S. B. Gelfand, C. S. Ravishankar, and E. J. Delp, "An iterative growing and pruning algorithm for classification tree design," IEEE Trans. Pattern Anal. Machine Intell., vol. 13, pp. 163--174, Feb. 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a posterior (SMAP) estimator [24] is used to segment images. An important contribution of our approach is that we introduce a multiscale context model which can capture complex aspects of both local and global contextual behavior. The method is based on the use of tree based classifiers [29] [30] to model the transition probabilities between adjacent scales in the multiscale structure. This multiscale structure is similar to previously proposed segmentation models [24] 31] 32] with the segmentations at each resolution forming a Markov chain in scale. However, the tree based ....

....our approach, class probability trees are used to represent , so the ground truth and segmentation will be used to construct and train the tree at each scale and for each of the four child pixels . We design the tree using the recursive tree construction (RTC) algorithm proposed by Gelfand et al. [30], together with a multivariate splitting rule based on the least squares estimation. We have found that this method is very robust and yields tree depths that produce accurate segmentations. Determining the proper tree depth is very important because a tree that is too deep will over parameterize ....

S. Gelfand, C. Ravishankar, and E. Delp, "An iterative growing and pruning algorithm for classification tree design," IEEE Trans. Pattern Anal. Machine Intell., vol. 13, pp. 163--174, Feb. 1991.

....two clusters whose merging results in the smallest increase in prediction error on the training set. Thus we form a binary tree where each node is associated with its optimal linear prediction filter for the conditional mean. To not overfit the classification model, we perform optimal tree pruning[45, 46] using a second data set for cross validation. 16 The matrices B k are computed as k = w R 1 k (48) where R k is the conditional sample covariance for class k (see Appendix) and w is a regularization parameter. The e#ect of w is similar to that of the scale parameter of a Gaussian ....

....clusters c k , c l whose merging results in the smallest M c k ,c l . This results in a binary tree where each node is associated with its optimal linear prediction filter for w s . The leaves of the tree are the VQ clusters. To not overfit the classification model, we perform optimal tree pruning[45, 46] using a second data set for cross validation. The pruning set s , w s is classified into the tree by assigning each data sample to the closest VQ cluster and to all of its parents in the tree. The prediction error for the pruning samples in each node is computed using the node filters ....

S. B. Gelfand, C. S. Ravishankar, and E. J. Delp. An iterative growing and pruning algorithm for classification tree design. IEEE Trans. on Pattern Analysis and Machine Intelligence, 13(2):163--174, February 1991.

.... based on the test) Nevertheless, it might happen that each remaining attribute taken individually does not improve the classi cation, while taken together they classify the data well [13] We know it is better to generate the entire tree and then to prune it (see for example [1] and [11]) Section 2 brie y presents an overview of existing decision trees pruning methods and sets out the question of pruning in uncertain domains. We focus on a quality index of a tree [6] which is able to point out sub populations of interest in large populations. This quality index can be used to ....

....of the class, the degree of pruning is not a ected by the number of classes, and it produces several trees pruned to various degrees. In agreement with Mingers [14] they state it is better to propose a family of trees pruned to di erent degrees than a single tree. Gelfand, Ravishankar, and Delp [11] propose a method where the data set is divided into two equal subsets and where iteratively the tree is build with one subset and pruned with the other one. An empirical evaluation with the waveform recognition problem [1] suggests the superiority of this method to the cost complexity pruning ....

S. B. Gelfand, C. S. Ravishankar, and E. J. Delp. An iterative growing and pruning algorithm for classi cation tree design. IEEE Transactions on Pattern Analysis and Machine Intelligence 13(2), pages 163-174, 1991.

....the partitions are typically shallow (i.e. of depth two) and mainly motivated by size constraints that single components have to meet. Optimality is typically described as the least number of components with as few as possibly connections. Similar structures, called classification trees (e.g. GRD91] are used as expressive decision trees over large sets of data. The internal nodes are labeled by distinguishing criteria and all leaf nodes are distinguishable. Finding expressive classification trees is computationally hard. Though various advanced techniques have been developed for these ....

Saul B. Gelfand, C. S. Ravishankar, and Edward J. Delp. An Iterative Growing and Pruning Algorithm for Classification Tree Design. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI13 (2):163--174, February 1991. 171

....Here the partitions are typically shallow (i.e. of depth two) and mainly motivated by size constraints that single components have to meet. Optimality is typically described as the least number of components with as few as possibly connections. Similar structures called classification trees (e.g. [GRD91]) are used as expressive decision trees over large sets of data. The internal nodes are labeled by distinguishing criteria and all leaf nodes are distinguishable. Finding expressive classification trees is computationally hard. Though various advanced techniques have been developed for these ....

Saul B. Gelfand, C. S. Ravishankar, and Edward J. Delp. An iterative growing and pruning algorithm for classification tree design. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-13(2):163--174, February 1991.

....can also say that they are present due to noise in the sample) Such branches must either not be built or be pruned. If we do not want to build them, we have to set out rules to stop the building of the tree. We know it is better to generate the entire tree and then to prune it (see for example [3][14]) With C.M. criteria, one can define a straightforward pruning method (which is called C.M. pruning because it goes with using a C.M. criterion to build the tree) perfectly coherent with the building of the tree [8] We will see below that C.M. pruning is not tied to the use of the pruned tree ....

S. B. Gelfand, C. S. Ravishankar, and E. J. Delp. An iterative growing and pruning algorithm for classification tree design. IEEE Transactions on Pattern Analysis and Machine Intelligence 13(2), pages 163--174, 1991.

....is to design a DT which is as small as possible. In this paper, we study the evolutionary design of the decision trees, and investigate some methods to improve the design efficiency. 1 Introduction It is known that decision trees (DTs) are very efficient for pattern recognition (see [Meisel73] [Gelfand91] and [Fu69] Actually, as long as pattern recognition is considered, a DT is more efficient than a neural network (NN) There are mainly two reasons. First, the computations in making decisions are simpler only one feature is used in each non terminal (hidden) node, and the only computation ....

....the node when it is considered as a sub tree. This parameter is useful for finding the fitness of a tree. The size of the root is the size of the whole tree, and the size of a terminal node is 1. Many results have been obtained during the last two decades for construction of BDTs (see [Meisel73] [Gelfand91] and [Fu69] To construct a BDT, it is assumed that a training set consisting of feature vectors and their corresponding class labels are available. The BDT is then constructed by recursively partitioning the feature space in such a way as to recursively generate the tree. This procedure involves ....

S. B. Gelfand, C. S. Ravishankar, and E. J. Delp, "An iterative growing and Pruning algorithm for classification tree design," IEEE Trans. on Pattern Analysis and Machine Intelligence, 13-2 (1991) 163--174

....can also say that they are present due to noise in the sample) Such branches must either not be built or be pruned. If we do not want to build them, we have to set out rules to stop the building of the tree. We know it is better to generate the entire tree and then to prune it (see for example [2][11]) With C.M. criteria, one can define a straightforward pruning method (which is called C.M. pruning because it goes with using a C.M. criterion to build the tree) perfectly coherent with the building of the tree [6] We will see below that C.M. pruning is not tied to the use of the pruned tree ....

S. B. Gelfand, C. S. Ravishankar, and E. J. Delp. An iterative growing and pruning algorithm for classification tree design. IEEE Transactions on Pattern Analysis and Machine Intelligence 13(2), pages 163--174, 1991.

....the partitions are typically shallow (i.e. of depth two) and mainly motivated by size constraints that single components have to meet. Optimality is typically described as the least number of components with as few as possibly connections. Similar structures, called classification trees (e.g. [8]) are used as expressive decision trees over large sets of data. The internal nodes are labeled by distinguishing criteria and all leaf nodes are distinguishable. Finding expressive classification trees is computationally hard. Though various advanced techniques have been developed for these ....

Saul B. Gelfand, C. S. Ravishankar, and Edward J. Delp. An iterative growing and pruning algorithm for classification tree design. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-13(2):163--174, February 1991.

....direction code of outside contour (RDC OC) From these features, we create some global features rst, and then select the useful features using GP. The de nition of the RDC OC features is shown in Fig. 2 [10] For example, for the character image shown in Fig.3, we get the following features: [3 1 2 2 1 0 0 0 0 3 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 3 1 2 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1] Fig. 3. Outside contour of the character 1 In these features, 0 means start of a straight line, 3 (or 4) means a left U turn point, and 3 (or 4) means a right U turn point. Clearly, these features cannot be used directly for recognition because there are many noises. For example, number pairs ....

....these features for practical character recognition, some kind of noise removing techniques must be studied. For the training samples given in Fig. 1, we just replace ( 1,1) or ( 2,2) by (0,0) After noise cleaning, we can nd the global features as follows: Feature[ 1] Number of 4 Feature[ 2]=Number of 3 Feature[ 3] Number of 2 Feature[ 4] Number of 1 Feature[ 5] Number of 0 Feature[ 6] Number of 1 Feature[ 7] Number of 2 Feature[ 8] Number of 3 Feature[ 9] Number of 4 Feature[10] Percentage of the longest straight line ....

[Article contains additional citation context not shown here]

S. B. Gelfand, C. S. Ravishankar, and E. J. Delp, An iterative growing and Pruning algorithm for classication tree design, IEEE Trans. on Pattern Analysis and Machine Intelligence, 13-2 (1991) 163-174

....the partitions are typically shallow (i.e. of depth two) and mainly motivated by size constraints that single components have to meet. Optimality is typically described as the least number of components with as few as possibly connections. Similar structures, called classification trees (e.g. [9]) are used as expressive decision trees over large sets of data. The internal nodes are labeled by distinguishing criteria and all leaf nodes are distinguishable. Finding expressive classification trees is computationally hard. Though various advanced techniques have been developed for these ....

Saul B. Gelfand, C. S. Ravishankar, and Edward J. Delp. An iterative growing and pruning algorithm for classification tree design. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-13(2):163-- 174, February 1991.

....is no greater than the best expected performance among n such schemes, one for each value of k. Part B of the theorem may be interpreted similarly. While a variety of rigorous results on the convergence and structural properties of pruning methods have appeared in the literature (see for example [3, 5, 7]) Theorem 1 appears to be the rst result giving bounds on the expected performance of a complexity based pruning scheme. Theorem 1 and related results on complexity regularization for classi cation [6] suggest that a constant times jT j 1=2 is an appropriate complexity penalty for a subtree ....

S.B. Gelfand, C.S. Ravishankar, and E.J. Delp, An iterative growing and pruning algorithm for classication tree design. IEEE Trans. PAMI, 13:163-174, 1991.

....training vector pairs, which we assume are independent realizations of ( ZX , A training vector pair is extracted from low and high resolution renderings of the same image. The training procedure, which is illustrated in Figure 4, is based on that given by Gelfand, Ravishankar, and Delp, in [9], suitably modified for the design of a regression tree rather than a classification tree. We first use one training set G to grow the tree, and then we use a different training set P to prune it back. Finally, we generate new interpolation filters for the terminal nodes using a very large ....

....the tree structured interpolator During the tree growing phase, we generate an increasing sequence of trees ( max . 2 , 1 M T T T , where max M is a user specified maximum number of terminal nodes. We select max M to be large enough so that ( max M T actually overfits the set G [9]. In our experiments, we have obtained reasonable interpolation results by setting max M to 500. This tends to lead to final tree sizes (i.e. after the pruning phase is complete) of between roughly 20 and 50 classes. To generate ( 1 # T from ( # T (for 1 # ) we split the terminal node with ....

S. B. Gelfand, C. S. Ravishankar, and E. J. Delp, An iterative growing and pruning algorithm for classification tree design, IEEE Trans. PAMI, 13(2), pp. 163-174, 1991.

....with respect to the REP method because it can only choose a tree in the set T 0 , T 1 , T 2 , T L instead of the set of all possible subtrees of T max . Consequently, if the most accurate subtree with respect to the pruning set is not in T 0 , T 1 , T 2 , T L , it cannot be selected [11]. Another aspect of the CART pruning strategy that deserves attention is the 1SE rule. Kittler and Devijver [14] have shown that the standard deviation of the empirical error count estimator e C , used with independent sets, is given by s(e ) e(1 e) N) c 1 2 where: e is the true ....

....Another method we have not considered is the iterative growing and pruning algorithm proposed by Gelfand, TABLE 8 AVERAGE SIZE OF TREES OBTAINED WITH DIFFERENT PRUNING METHODS 490 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 19, NO. 5, MAY 1997 Ravishankar, and Delp [11]. The reasons are mainly three. Firstly, because for space constraints we decided to concentrate our attention on non backtracking top down approaches to decision tree induction, while Gelfand et al. frame their pruning method into a growing pruning approach [29] Secondly, because the pruning ....

S.B. Gelfand, C.S. Ravishankar, and E.J. Delp, "An Iterative Growing and Pruning Algorithm for Classification Tree Design," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 2, pp. 138-150, 1991. ESPOSITO ET AL.: A COMPARATIVE ANALYSIS OF METHODS FOR PRUNING DECISION TREES 491

....ae ; E ae [ fR ae g) Each singleton in B i represents a single segment. We will refer to these events as ground segment events, since such events can not be refined. There is a correspondence between generating a sequence of T covers, and generating classification and regression trees [10] 12] [26]. Classification and regression trees are used to represent a sample space efficiently, often for the purpose of pattern recognition. In terms of classification and regression trees, T refinement corresponds to the notion of impurity reduction through partitioning [12] The goal in the ....

S. B. Gelfand, C. S. Ravishankar, and E. J. Delp. An iterative growing and pruning algorithm for classification tree design. IEEE Trans. Pattern Anal. Machine Intell., 13(2):163--174, February 1991.

....tree classi er, besides its speed, is the possibility to interpret the decision rule in terms of individual features. This makes decision trees attractive for interactive use by experts. Like neural networks, decision trees can be easily overtrained, which can be avoided by using a pruning stage [63], 106] 128] Decision tree classi cation systems such as CART [22] and C4.5 [129] are available 43 in the public domain 4 and therefore, often used as a benchmark. One of the most interesting recent developments in classi er design is the introduction of the support vector classi er by ....

S. B. Gelfand, C. S. Ravishankar, and E. J. Delp, \An iterative growing and pruning algorithm for classication tree design," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 2, pp. 163-174, 1991.

....the right tree size. Kohavi (1995) shows that the :632 bootstrap has higher bias but lower variance than cross validation, noting that it can be preferable for small sample sizes. Later, Efron and Tibshirani (1997) proposed an improved bootstrap estimator, the :632 bootstrap, with lower bias. Gelfand et al. 1991) modify CART s pruning procedure by interleaving the growing and pruning phases: a tree is grown using one half of the data, then pruned using the other half. In subse REDUCED ERROR PRUNING WITH SIGNIFICANCE TESTS 33 quent iterations, the existing tree continues to be modified by these two ....

Gelfand, S. B., Ravishankar, C. S. & Delp, E. J. (1991). An iterative growing and pruning algorithm for classification tree design. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-13(2), 163--174.

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S. Gelfand, C. Ravishankar, and E. Delp, "An iterative growing and pruning algorithm for classification tree design," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 2, pp. 163--174, February 1991.

No context found.

Saul Gelfand, C. Ravishankar, and Edward Delp, "An iterative growing and pruning algorithm for classification tree design," IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 13, no. 2, pp. 163--174, February 1991.

....spot in the feature image in Figure 9 (c) directly overlay both the central mass and the spicules of the lesion. 4 Classification Algorithm A sequential hierarchical decision scheme has been shown to achieve better performance than employing a single best set of features in a one step decision [20, 21]. A Binary Classification Tree (BCT) is simple, fast, and e#cient type of hierarchical classifier. This tree structured classification approach has several advantages over more traditional nonparametric methods such as the nearest neighbor method [20] BCT does automatic stepwise feature ....

....misclassified points in the training set . The final classifier can be compactly stored . BCT e#ciently classifies new data . BCT provides easily understood and interpreted information regarding the predictive structure of the data We choose the iterative growing and pruning algorithm proposed in [21] for our classification tree design because it not only produces trees with higher classification accuracy, but also requires less computation than other widely used tree design algorithms, such as CART [20] Considering that there is redundancy in mapping the feature space by spatially adjacent ....

S. B. Gelfand, C. S. Ravishankar, and E. J. Delp, "An iterative growing and pruning algorithm for classification tree design," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 2, pp. 163--174, February 1991.

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S. B. Gelfand, C. S. Ravishankar, and E. J. Delp, "An iterative growing and pruning algorithm for classification tree design," IEEE Trans. Pattern Anal. Machine Intell., vol. 13, pp. 163--174, Feb. 1991.

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S. Gelfand, C. Ravishankar, E. Delp, An iterative growing and pruning algorithm for classification tree design, IEEE Trans. Pattern Anal. Machine Intell. 13 (2) (1991) 138--150.

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S. Gelfand, C. Ravishankar, and E. Delp. An Iterative Growing and Pruning Algorithm for Classi#cation Tree Design. 13:302#320, 1991.

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S. B. Gelfand, C. S. Ravishankar, and E. J. Delp. An iterative growing and pruning algorithm for classication tree design. IEEE Transactions on Pattern Analysis and Machine Intelligence, pages 163-174, 1991.

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Saul B. Gelfand, C. S. Ravishankar, and Edward J. Delp. An iterative growing and pruning algorithm for classi#cation tree design. IEEE Transaction on Pattern Analysis and Machine Intelligence, 13#2#:163#174, February 1991.

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