C. E. Brodley, P. E. Utgoff, "Multivariate Decision Trees," Machine Learning 19, pp. 45, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the concept, respectively. As a result, the concept has correctly classified 80.1 of the testing segments or 87.7 of the 65 records. Keywords: artificial neural network, machine learning, decision tree, electroencephalogram 1. Introduction Machine learning and neural network techniques [1 6] have been successfully used to learn classification models, or concepts, from real world data including electroencephalograms (EEGs) 7 13] These methods explore the given set of the input variables, or features, assumed to represent the classification problem and discard those which are not ....

.... the given set of the input variables, or features, assumed to represent the classification problem and discard those which are not relevant to the classification problem, e.g. corrupted by a noise, because such input variables can seriously hurt the generalization ability of the induced concepts [1 6, 11 13]. To discard the irrelevant features a number of feature selection methods have been suggested some of which are based on a greedy, or hill climbing, strategy [1, 4, 5] Being applied to multivariate classification problems the learning methods based on such a strategy are able to find out a ....

[Article contains additional citation context not shown here]

C. Brodley, P. Utgoff. Multivariate Decision Trees. COINS Technical Report 92-82, Amhert, MA: University of Massachusetts, 1992.

....based on the FST classifier, which performs the best when each class has a Gaussian distribution in the feature space. Since the distributions in the feature space are unknown, how the 3 D features would perform in other kinds of classifiers is an open question. Classifiers based on decision trees [1] and neural networks (e.g [10] are good choices for this purpose. ....

C. Brodley and P. Utgoff, "Multivariate Decision Trees," Machine Learning, 19, pp. 45-77, 1995.

.... that S 0 = fX 2 S j f(X) 0g, S 1 = fX 2 S j f(X) 1g, S = S 0 [ S 1 , and S 0 S 1 = Commonly f is a single feature selected via some impurity measure, e.g. entropy, gini, Laplace, which yields axisparallel partitions over the instance space, but other combinations are possible [2, 8]. The same methodology is recursively applied on S 0 and S 1 to construct the left and right subtrees respectively. A subset S represents a leaf if all ex amples in S belong to the same class, or if jS j fi, where fi is user defined; the majority class in S is associated with that ....

Brodley C. E., Utgoff P. E.: Multivariate Decision Trees. Machine Learning, 19:1, (1995) 45--78

....in the machine learning literature. An extension of linear discriminants are linear machines [364] which are linear structures that can discriminate between multiple classes. In the machine learning liter ature, Utgoff et al. explored decision trees that used linear machines at internal nodes [49, 115]. Locally Opposed Clusters of Objects: Sklansky and his students developed several piecewise linear discriminants based on the principle of locally opposed clusters of objects. Wassel and Sklansky [496, 450] suggested a procedure to train a linear split to minimize the error probability. Using ....

.... 0 (3.1) where al, ad l are real valued coefficients. Because these tests are equivalent to hy perplanes at an oblique orientation to the axes, we call this class of decision trees oblique decision trees. Trees of this form have also been called linear (Section 2.3. 2) and mul tivariate [49] . We prefer the term oblique to aid geometric intuition and because multivariate includes non linear combinations of the variables, i.e. curved surfaces. It is clear that these are simply a more general form of axis parallel trees, since by setting ai 0 for all coefficients but one, the ....

[Article contains additional citation context not shown here]

C^R^ E. BRODEY AND P^U E. UTGOFF. Multivariate decision trees. Machine Learning, 19:45-77, 1995.

....in that they only generally use one variable to make their splits. Multivariate decision trees generalise this to allow rules at non terminal nodes to take the form: if g h h j # (2.36) is a threshold. These have been considered by Breiman et al. 21] and Brodley and Utgoff [26]. The gating network formalism of the mixture of experts is a generalisation of these concepts. Breiman et al. 21, pp. 132 134] used a backward selection search method to delete attributes from the summation hfj , starting from the complete set of attributes ( Quinlan [186, pp. 96 98] ....

....is typically slow in comparison with searches for univariate splits and second, the combination of attributes is less interpretable than univariate splits, especially if the overall space of attributes is large. Priors on small numbers of combinations are therefore desirable. Brodley and Utgoff [26] used a hill climbing search procedure to find the parameters of the splitting rule, and reported that the resulting trees are more accurate than univariate trees. Soft splits Soft splits are those in which the split function is smoothed to allow for a continuous transition across a threshold ....

[Article contains additional citation context not shown here]

Brodley, C. E. and Utgoff, P. E. [1995], `Multivariate decision trees', Machine Learning 19(1), 45-- 77.

....no. 3, pp. 188 190, 1996. 5] S. Verdu, Multiuser Detection. Cambridge, U.K. Cambridge Univ. Press, 1998. 6] B. Aazhang, B. Paris, and G. Orsak, Neural networks for multiuser detection in code division multiple access communications, IEEE Trans. Commun. vol. 40, pp. 1212 1222, July 1992. [7] U. Mitra and H. V. Poor, Adaptive receiver algorithms for near far resistant CDMA, IEEE Trans. Comm. vol. 43, pp. 1713 1724, Feb. Mar. Apr. 1995. 8] K. Ko, S. Choi, C. Kang, and D. Hong, Simplified multiuser receiver of DS CDMA system, in Proc. IJCNN 01, vol. 3, 2001, pp. 1977 1982. ....

....to CART to get out of local optima: A small random vector is added to www m after convergence through backfitting. This perturbs all coefficients together and causes a conjugate jump in the coefficient space. In the linear machine decision trees (LMDT) algorithm, proposed by Brodley and Utgoff [7], with K classes, a node is allowed to have K children. For each child, a separate coefficient vector is used to separate the instances of that class from the other classes. There is an iterative algorithm that adjusts the coefficients to minimize the number of misclassifications, rather than an ....

C. E. Brodley and P. E. Utgoff, "Multivariate decision trees," Machine Learning, vol. 19, pp. 45--77, 1995.

....decision tree construction. The goal of feature minimization is to construct good decisions using as few features as possible. By minimizing the number of features used at each decision, understandability of the resulting tree is increased and the number of data evaluations is decreased [7]. Feature minimization is not necessary in univariate decision tree algorithms in which each decision in the tree is based on a single feature or attribute. Note that in this paper we use the term feature and attribute interchangeably. For example, in a credit card approval application a ....

....that adds and or deletes attributes around an existing decision construction algorithm that minimizes some measure of the classification error. We propose directly changing the underlying discrimination algorithm. Some common approaches to feature minimization are based on greedy heuristics [16, 7]. Sequential Backward Elimination (SBE) and Sequential Forward Elimination (SFE) 7] involve searching the feature space for features that do not contribute (SBE) or contribute (SFE) to the quality of the decision. In SBE an initial discriminant function is constructed using all of the features ....

[Article contains additional citation context not shown here]

C. E. Brodley and P. E. Utgo#. Multivariate decision trees. Machine Learning, 19(1):45-- 77, 1995.

....and the latter with a candidate set consisting of all original features. These searches must be monitored to prevent cycling. There are further generalizations of these basic procedures such as backward stepwise elimination SLASH (BSE SLASH) 36] and Greedy Sequential Backward Elimination (GBSE) [30]. Optimal Brain Damage (OBD) 92] is a procedure to set the weights of an artificial neural network (ANN) to zero, but when applied to weights associated with input features, this is synonymous with feature selection. The idea of OBD is to delete parameters with small saliency , or parameters ....

C. E. Brodley and P. E. Utgoff. Multivariate decision trees. Machine Learning, 19(1):45--77, 1995.

....and John[59] indicate that the results of C4:5 are improved by applying a wrapper feature selection algorithm during classifier design. Ongoing research in the decision tree literature seeks improved methods of selecting features to split the training data, i.e. feature selection; see Brodley[17], Fisher[38] Lopez de Mantaras[70] Mingers[78] and Murthyet al..[81, 82] Decision trees can be classed as wrappers if the constructed tree is used for classification, or as filters, if the tree is used to select features that will subsequently be used for another algorithm, for example ....

C.E. Brodley and P.E. Utgoff. Multivariate decision trees. Machine Learning, 19:45 -- 77, 1995.

....highly accurate trees. However, simulated annealing converges very slowly, and the DT inducer has to examine a large number of hyperplanes, making it inadequate for large data sets. Other related work in this area includes the Linear Machine Decision Trees (LMDT) system (Utgo Brodley, 1991; Brodley Utgo , 1995). The LMDT algorithm is very di erent from the other systems. Instead of using a test similar to Equation (1) at each node, the LMDT has a set of R linear discriminant functions g i (X) W T i X and assigns class i 2 f1; Rg to the instance described by X = x 1 ; x d ) if 8i; i 6= j; ....

Brodley, C. E., & Utgo, P. E. (1995). Multivariate decision trees. Machine Learning , 19 , 45-77.

....decision tree construction. The goal of feature minimization is to construct good decisions using as few features as possible. By minimizing the number of features used at each decision, understandability of the resulting tree is increased and the number of data evaluations is decreased [6]. Feature minimization is not necessary in univariate decision tree algorithms in which each decision in the tree is based on a single feature or attribute. Note that in this paper we use the term feature and attribute interchangeably. For example, in a credit card approval application a ....

....while maintaining a specific level of accuracy. We will be using mathematical programming methods to construct the decisions. In contrast, other common approaches to feature minimization are based on heuristics. Sequential Backward Elimination (SBE) and Sequential Forward Elimination (SFE) [6] involve searching the feature space for features that do not contribute (SBE) or contribute (SFE) to the quality of the decision. In SBE an initial discriminant function is constructed using all of the features and then features are removed sequentially from the problem until some stopping ....

[Article contains additional citation context not shown here]

C. E. Brodley and P. E. Utgoff. Multivariate decision trees. Machine Learning, 19(1):45--77, 1995.

....works by partitioning the color space with linear boundaries (e.g. planes in 3 dimensional spaces) A particular pixel is then classified according to which partition it lies in. This method is convenient for learning systems such as neural networks (NNs) or multivariate decision trees (MDTs) [2]. A second approach is to use nearest neighbor classification. Typically several hundred pre classified exemplars are employed, each having a unique location in the color space and an associated classification. To classify a new pixel, a list of the K nearest exemplars are found, then the pixel ....

C. E. Brodley and P. E. Utgoff. Multivariate decision trees. Machine Learning, 1995.

....works by partitioning the color space with linear boundaries (e.g. planes in 3 dimensional spaces) A particular pixel is then classi ed according to which partition it lies in. This method is convenient for learning systems such as neural networks (ANNs) or multivariate decision trees (MDTs) [3]. A second approach is to use nearest neighbor classi cation. Typically 3 several hundred pre classi ed exemplars are employed, each having a unique location in the color space and an associated classi cation. To classify a new pixel, a list of the K nearest exemplars are found, then the pixel ....

C.E. Brodley and P.E. Utgo. Multivariate decision trees. Machine Learning, 1995.

....search is carried out again. Otherwise, the second mechanism is used. That is, the hill climbing search starts again with another randomly selected start point. This technique allows multiple local searches. OC1 is shown to be more accurate than univariate tree learning [Murthy et al. 1994] Brodley and Utgoff [1995] explore and review four methods, including the Cart method, of generating linear combination tests for decision tree learning. It is experimentally demonstrated that constructing linear combination tests generally improves the accuracies of the resulting decision trees over univariate trees. ....

C.E. Brodley and P.E. Utgoff, Multivariate decision trees. Machine Learning, 19, 45-77.

No context found.

C.E. Brodley and P.E. Utgoff. Multivariate decision trees. Machine Learning, to appear.

No context found.

C. E. Brodley, P. E. Utgoff, "Multivariate Decision Trees," Machine Learning 19, pp. 45, 1995.

No context found.

C. E. Brodley and P. E. Utgoff, "Multivariate decision trees," Mach. Learn., vol. 19, pp. 45--77, 1995.

No context found.

Brodley, C. E., & Utgo#, P. #1995#. Multivariate decision trees. Machine Learning, 19, 45#77.

No context found.

C.E. Brodley and P.E. Utgo. Multivariate decision trees. Machine Learning, 19:45-77, 1995.

No context found.

C. E. Brodley and P. E. Utgoff, "Multivariate decision trees," Mach. Learn., vol. 19, pp. 45--77, 1995.

No context found.

C. E. Brodley and P. E. Utgoff, "Multivariate decision trees," Mach. Learn., vol. 19, pp. 45--77, 1995.

No context found.

Brodley, C., Utgoff, P.: Multivariate Decision Trees. COINS Technical Report 92-82, University of Massachusetts, Amhert, MA (1992)

No context found.

Carla E. Brodley and Paul E. Utgo#. Multivariate decision trees. Machine Learning, 19:45# 77, 1995.

No context found.

Brodley, C. E., Utgoff, P. E. (1995). Multivariate Decision Trees, In Machine Learning, 19, 45-77.

No context found.

Brodley, C. E., Utgoff, P. E. (1995). Multivariate Decision Trees, In Machine Learning, 19, 45-77.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC