Murthy, S. K., Kasif, S., and Salzberg, S. (1994). A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 2:1--33.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....classification. The node can test one or more of the input features. A DT is multivariate one, if its nodes test more than one of the features. The multivariate DT is much shorter than that which tests a single feature [1 6] To learn concepts presented by numerical attributes the authors [2 6] suggested the multivariate DTs with Threshold Logical Units (TLUs) or single neurons. Such multivariate DTs are known also as the oblique DTs. In this paper we describe a neural network technique we developed to induce the multi class concepts from large scale clinical EEGs. In our research we ....

S. Murthy, S. Kasif, S. Salzberg. A System for Induction of Oblique Decision Trees. Journal of Artificial Intelligence Research, 2:1-33, 1994.

....a training phase is necessary to build either the decision tree or the centroids or to estimate probability distributions. In the fourth way, training instances are used only when the system is asked to classify a new page. WebClass generates a univariate decision tree, by means of the system OC1 [13], for each class C , by considering training documents of class C i as positive examples and all remaining documents as negative examples. 4 Therefore, the result of the classification process can be: 1) no classification (the document is not stored) It is worthwhile observing that the ....

S.K. Murthy, S. Kasif & S. Salzberg (1994). A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 2, 1-32.

....[12] which exploit a greedy heuristic or hill climbing strategy to find out input variables which efficiently split the training data into classes. To induce linear concepts, multivariate or oblique DTs have been suggested which exploit the threshold logical units or so called perceptions [13] [16]. Such multivariate DTs known also as Linear Machines (LM) are able to classify linearly separable examples. Using the algorithms [8] 13] 15] the LMs can also learn to classify non linearly separable examples. However, such DT methods applied for inducing multi scale problems from real ....

....able to classify linearly separable examples. Using the algorithms [8] 13] 15] the LMs can also learn to classify non linearly separable examples. However, such DT methods applied for inducing multi scale problems from real large scale data become impractical due to large computations [15] [16]. Another approach to multiple classification is based on pairwise classification [17] A basic ides behind this method is to transform a q class problem into q(q 1) 2 binary problems, one for each pair of classes. In this case the binary decision problems are presented by fewer training ....

Murthy, S., Kasif, S., Salzberg, S.: A System for Induction of Oblique Decision Trees. J. Artificial Intelligence Research 2 (1994) 1-33

.... Problem Training Numeric Symbolic Classes BC 286 0 9 2 HD 303 5 8 2 HE 155 6 13 2 HO 386 7 15 2 IR 150 4 0 3 LY 141 2 16 4 SO 47 0 35 4 V1 435 0 16 2 VO 435 0 15 2 The average accuracy scores of BETS and a set of well known and established machine learning algorithms [12] 1] 5] 4] [11] are presented in Table 2. It is important to point out that all the systems, including BETS, were executed with their proclaimed default values in their performance parameters. However, accuracy is not the sole comparison dimension of machine learning algorithms. Depending of the kind of ....

Murthy, S. K., Kasif, S., & Salzberg, S.: A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 2 (1994) 1-32

....where each t k is closer to the same u i than to any other u j . These comparisons will be used to compute a local linear approximation of the assessment function in the surroundings of u . The procedure followed to find a linear function with coefficients w = a 1 , a d ) is taken from OC1 [14] only slightly modified for this purpose. In fact, what we are looking for is a vector w such that w(t 1 t 2 ) 0 as many times as possible. We can start with w being the average of the normalized differences w = a 1 , a d ) Average (t 1 t 2 ) t 1 t 2 t 1 ,t 2 cluster(u ) 8) ....

Murthy, S. K., Kasif, S., Salzberg, S.: A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, (1994) 2, 1-32

....are used. The first method is the well known C4.5 machine learning method developed by Quinlan [3] C4.5 induces trees that partition feature space into equivalence classes using axis parallel hyperplanes (e.g. in 2D this would consist of horizontal and vertical lines) The second approach is OC1 [4] which is a generalisation in that, rather than checking the value of a single attribute at each node, it tests a linear combination of attributes. Feature space is consequently partitioned by oblique hyperplanes. The third method is an ensemble of neural networks that are trained on di#erent ....

S.K. Murthy, S. Kasif, and S. Salzberg. System for induction of oblique decision trees. Journal of Artificial Intelligence Research, 2:1--33, 1994.

....with the noise and the variability in shape aspect ratio within classes, makes the discrimination task based on shape alone difficult. The data set of 260 samples was split into equal training and testing parts, and classification was performed using Murthy et al. s oblique decision trees [2] applied to two measures at a time. In addition to the ellipticity, rectangularity, and triangularity measures two sets of moment invariants were considered (those invariant to similarity transforms as well as affine invariants) and the standard shape descriptors of eccentricity, circularity, ....

S.K. Murthy, S. Kasif, and S. Salzberg. System for induction of oblique decision trees. Journal of AI Research, 2:1--33, 1994.

....[21] This uses various metrics (mentioned above) to revise the existing tree inexpensively. DMTI often produces dramatic improvements over ITI but was not used in our experiments. 2. 3 OC1 Oblique Classifier OC1 (Oblique Classifier) is a system for the induction of oblique decision trees [26]. The software can be obtained from ftp.cs.jhu.edu in directory pub oc1. In oblique decision trees each node may contain a multivariate attribute test. OC1 only works in domains where all attributes are numeric (ordinal real or integer) and class labels integer valued. Attributes with missing ....

....method of finding the best split. The basic algorithm for finding the best split at each node of a decision tree is summarized in Algorithm 3 below. OC1 uses a special perturbation algorithm to perturb the hyper plane H. The algorithm halts when the split reaches the minimum impurity measure [26]. OC1 works on a wide range of impurity measures such as Information Gain, The Gini Index, The Twoing Rule, Max Minority, Sum Minority and Sum of Variances [26] OC1 uses randomization techniques to escape local minimum, when no perturbation of any single coe#cient hyper plane will decrease the ....

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Murthy S. K. Kasif S. Salzbeg S. A system for induction of oblique decision trees. Journal of Artificial Intelligence Research 2, 3(4):1--32, 1994.

....III software, as the traffic descriptors of similar shapes are clustered into the same traffic class. After the clustering operation, traffic classes and content features were used to generate the decision tree classifier. The decision tree classifier was estimated offline by OC1 software [79], a supervised machine learning system based on oblique decision trees. Decision trees of this form consist of a linear combination of the attributes (in our case content features) at each internal node and can be viewed simply as a more general form of axis parallel univariate decision trees. In ....

....in the training pool is marked according to its utility class. The decision tree generator starts its operation after utility function clustering is completed. The generator is also based on machine learning techniques. However, compared to clustering module, supervised classification is used [79]. The decisiontree generator determines the decision tree by using (i) utility classes derived by the utility clustering module and (ii) content features, extracted by the content analyzer. At this point, the decision tree generator does not use parameters describing utility functions. Instead, ....

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S. K. Murthy, S. Kasif, and S. Salzberg, "A System for Induction of Oblique Decision Trees", Journal of Artificial Intelligence Research, 1994.

....range into tens of thousands, and matrix inversion takes time cubic in n or m. Fung, Mangasarian and Musicant experimented with m typically between 6 and 34 (maximum 123) Our data sets have 30000 to 1229663 dimensions. Our approach may be regarded as a punch between oblique decision trees (ODTs) [15], which tries to find non orthogonal hyperplane cuts in the decision tree setting, and an extreme case of boosting [18] in which instances separated with the help of existing linear projections are completely removed from consideration. Inducing an ordinary decision tree over the raw term space ....

S. K. Murthy, S. Kasif, and S. Salzberg. A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 2:1--32, 1994.

....that we developed were evaluated by C4.5, a decision tree software package. We extended C4.5 to incorporate the boosting algorithm described in [1] and [4] C4.5 forms decisions based on axis parallel hyper planes as opposed to work by Salzberg that allows arbitrary hyper planes as separators [13]. Our extension of C4.5 takes a set of examples, S = f(x 1 ; y 1 ) x m ; y m )g and produces a set of decision trees, T 1 ; T j , and a set of weights, w 1 ; w j . x i is a vector of attribute values, in which each attribute corresponds to a metric, and y i is a class( donor ....

S. Murthy, S. Kasif, and S. Salzberg. A system for induction of oblique decision trees. Journal of Arti cial Intelligence Research, 2:1-32.

....discriminators. Decisions at the internal nodes can be simple splits on a single feature or any other linear or nonlinear discriminators. Other classifiers are special cases of decision forests. In this study the decision trees use oblique hyperplanes to split the data at each internal node [16]. The hyperplanes are derived using a simplified Fisher s method [7] i.e. by looking for the error minimizing hyperplane perpendicular to a line connecting the centroids of two classes. Assuming no class ambiguity, the tree can always be fully split, and trees constructed this way are usually ....

Murthy, S., Kasif, S., Salzberg, S., A System for Induction of Oblique Decision Trees, J. of Artificial Intelligence Research, 2, 1, 1994, 1-32.

....Similarly, an area which shows poor productivity that is located on the top of a hill is more likely to be wind eroded or over grazed than salt affected, while an area with poor productivity that is located in a valley is likely to be saline. For this reason, a conditional probabilistic network [4, 9] has been investigated for combining individual year maximum likelihood classifications with landform data to produce salinity maps for each date. The advantage of using a conditional probabilistic network is that it provides a framework for including prior knowledge about relationships between ....

....a leaf is reached. Decision trees for producing salinity maps have been produced using Landsat data from two seasons (1989 and 1990) and landform attributes (water accumulation logarithmically scaled and downhill slope) Two induction algorithms were assessed and compared: c4.5 [11] and oc1 [9]. Each classifier is tested using a range of available options. For c4.5, the options relate to the severity of pruning (reducing the depth of the tree to avoid overtraining) and the minimum amount of training objects required to be classified by each leaf of the tree. For oc1, the options relate ....

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Murphy, S.K., Kasif, S. and Salzberg, S. (1994), "A system for induction of oblique decision trees", Journal of Artificial Intelligence Research, Vol. 2, pp 1-32.

....USA (e mail: andrew kusiak uiowa.edu) Publisher Item Identifier S 1042 296X(01)04816 9. pruning techniques similar to the techniques used in ID3 and similar to the conditional rules used in AQ. IB: The instance based learning algorithm [15] OC1: The oblique decision tree algorithm [16]. T2: The two level error minimizing decision tree algorithm [17] LERS: Learning from examples using rough sets system [18] Examples of other algorithms and developments in learning and data mining can be found in [19] 22] For a survey of important applications of machine learning, see ....

S. K. Murthy and S. Salzberg, "A system for the induction of oblique decision trees," J. Artif. Intell. Res., vol. 2, no. 1, pp. 1--33, 1994.

.... Multistage interference cancellation for an MC CDMA systems with carrier frequency offset, Proc. IEEE ICOIN 13, pp. 4C3.1 4C3.6, 1999. 13] Multiuser detector with an ability of channel estimation using an RBF network in an MC CDMA system, in Proc. IJCNN 2000, vol. 5, 2000, pp. 348 353. [14] W. C. Jakes, Microwave Mobile Communications. New York: Wiley, 1974. Omnivariate Decision Trees Olcay Taner Yldz and Ethem Alpaydn Abstract Univariate decision trees at each decision node consider the value of only one feature leading to axis aligned splits. In a linear multivariate decision ....

....between the univariate, linear multivariate and nonlinear multivariate splits is shown on an example in Fig. 1. II. TRAINING DECISION TREES Training corresponds to constructing the tree given a training set. Finding the smallest decision tree that classifies a training set correctly is NP hard [14]. For large training sets and input dimensions, even for the univariate case, one cannot exhaustively search through the complete space of possible decision trees. Decision tree algorithms are thus greedy in that at each step, we decide on one decision node. Assuming a model for fm (univariate, or ....

[Article contains additional citation context not shown here]

S. K. Murthy, S. Kasif, and S. Salzberg, "A system for induction of oblique decision trees," J. Artificial Intell. Res., vol. 2, pp. 1--32, 1994.

....(uncertainty in some measurements) Training samples are hierarchically split into smaller and homogeneous groups (usually) taking into account only one feature at a time. Classification is made by dropping the patterns through a binary tree while performing simple tests on a feature at each step [1, 5]. DT construction implies some kind of selection among the features initially available. Instead of assigning higher weights to highly discriminant features as in the case of feedforward neural nets [9] discriminant features are usually used in the first levels of the tree. Nevertheless, because ....

Murthy, S.K.; Kasif, S. and Salzberg, S.; "A System for Induction of Oblique Decision Trees", Journal of Artificial Intelligence Research, 2, 1994, pp. 1-32.

....combines the best features of both ID3 [4] and AQ [5] where it uses pruning techniques similar to the techniques used in ID3 and related to the conditional rules used in AQ. IB: The instance based learning algorithms by Aha [11] OC1: The Oblique decision tree algorithm by Murthy and Salzberg [12]. 1521 334X 00 10.00 2000 IEEE 346 IEEE TRANSACTIONS ON ELECTRONICS PACKAGING MANUFACTURING, VOL. 23, NO. 4, OCTOBER 2000 T2: The two level error minimizing decision tree by Auer et al. 13] It minimizes the number of errors and discretizes continuous attributes. LERS: Learning from Examples ....

S. K. Murthy and S. Salzberg, "A system for the induction of oblique decision trees," J. Artif. Intell. Res., vol. 2, no. 1, pp. 1--33, 1994.

....they use different algorithms to choose a decision boundary. Information Gain This is the classic method used in Quinlan s ID3 [9] It measures the information gained from a particular split. Gini Index This metric is based on the Gini Criterion by Breiman [3] but modified as in OC1 by Murthy [8]. The Gini Index measures the probability of misclassifying a set of instances. Twoing Rule This metric, which was also used in Murthy s OC1 and proposed by Breiman, compares the number of examples in each category on each side of the proposed split. T statistic Our approach is based on the ....

....best on pole balancing, but could not be used on the RARS domain. Overall, the t test approach was the clear winner. 4 Future Work and Conclusions Following recent work in the decision tree literature, we will augment our approach to use oblique instead of axis parallel decision boundaries [8]. Oblique boundaries lead to smaller decision trees by allowing each node to use several input variables. We have evaluated four methods for selecting the decision boundaries. In our future work, we plan to explore some alternative approaches with a view to characterizing how well each approach ....

Sreerama K. Murthy, Simon Kasif, and Steven Salzberg. A system for induction of oblique decision trees. JAIR, 2:1--33, 1994.

....phase i. However, as we shall show, it is possible to effectively parallelize ensemble techniques of this kind. 4 Experimental Setting Ensemble techniques may be used with any weak learner as the underlying data mining technique. In our experiments we use the oblique decision tree predictor, OC1 [10]. Decision trees are usually constrained to test a single attribute at each internal node. OC1 allows a linear combination of attributes to be tested at internal nodes. Geometrically, a decision tree partitions the attribute space into regions delimited by axis parallel hyperplanes, while OC1 may ....

Sreerama K. Murthy, Simon Kasif, and Steven Salzberg. A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 2:1--32, 1994.

....the generated anthropomorphic models. With regard to the other approaches examined here, such as the ID3 and C4.5 algorithms, the induced models while being readable tend to be large and consequently makes understanding very difficult. In the case of neural networks and oblique decision trees [14], the induced knowledge is encoded in vectors of weights (and biases) which may prove difficult for a user to interpret and understand. Table 5: Comparison of results obtained using a variety of machine learning techniques on the road classification problem. Approach. # of Features used ....

Murphy, S.K., S. Kasif, and S. Salzburg, A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 1994. 2: p. 1-33.

....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 Cardie[19] uses decision trees to select the features for a case based learning ....

S. Murthy, S. Kasif, and S. Salzberg. A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 2:1--32, 1994.

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S. K. Murthy, S. Kasif, and S. Salzberg. A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 2:1--33, 1994.

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Murthy, S. K., Kasif, S., and Salzberg, S. (1994). A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 2:1--33.

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Murthy, S. K., Kasif, S., and Salzberg, S. (1994). A system for the induction of oblique decision trees. Journal of Artificial Intelligence Research, 2:1--33.

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S. K. Murthy, S. Kasif, and S. Salzberg. A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 2:1--32, 1994.

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S. K. Murthy, S. Kasif, and S. Salzberg. A system for the induction of oblique decision trees. Journal of Artificial Intelligence Research, 2:1--33, 1994.

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Murthy, S., Kasif, S., Salzberg, S.: System for induction of oblique decision trees. J. Artif. Intell. Res. 2, 1--32 (1994)

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S. K. Murthy, S. Kasif, and S. Salzberg. A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 1994.

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S. K. Murthy, S. Kasif, and S. Salzberg, "A system for induction of oblique decision trees," J. Artif. Intell. Res., 1994.

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Murthy S., Kasif S., and Salzberg S. A system for induction of oblique decision trees. J. Artificial Intelligence Research, 2(1):1--32, 1994.

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Murthy, S. K., Kasif, S., & Salzberg, S.: A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 2 (1994) 1-32

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MURTHY, S. K., KASIF, S., & SALZBERG, S.: A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 2, pp. 1-32, (1994).

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MURTHY, S., S. KASIF and S. SALZBERG (1994) A system for induction of oblique decision trees, Journal of Artificial Intelligence Research, 2, 1--32.

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MURTHY, S. K., KASIF, S., & SALZBERG, S.: A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 2, pp. 1-32, (1994).

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S. K. Murthy, S. Kasif, and S. Salzberg, "A system for induction of oblique decision trees," J. Artif. Intell. Res., 1994.

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Sreerama K. Murthy, Simon Kasif, and Steven Salzberg. A System for Induction of Oblique Decision Trees. Journal of Artificial Intelligence Research, 2:1--32, 1994.

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Murphy, S.K., S. Kasif, and S. Salzburg, A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 1994. 2: p. 1-33.

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S. K. Murthy, S. Kasif, and S. Salzberg. A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 2, August 1994.

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S.K. Murty, S. Kasif and S. Salzberg. A System for Induction of Oblique Decision Trees. Journal of Artificial Intelligence Research, 2:1-32, 1994.

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S. K. Murthy, S. Kasif, and S. Salzberg. A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 2, August 1994.

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Murthy, S., Kasif, S., Salzberg, S.: A system for the induction of oblique decision trees. Journal of Artificial Intelligence Research 2 (1994) 1--33

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S.K. Murthy, S. Kasif, and S. Salzberg. System for induction of oblique decision trees. Journal of Artificial Intelligence Research, 2:1--33, 1994.

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Sreerama K. Murthy, Simon Kasif, and Steven Salzberg, \A system for induction of oblique decision trees," Journal of Arti cial Intelligence Research, vol. 2, pp. 1-32, 1994.

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Murthy, S. K., Kasif, S. and Salzberg, S. A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 1994. Morgan Kaufmann Publishers.

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S. K. Murthy, S. Kasif, and S. Salzberg, "A system for induction of oblique decision trees," J. Artif. Intell. Res., 1994.

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S. K. Murthy, S. Kasif, and S. Salzberg, "A system for induction of oblique decision trees," J. Artific. Intell. Res., vol. 2, no. 1, pp. 1--32, 1994.

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Murthy, S. K., Kasif, S., and Salzberg, S. A System for Induction of Oblique Decision Trees. Journal of Arti - cial IntelligenceResearch, (2):1-33, 1994.

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S. Murty, S. Kasif, and S. Salzberg. A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 2:1--32, 1994.

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Murthy S., Kasif S., Salzberg S.: A system for Induction of Oblique Decision Tree, Journal of Artificial Intelligence Research, 2, 1994, pp. 1-32

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S. Murthy, S. Kasif, S. Salzberg. A System for Induction of Oblique Decision Trees. Journal of Artificial Intelligence Research, 2:1-33, 1994.

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