On the isomorphism problem for decision trees and decision lists

Arvind, Vikraman; Köbler, Johannes; Kuhnert, Sebastian; Rattan, Gaurav; Vasudev, Yadu

doi:10.1016/j.tcs.2015.01.025

Cited by 7 publications

(3 citation statements)

References 15 publications

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“…Decision tree [33, 34] is a type of classifier that regards the dataset to be an entire set, yet recursively divides this set into subsets as well according to a certain standard. During the latter process, all subsets are divided to the extent that they have no attributes to divide further or all samples in every subset belong to a uniform category.…”

Section: Methodsmentioning

confidence: 99%

Prediction of postoperative complications of pediatric cataract patients using data mining

et al. 2019

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BackgroundThe common treatment for pediatric cataracts is to replace the cloudy lens with an artificial one. However, patients may suffer complications (severe lens proliferation into the visual axis and abnormal high intraocular pressure; SLPVA and AHIP) within 1 year after surgery and factors causing these complications are unknown.MethodsApriori algorithm is employed to find association rules related to complications. We use random forest (RF) and Naïve Bayesian (NB) to predict the complications with datasets preprocessed by SMOTE (synthetic minority oversampling technique). Genetic feature selection is exploited to find real features related to complications.ResultsAverage classification accuracies in three binary classification problems are over 75%. Second, the relationship between the classification performance and the number of random forest tree is studied. Results show except for gender and age at surgery (AS); other attributes are related to complications. Except for the secondary IOL placement, operation mode, AS and area of cataracts; other attributes are related to SLPVA. Except for the gender, operation mode, and laterality; other attributes are related to the AHIP. Next, the association rules related to the complications are mined out. Then additional 50 data were used to test the performance of RF and NB, both of then obtained the accuracies of over 65% for three classification problems. Finally, we developed a webserver to assist doctors.ConclusionsThe postoperative complications of pediatric cataracts patients can be predicted. Then the factors related to the complications are found. Finally, the association rules that is about the complications can provide reference to doctors.Electronic supplementary materialThe online version of this article (10.1186/s12967-018-1758-2) contains supplementary material, which is available to authorized users.

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Section: Methodsmentioning

confidence: 99%

Prediction of postoperative complications of pediatric cataract patients using data mining

et al. 2019

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“…And the proposed code approach was shown to be applicable to the whole problem space of mechanism topology identification. Arvind et al (2015) presented Boolean functions to study the complexity of isomorphism testing. The functions were illustrated by decision trees or decision lists.…”

Section: Introductionmentioning

confidence: 99%

A simple and efficient method for isomorphism identification of planar kinematic chains

Cai

Zhang

et al. 2021

Soft Comput

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Isomorphism identification plays an important role in structural design and innovative design.Based on the adjacency matrix and loop theory, a new method is proposed in this paper to identify the isomorphic kinematic chains. It enriches the application of loop-based theory for isomorphism identification. In the kinematic chain, links and joints are connected alternatively and every link corresponds to a fixed link degree. Due to the inherent characteristics, the labeled sequence of links can be random, which does not affect the result of isomorphism identification. By the programming software MATLAB, some examples with 6-, 8-, 10-, 11-, 12-link kinematic chains, and 15-vertex topological graphs are presented. Results show that the proposed method applies to topology graphs and kinematic chains with one or multiple joints. Compared with other methods, the proposed method is confirmed correctly. And there is no counterexample. It lays a solid foundation for structural synthesis in the future.

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“…It can be shown that decision lists are a strict generalization of both DNFs and CNFs [16,23]. Following Rivest's original work, decision lists have been studied both in complexity theory [2,5,6,8,11,17,25] as well as learning theory [3,7,12,15,19,26,27].…”

Section: Introductionmentioning

confidence: 99%

Decision list compression by mild random restrictions

Lovett¹,

Wu²,

Zhang³

2019

Preprint

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A decision list is an ordered list of rules. Each rule is specified by a term, which is a conjunction of literals, and a value. Given an input, the output of a decision list is the value corresponding to the first rule whole term is satisfied by the input. Decision lists generalize both CNFs and DNFs, and have been studied both in complexity theory and in learning theory.The size of a decision list is the number of rules, and its width is the maximal number of variables in a term. We prove that decision lists of small width can always be approximated by decision lists of small size, where we obtain sharp bounds (up to constants). This in particular resolves a conjecture of Gopalan, Meka and Reingold (Computational Complexity, 2013) on DNF sparsification.An ingredient in our proof is a new random restriction lemma, which allows to analyze how DNFs (and more generally, decision lists) simplify if a small fraction of the variables are fixed. This is in contrast to the more commonly used switching lemma, which requires most of the variables to be fixed.

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On the isomorphism problem for decision trees and decision lists

Cited by 7 publications

References 15 publications

Prediction of postoperative complications of pediatric cataract patients using data mining

Prediction of postoperative complications of pediatric cataract patients using data mining

A simple and efficient method for isomorphism identification of planar kinematic chains

Decision list compression by mild random restrictions

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