Multivariate Decision Trees

By Carla E. Brodley, Paul E. Utgoff. 1995

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Citations in the corpus

Mathematical optimization in classification and regression trees (2021, background): “Trees implementing oblique cuts are more versatile and tend to generate smaller trees with better performance (Brodley and Utgoff 1995; Li et al. 2003).”
An introduction to decision tree modeling (2004, methodology): “Although commonly used with other pattern recognition techniques, these approaches are equally applicable within the decision tree structure (as seen in the determination of multivariate linear partitions [24,25]).”
Recent advances in decision trees: an updated survey (2022, background): “However, as noted by Brodley and Utgoff (1995), there is a flip-side to the inclusion of multivariate splits: the higher approximation ability of multivariate tree splits may make the trees much shallower than their univariate counterparts (as illustrated in Fig.”
Multivariate decision trees using linear discriminants and tabu search (2003, background): “First, the computational time complexity is quadratic in [7], which is still considered slow when and tree size are large.”
An instance level analysis of data complexity (2014, unknown): “5, IB1, and thermal linear machine (Brodley and Utgoff, 1995)).”
Top-down induction of decision trees classifiers - a survey (2005, background): “[76] T1 A one-level decision tree that classiﬁes instances using only one attribute.”
Recursive Feature Generation for Knowledge-based Learning (2018, methodology): “Another example is the LDMT algorithm (Brodley & Utgoff, 1995), which generates linear combinations of existing features.”
Functional Trees (2001, background): “One of the most comprehensive studies of multivariate trees has been presented by Brodley and Utgoff (1995).”
Computational intelligence methods for rule-based data understanding (2004, unknown): “Several researchers [44]–[48] have proposed various approaches for computing the hyperplane weight coefficients for each node of the tree, applying such techniques as simulated annealing, randomization, regression, linear programming, and neural-inspired algorithms.”
Supervised classification and mathematical optimization (2013, background): “However, multivariate counterparts might be better in terms of accuracy [37] [180].”
Weighted Oblique Decision Trees (2019, methodology): “Generally, oblique decision trees simplify tree structure and achieve better performance (Breiman et al. 1984; Heath, Kasif, and Salzberg 1993; Brodley and Utgoff 1995; Loh and Shih 1997; Amasyali and Ersoy 2008; Robertson, Price, and Reale 2013; Kontschieder et al. 2015).”
The Inverse Classification Problem (2010, background): “A huge amount of research[1-11] has been dedicated to the development of scalable and effective classification algorithms.”
On Explaining Decision Trees (2020, background): “We consider univariate decision trees (as opposed to multivariate decision trees [16]); hence, a non-terminal node is associated with a single feature x i , and each outgoing edge is associated with one (or more) values from D i .”
A Comparison of Prediction Accuracy, Complexity, and Training Time of Thirty-Three Old and New Classification Algorithms (2000, methodology): “We include some decision tree algorithms that are not included in the STATLOG Project, such as S-PLUS tree (Clark & Pregibon, 1993), T1 (Auer, Holte, & Maass, 1995; Holte, 1993), OC1 (Murthy, Kasif, & Salzberg, 1994), LMDT (Brodley & Utgoff, 1995), and QUEST(Loh & Shih, 1997).”
Classification Based on Decision Tree Algorithm for Machine Learning (2021, unknown): “5), Classification And Regression Tree(CART) [44], CHi-squared Automatic Interaction Detector(CHAID) [45], Multivariate Adaptive Regression Splines (MARS) [46], Generalized, Unbiased, Interaction Detection and Estimation (GUIDE), Conditional Inference Trees (CTREE) [47],[48], Classification Rule wit”