TC.1977.1674938, author = {H.J. Payne and W.S. Meisel}, title = {An Algorithm for Constructing Optimal Binary Decision Trees}, journal ={IEEE Transactions on Computers}, volume = {26}, number = {9}, issn = {00189340}, year = {1977}, pages = {905916}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1977.1674938}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  An Algorithm for Constructing Optimal Binary Decision Trees IS  9 SN  00189340 SP905 EP916 EPD  905916 A1  H.J. Payne, A1  W.S. Meisel, PY  1977 KW  Decision trees KW  dynamic programming KW  logic optimization KW  nonlinear regression KW  pattern recognition. VL  26 JA  IEEE Transactions on Computers ER   
We consider the problem of optimally partitioning an ndimensional lattice, L = L, X ... X LN, where Lj is a onedimensional lattice with kj elements, by means of a binary tree into specified (labeled) subsets of L. Such lattices arise from problems in pattern classification, in nonlinear regression, in defining logical equations, and a number of related areas. When viewed as the partitioning of a vector space, each point in the lattice corresponds to a subregion of the space which is relatively homogeneous with respect to classification or range of a dependent variable. Optimality is defined in terms of a general cost function which includes the following: 1) minmax path length (i. e., minimize the maximum number of nodes traversed in making a decision); 2) minimum number of nodes in the tree; and 3) expected path length. It is shown that an optimal tree can be recursively constructed through the application of invariant imbedding (dynamic programming). An algorithm is detailed which embodies this recursive approach. The algorithm allows the assignment of a "don't care" label to elements of L.
Index Terms:
Decision trees, dynamic programming, logic optimization, nonlinear regression, pattern recognition.
Citation:
H.J. Payne, W.S. Meisel, "An Algorithm for Constructing Optimal Binary Decision Trees," IEEE Transactions on Computers, vol. 26, no. 9, pp. 905916, Sept. 1977, doi:10.1109/TC.1977.1674938
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